Nghengu123/Al_Challenge · Datasets at Hugging Face

id int64 14.8k 60.8k	category stringclasses 15 values	Problem stringlengths 5 4.31k	Rationale stringlengths 0 6.77k	options stringlengths 0 943	correct stringclasses 915 values
14,982	general	a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 5 gallons of water and 10 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?	"nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 10 gallons salt is added and 5 gallons of water is added . so salt now becomes - > ( 0.2 x + 10 ) and water - - > ( 0.6 x + 5 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 10 ) = ( 0.6 x + 5 ) / 2 = 0.4 x + 20 = 0.6 x + 5 = > 0.2 x = 15 solving , x = 75 answer : b"	a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175	b
14,983	physics	two trains of equal lengths take 15 sec and 20 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?	"speed of the first train = 120 / 15 = 8 m / sec . speed of the second train = 120 / 20 = 6 m / sec . relative speed = 8 + 6 = 14 m / sec . required time = ( 120 + 120 ) / 14 = 17 sec . answer : c"	a ) 16 sec , b ) 12 sec , c ) 17 sec , d ) 21 sec , e ) 23 sec	c
14,984	gain	the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 13 percent , what was the annual interest rate last year ?	13 = 1.1 * x x = 11.81 % answer d )	a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 11.81 % , e ) 11.50 %	d
14,985	gain	the area of a circle is increased by 300 % . by what percent has the radius of the circle increased ?	"the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the radius ( area = π r ^ 2 ) , therefore the radius must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : c"	a ) 400 % , b ) 200 % , c ) 100 % , d ) 600 % , e ) 800 %	c
14,986	general	562 ã — 99 = ?	"562 ã — ( 100 - 1 ) 56200 - 562 = 55638 answer c"	a ) 55684 , b ) 55432 , c ) 55638 , d ) 44530 , e ) 44538	c
14,987	physics	angelina walked 150 meters from her home to the grocery at a constant speed . she then walked 200 meters to the gym at double the speed . she spent 10 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?	let the speed be x . . . so time taken from home to grocery = 150 / x . . the speed to gym = 2 x . . so time taken = 200 / 2 x = 100 / x . . its given 150 / x - 100 / x = 10 50 / x = 10 x = 5 m / secs . . so grocery to gym = 2 * 5 = 10 m / s . . . answer : d	a ) 2 , b ) 3 , c ) 4 , d ) 10 , e ) 12	d
14,988	geometry	find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm ?	"1 / 2 * 20 ( 5 + 4 ) = 90 cm 2 answer : e"	a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 90 cm 2	e
14,989	general	there are 200 female managers in a certain company . find the total number y of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .	"{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."	a ) 300 , b ) y = 400 , c ) y = 500 , d ) y = 600 , e ) none of these	c
14,990	general	find large number from below question the difference of two numbers is 2500 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder	"let the smaller number be x . then larger number = ( x + 1365 ) . x + 2500 = 6 x + 15 5 x = 2485 x = 497 large number = 497 + 1365 = 2997 d"	a ) 3345 , b ) 1250 , c ) 1540 , d ) 2997 , e ) 1635	d
14,991	general	here is a simple arithmetical puzzle in his own flowery , poetical language . if one - fifth of a hive of bees flew to the badamba flower , one - third flew to the slandbara , 3 times the difference of these two numbers flew to an arbour , and one bee continued to fly about , attracted on each side by the fragrant ketaki and malati , what was the total number of bees ?	b 15 the number of bees was 15	a ) 11 , b ) 15 , c ) 18 , d ) 17 , e ) 19	b
14,992	general	what is the range of all the roots of \| x ^ 2 - 1 \| = x ?	we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 1 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 1 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 2 or x = 1 i guess range is 2 - 1 = 1 d	a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0	d
14,993	geometry	the radius of a sphere is increased by 50 % . the increase in surface area of the sphere is :	"explanation : take radius 100 . then surface area is 4 × π π × 100 × 100 . after increase radius by 50 % the radius becomes 100 + 50 % of 100 = 150 then new surface area is 4 × π π × 150 × 150 then put the values into formula of percentage = 4 π 1502 − 4 π 10024 π 1002 × 1004 π 1502 − 4 π 10024 π 1002 × 100 = 125 % answer : b"	a ) 168 , b ) 125 , c ) 186 , d ) 197 , e ) 191	b
14,994	other	a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . what is the greatest two digit prime saturated integer ?	"clearly d a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . 96 has more number of smaller prime factor thats the clue ! ! = d"	a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95	d
14,995	gain	if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 900 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 922.50 . what is the value of x ?	simple way to solve this question is to use options . from si , we know that x * y = 45,000 . now , put the value of x = 9000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 9000 + 5 % of 9000 = 9450 . 2 nd year , amount = 9450 + 5 % of 9450 = 9922.50 . we can see after 2 years interest = 9922.50 - 9000 = 922.50 . hence , it satisfies the question . hence a is the correct answer	a ) 9000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000	a
14,996	general	in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 17 to the thrice of the remainder . the dividend is	"divisor = ( 6 * 3 ) + 17 = 35 5 * quotient = 35 quotient = 7 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 7 ) + 6 = 146 . b )"	a ) 74 , b ) 146 , c ) 86 , d ) 92 , e ) 98	b
14,997	gain	the sale price of a trolley bag including the sale tax is rs . 280 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :	"explanation : 112 % of s . p . = 280 s . p . = rs . ( 280 x 100 / 112 ) = rs . 250 . c . p . = rs ( 100 / 125 x 250 ) = rs 200 answer : a"	a ) rs 200 , b ) rs 220 , c ) rs 260 , d ) rs 280 , e ) none of these	a
14,998	physics	walking with 4 / 5 of my usual speed , i miss the bus by 3 minutes . what is my usual time ?	speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 3 4 - - - - - - - - - ? è 12 answer : e	a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 12 min	e
14,999	gain	if c is 20 % of a and 10 % of b , what percent of a is b ?	answer = e 20 a / 100 = 10 b / 100 b = 20 a / 10 = 200 a / 100 = 200 %	a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 200 %	e
15,000	gain	a 18 % stock yielding 12 % is quoted at :	"income of rs 12 on investment of rs 100 income of rs 18 on investment of ? = ( 18 * 100 ) / 12 = 150 answer : e"	a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 120 , e ) s . 150	e
15,001	other	find the number of zeroes at the end of 50 !	"calculate division by 5 and 25 50 / 5 = 10 50 / 25 = 2 total = 12 answer : c"	a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14	c
15,002	gain	at a certain university , 68 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?	total women = 68 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 22 % but question wants to know the percent of men that are tenured 22 % / 40 % = 55 % c	a ) 25 , b ) 37.5 , c ) 55 , d ) 62.5 , e ) 75	c
15,003	physics	a man can row upstream at 25 kmph and downstream at 65 kmph , and then find the speed of the man in still water ?	"us = 25 ds = 65 m = ( 65 + 25 ) / 2 = 45 answer : a"	a ) 45 , b ) 86 , c ) 30 , d ) 78 , e ) 38	a
15,004	gain	a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 50 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?	"anyway , in this question , there is no discount but the mark up is given as 50 % of the selling price . so it is not 50 % of $ 150 but instead , 50 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 50 % of s = s s = 300 profit = 150 which is calculated on cost price in % terms . so 150 / 150 * 100 = 100 % is profit . c"	a ) 60 % , b ) 70 % , c ) 100 % , d ) 90 % , e ) 80 %	c
15,005	general	sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 8 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?	let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 8 x = 7 / 8 x so if gold card balance is transferred then the rest unspent will be 7 / 8 x - x / 6 = 17 / 24 x so the ans is c	a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 24 , d ) 19 / 30 , e ) 11 / 15	c
15,006	other	two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number is :	"( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 12 = > 3 x = 36 answer : a"	a ) 36 , b ) 77 , c ) 88 , d ) 55 , e ) 221	a
15,007	gain	in a particular state , 70 % of the counties received some rain on monday , and 55 % of the counties received some rain on tuesday . no rain fell either day in 35 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?	70 + 55 + 35 = 160 % the number is 60 % above 100 % because 60 % of the counties were counted twice . the answer is d .	a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %	d
15,008	gain	the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half yearly is	"solution amount of rs . 100 for 1 year when compounded half yearly = rs . [ 100 x ( 1 + 3 / 100 ) 2 ] = rs . 106.09 % . effective rate = ( 106.09 - 100 ) % = rs . 6.09 % . answer d"	a ) 6.06 % , b ) 6.07 % , c ) 6.08 % , d ) 6.09 % , e ) none	d
15,009	gain	a 340 - liter solution of kola is made from 80 % water , 6 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?	denominator : 340 + 10 + 3.2 + 6.8 = 360 numerator : 340 ( 1 - . 80 - . 06 ) + 3.2 340 ( 0.14 ) + 3.2 47.6 + 3.2 50.8 ratio : 50.8 / 360 = 0.14 answer : e	a ) 6 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 14 % .	e
15,010	physics	a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 198 , how many hours overtime did he work ?	"at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 198 - $ 120 = $ 78 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 78 / $ 6 = 13 ans is e"	a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 13	e
15,011	physics	there are 24 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?	"the total number of stations = 26 from 26 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 26 p 2 ways . 26 p 2 = 26 * 25 = 650 answer : c"	a ) 800 , b ) 820 , c ) 650 , d ) 870 , e ) 900	c
15,012	gain	fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.64 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?	let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.64 9.9 - 45 x + 36 x = 8.64 9 x = 1.26 x = 0.14 the answer is e .	a ) 8 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 14 %	e
15,013	physics	a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 5 days . in how many days can they complete the remaining work ?	"work done by a in 5 days = 5 / 10 = 1 / 2 remaining work = 1 / 2 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 1 / 2 * 6 / 1 = 3 days . answer : e"	a ) 6 days , b ) 2 days , c ) 8 days , d ) 4 days , e ) 3 days	e
15,014	general	a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 70 , how many coins of each type are there ?	"let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 70 ⇒ 1.75 x = 70 ⇒ x = 40 coins answer c"	a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 25 coins , e ) none of these	c
15,015	general	the product of two numbers is 120 and the sum of their squares is 289 . the sum of the number is ?	let the numbers be x and y . then , xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . option a	a ) 23 , b ) 25 , c ) 27 , d ) 31 , e ) 35	a
15,016	general	one millisecond is 0.001 of a second . the costs for a single run of a computer program are $ 1.07 for operating - system overhead , $ 0.023 per millisecond of computer time , and $ 5.35 for the mounting of a data tape . what is the total of these 3 costs for 1 run of a program that requires 1.5 seconds of computer time ?	operating system overhead for 1 run = 1.07 $ mounting of data tape = 5.35 $ cost per 1 millisecond of computer time = . 023 $ total cost of 1 run of a program that requires 1.5 seconds of computer time = 1.07 + ( . 023 * 1500 ) + 5.35 = 1.07 + 34.5 + 5.35 = 40.92 $ answer e	a ) $ 7.15 , b ) $ 8.87 , c ) $ 28.96 , d ) $ 35.57 , e ) $ 40.92	e
15,017	physics	the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of rs . 800 per sq . meter .	"explanation : area = 5.5 × 3.75 sq . metre . cost for 11 sq . metre . = rs . 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : option d"	a ) rs . 12000 , b ) rs . 19500 , c ) rs . 18000 , d ) rs . 16500 , e ) rs . 17500	d
15,018	physics	by travelling at 50 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?	"let the time taken to reach the destination be 3 x hours . total distance = 50 * 3 x = 150 x km he covered 2 / 3 * 150 x = 100 x km in 1 / 3 * 3 x = x hours so , the remaining 50 x km , he has to cover in 2 x hours . required speed = 50 x / 2 x = 25 kmph . answer : c"	a ) 23 kmph , b ) 24 kmph , c ) 25 kmph , d ) 26 kmph , e ) 27 kmph	c
15,019	general	5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 60 only . men â € ™ s wages are ?	"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 60 rs . 5 m + 5 m + 5 m - - - - - 60 rs . 15 m - - - - - - 60 rs . = > 1 m = 4 rs . answer : c"	a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 3 rs	c
15,020	general	what least value should be replaced by * in 483 * 4312 so the number become divisible by 6	"explanation : trick : number is divisible by 6 , if sum of all digits is divisible by 3 and 2 , last digit is 2 so it is dividable by 2 so ( 4 + 8 + 3 + * + 4 + 3 + 1 + 2 ) = 25 + * should be divisible by 6 , 15 + will be divisible by , so that least number is 2 . answer : option d"	a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 7	d
15,021	general	line q has the equation 5 y – 3 x = 90 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )	5 y - 3 x = 90 and so y = 3 x / 5 + 18 when x = 0 , then y = 18 . when y = 0 , then x = - 30 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 30 , 0 ) , 0 = - 5 ( - 30 ) / 3 + c the y - intercept is c = - 50 . thus the perpendicular line s can have y - intercepts from - 49 up to 17 . the number of possible lines is 49 + 17 + 1 = 67 the answer is d .	a ) 58 , b ) 61 , c ) 64 , d ) 67 , e ) 70	d
15,022	gain	the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 275 , then the mean profit for the last 15 days would be	"average would be : 350 = ( 275 + x ) / 2 on solving , x = 425 . answer : d"	a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 425 , e ) none of these	d
15,023	gain	100 liter solution of cool - drink is made from 10 % jasmine water . if 5 liters of jasmine and 10 liters of water were added to the solution , what percent of the solution is jasmine ?	denominator 100 + 5 + 10 115 numerator 100 * 0.1 = 10 - - - > jasmine water 10 + 5 = 15 - - - > new content of jasmine water in new solution ratio 3 / 23 answer is b	a ) 1 / 13 , b ) 2 / 23 , c ) 3 / 31 , d ) 4 / 15 , e ) 2 / 3	b
15,024	general	in 1990 the budgets for projects q and v were $ 700,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?	"let the no of years it takes is x . 700 + 30 x = 780 - 10 x - - > 40 x = 80 and x = 2 . thus , it happens in 1992 . a ."	a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996	a
15,025	gain	a person buys an article at rs . 350 . at what price should he sell the article so as to make a profit of 30 % ?	"cost price = rs . 350 profit = 30 % of 350 = rs . 105 selling price = cost price + profit = 350 + 105 = 455 answer : a"	a ) 455 , b ) 277 , c ) 269 , d ) 261 , e ) 281	a
15,026	physics	working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel four times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?	"w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 4 and w = 4 s then we have 1 / ( 4 * s ) + 1 / s = 1 / 4 < = > 5 / ( 4 * s ) = 1 / 4 < = > s = 5 ans : c"	a ) 4 , b ) 6 , c ) 5 , d ) 9 , e ) 12	c
15,027	other	thomas ' s age and matt ' s age are in the ratio 3 : 5 . two years ago the ratio of their ages was 5 : 9 . find the ratio of their ages 4 years hence ?	let ages of thomas and matt be x and y respectively . x / y = 3 / 5 = > x = 3 / 5 y ( x - 2 ) / ( y - 2 ) = 5 / 9 = > 9 x - 18 = 5 y - 10 = > 9 x = 5 y + 8 but x = 3 / 5 y 9 * 3 / 5 y = 5 y + 8 27 y = 25 y + 40 = > y = 20 years = > x = 3 * 20 / 5 = > 12 years ratio of their ages four years hence , ( 12 + 4 ) / ( 20 + 4 ) = 16 / 24 . = > 2 : 3 answer : b	a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6	b
15,028	general	the average of first 11 prime numbers is ?	"sum of 11 prime no . = 160 average = 160 / 11 = 14.55 answer : a"	a ) 14.55 , b ) 11.11 , c ) 12.11 , d ) 13.11 , e ) 14.11	a
15,029	gain	if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what is the compound interest on the same at the same rate and for the same time ?	"simple interest for 2 years = rs . 50 ie . for 1 years rs . 25 . . in the first year the s . i and c . i are same ie . rs . 25 . so in the 2 nd year in c . i calculated for 1 years interest also . so in second years for rs . 25 interest is 25 * 5 / 100 = 1.25 . so total c . p = 51.25 . answer : b"	a ) rs . 52 , b ) rs . 51.25 , c ) rs . 54.25 , d ) rs . 60 , e ) rs . 70	b
15,030	general	exactly 3 / 8 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?	"the total number of the people in the room must be a multiple of both 8 and 12 ( in order 3 / 7 and 5 / 13 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 8 and 12 , which is 96 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 96 people in the room . therefore there are 3 / 8 * 96 = 36 people in the room under the age of 21 . answer : b ."	a ) 21 , b ) 36 , c ) 39 , d ) 60 , e ) 65	b
15,031	general	a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are :	"explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark answer : a ) 500"	a ) 500 , b ) 387 , c ) 298 , d ) 267 , e ) 191	a
15,032	general	the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 148 , what is the difference between the ages of patrick and monica ?	"ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 148 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"	a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18	b
15,033	physics	a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 340 m long ?	"speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 340 = 700 m required time = 700 * 2 / 25 = 56 sec answer : a"	a ) 56 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec	a
15,034	general	a motorist travels to a place 150 km away at an average speed of 50 km / hr and returns at 30 km / hr . his average speed for the whole journey in km / hr is ?	explanation : average speed = ( 2 xy ) / ( x + y ) km / hr = ( 2 * 50 * 30 ) / ( 50 + 30 ) km / hr . 37.5 km / hr . answer : c	a ) 37.9 , b ) 37.53 , c ) 37.5 , d ) 37.1 , e ) 37.4	c
15,035	general	48.95 - 32.006 = ?	"48.950 - 32.006 - - - - - - - - - 16.944 answer is d"	a ) 16.089 , b ) 16.35 , c ) 16.89 , d ) 16.944 , e ) none of them	d
15,036	general	the average age of 20 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?	"age of the 15 th student = 20 * 15 - ( 14 * 5 + 16 * 9 ) = 300 - 214 = 86 years answer is b"	a ) 79 , b ) 86 , c ) 95 , d ) 72 , e ) 80	b
15,037	general	a vessel of capacity 2 litre has 30 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?	"30 % of 2 litres = 0.6 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 3.0 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 30 % answer : a"	a ) 30 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .	a
15,038	general	what is the 4 digit no . in which the 1 st digit is 1 / 3 of the second , the 3 rd is the sum of the 1 st and 2 nd , and the last is 3 times the second ?	first digit is 1 / 3 second digit = > the numbers can be 1 & 3 , 2 & 6 , 3 & 9 . first + second = third = > we can eliminate 3 & 9 since 3 + 9 = 12 . last is 3 times the second = > we can eliminate option 2 & 6 since 3 * 6 = 18 . hence the number is 1349 c	a ) 1123 , b ) 1234 , c ) 1349 , d ) 1455 , e ) 1567	c
15,039	physics	the distance between two cities a and b is 1410 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?	"explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 1410 . therefore , 60 x + 75 ( x - 1 ) = 1410 . = > x = 3 . so , they meet at ( 8 + 11 ) i . e , 7 pm . answer : b"	a ) 09 pm , b ) 07 pm , c ) 11 pm , d ) 05 am , e ) 03 am	b
15,040	physics	a train running at the speed of 30 km / hr crosses a pole in 9 sec . what is the length of the train ?	"speed = 30 * 5 / 18 = 25 / 3 m / sec length of the train = speed * time = 25 / 3 * 9 = 75 m answer : a"	a ) 75 m , b ) 180 m , c ) 324 m , d ) can not be determined , e ) none of these	a
15,041	physics	how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 150 m length ?	"speed = 70 * 5 / 18 = 19.4 m / sec total distance covered = 120 + 150 = 270 m . required time = 270 / 19.4 ' = 13.9 sec . answer : b"	a ) 12.7 sec , b ) 13.9 sec , c ) 18.1 sec , d ) 17.1 sec , e ) 19.7 sec	b
15,042	general	for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 3,675 , what is the least possible value of k ?	"we basically need 5,5 , 3,7 and 7 in the number . 14 ! , has 3 , 5 , 7 , 10 , 14 now 10 = 2 x 5 14 = 2 x 7 cross check : k ! = 3675 * m ( m is a positive integer ) k ! = 3 * 5 * 5 * 7 * 7 14 ! has all the numbers above . . therefore b . . ! answer : b"	a ) 12 , b ) 14 , c ) 15 , d ) 21 , e ) 25	b
15,043	general	if 2 ^ ( 2 w ) = 8 ^ ( w − 6 ) , what is the value of w ?	"2 ^ ( 2 w ) = 8 ^ ( w − 6 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 6 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 18 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 18 w = 18 the answer is c ."	a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24	c
15,044	general	5 friends visited a fruit stall , and everyone decided to contribute equally to the total bill of $ 100 . if one of the friends had a coupon for 6 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?	at the non - discounted price , each friend would pay $ 20 , as $ 100 divided by 5 friends is $ 20 per friend . but if the bill is 6 % off , then each friend would pay 6 % less . 6 % of $ 20 is $ 1.2 , so each friend saves $ 1.2 and pays the remaining 18.8 correct option : option b	a ) 18 , b ) 18.8 , c ) 19 , d ) 17.8 , e ) 17.9	b
15,045	physics	dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 46 of gas ?	"46 / 4 = 11.5 gallons 11.5 * 32 = 368 miles the answer is c ."	a ) 124 , b ) 256 , c ) 368 , d ) 424 , e ) 512	c
15,046	gain	at what price must an book costing $ 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?	"c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 95 / 100 ) = 59.375 mp = 62.5"	a ) 72.5 , b ) 55.5 , c ) 62.5 , d ) 82.5 , e ) 60.5	c
15,047	other	a certain bag contains 60 balls — 22 white , 10 green , 7 yellow , 15 red , and 6 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?	"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 10 + 17 ) / 60 = 39 / 60 = 0.65 . answer : b ."	a ) 0.09 , b ) 0.65 , c ) 0.54 , d ) 0.85 , e ) 0.91	b
15,048	general	solution for 1.35 + . 123 + . 321	"1.35 + . 123 + . 321 = 0 0 = 0 - 1.35 - 0.123 - 0.321 0 = - 1.794 answer : b"	a ) 2.91 , b ) 1.794 , c ) 1.338 , d ) 1.986 , e ) 1.999	b
15,049	geometry	carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 9 inches long , how wide is jordan ' s rectangle , in inches ?	"area of first rectangle is 12 * 15 = 180 hence area of second would be 9 x = 180 x x = 20 answer is d"	a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21	d
15,050	gain	a , b and c start a business each investing 20000 . after 5 months a withdrew 10000 , b withdrew 15000 and c invests 5000 more . at the end of the year , a total profit of 58000 was recorded . find the share of b .	ratio of the capitals of a , b and c = 20000 ã — 5 + 10000 ã — 7 : 20000 ã — 5 + 5000 ã — 7 : 20000 ã — 5 + 25000 ã — 7 = 170000 : 135000 : 275000 = 170 : 135 : 275 . b â € ™ s share = ( 58000 ã — 135 â „ 580 ) = 13500 answer d	a ) 20,000 , b ) 21,200 , c ) 28,200 , d ) 13,500 , e ) none of these	d
15,051	general	a two digit number is 18 less than the square of the sum of its digits . how many such numbers are there ?	option 2 take n = 10 a + b . given that , ( 10 a + b ) + 18 = k 2 = ( a + b ) 2 given number = k 2 - 18 = ( 10 a + b ) that means , when we add 18 to the given number it should be a perfect square . so k 2 takes the following values . 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , . . . . 1 to 16 are ruled out as if we subtract 18 from them , the resulting number is a single digit number . now 25 - 18 = 7 36 - 18 = 18 49 - 18 = 31 64 - 18 = 46 81 - 18 = 63 100 - 18 = 82 121 - 18 = 103 now 63 , 82 satisfies . answer : d	a ) 2233 , b ) 2222 , c ) 2211 , d ) 6382 , e ) 23,17	d
15,052	physics	a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 380 m long platform ?	"let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 380 ) / 36 * 5 / 18 = 50 min . answer : a"	a ) 50 , b ) 27 , c ) 29 , d ) 47 , e ) 28	a
15,053	general	a corporation that had $ 10 billion in profits for the year paid out $ 500 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )	"required answer = [ employee benefit / profit ] * 100 = [ ( 500 million ) / ( 10 billion ) ] * 100 = [ ( 500 * 10 ^ 6 ) / ( 10 * 10 ^ 9 ) ] * 100 = ( 50 / 1000 ) * 100 = 5 % so answer is ( c )"	a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 %	c
15,054	physics	if 24 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?	"if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 24 lines is 24 c 2 = 276 the answer is a ."	a ) 276 , b ) 350 , c ) 425 , d ) 512 , e ) 648	a
15,055	general	a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2490 ?	"let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 a ' s share in the profit of rs . 2490 = 20 ( 2490 / 60 ) = rs . 830 . answer : b"	a ) rs . 832 , b ) rs . 830 , c ) rs . 822 , d ) rs . 812 , e ) rs . 810	b
15,056	physics	a car takes 6 hours to cover a distance of 144 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?	"time = 6 distence = 144 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 144 / 9 = 16 kmph d )"	a ) 50 kmph , b ) 60 kmph , c ) 65 kmph , d ) 16 kmph , e ) none	d
15,057	general	when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 2 / 3 of the remaining balance , what will be the final balance in her bank account ?	"as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 2 / 3 of 300 = 200 total amount in her account = 500 answer d"	a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 575	d
15,058	general	on a certain date , pat invested $ 6,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24,000 , in how many years total will the total value of the investment plus interest increase to $ 48,000 ?	"24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."	a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24	a
15,059	physics	a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 40 percent .	1 hr = 20 percent . thus 15 min = 5 percent . now to charge 40 percent 120 min . answer : a	a ) 120 , b ) 150 , c ) 175 , d ) 160 , e ) 130	a
15,060	general	a train starts full of passengers at the first station it drops 1 / 3 of the passengers and takes 280 more at the second station it drops one half the new total and takes 12 more . on arriving at the third station it is found to have 242 passengers . find the no of passengers in the beginning ?	let no of passengers in the beginning be x after first station no passengers = ( x - x / 3 ) + 280 = 2 x / 3 + 280 after second station no passengers = 1 / 2 ( 2 x / 3 + 280 ) + 12 1 / 2 ( 2 x / 3 + 280 ) + 12 = 242 2 x / 3 + 280 = 2 * 230 = 460 - 280 = 180 2 x / 3 = 180 x = 270 . so the answer is option b ) 270 .	a ) 292 , b ) 270 , c ) 192 , d ) 144 , e ) 168	b
15,061	geometry	a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 4 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )	let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 4 gms in 400,000 cm ^ 3 , x = 4 * 400,000 = 1 , 600,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 1 , 600,000 + 1 , 800,000 = 2 , 400,000 answer : b	['a ) 5 , 500,000', 'b ) 2 , 400,000', 'c ) 55,000', 'd ) 28,000', 'e ) 280']	b
15,062	general	a retailer bought a coat at wholesale and marked it up 90 % to its initial price of $ 76 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?	let x be the wholesale price . then 1.9 x = 76 and x = 76 / 1.9 = 40 . to achieve a 100 % markup , the price needs to be $ 80 . the retailer needs to increase the price by $ 4 more . the answer is b .	a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10	b
15,063	other	the hcf of two numbers is 40 and the other two factors of their lcm are 11 and 12 . what is the largest number .	"explanation : hcf of the two numbers = 40 hcf will be always a factor of lcm 40 is factor of lcm other two factors are 11 & 12 then the numbers are ( 40 * 11 ) and ( 40 x 12 ) = 440 and 480 answer : option d"	a ) 462 , b ) 450 , c ) 488 , d ) 480 , e ) 555	d
15,064	physics	in 110 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :	"distance covered by b in 9 sec . = 110 / 45 x 9 m = 22 m . a beats b by 20 metres . answer : option c"	a ) 20 m , b ) 25 m , c ) 22 m , d ) 9 m , e ) 12 m	c
15,065	geometry	three interviewers , a , b , and c are interviewing 50 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer a admitted 20 applicants , b admitted 22 applicants , and c admitted 20 applicants , at least how many applicants get the admission ?	"if a admitted 20 are overlapping with b admission of 22 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : b"	a ) 4 , b ) 0 , c ) 6 , d ) 8 , e ) 12	b
15,066	general	there are 408 boys and 288 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .	explanation : hcf ( 408 , 288 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 288 / 24 = 17 + 12 = 29 answer : e	a ) 31 , b ) 32 , c ) 35 , d ) 30 , e ) 29	e
15,067	physics	walking at 6 / 7 th of his usual speed , a man is 25 mins too late . his usual time is	"as the distance is same s * t = 6 / 7 s * ( t + 25 ) solving this we get t = 150 sec 150 / 60 = 2.5 hrs answer : c"	a ) 7.5 hrs , b ) 1.5 hrs , c ) 2.5 hrs , d ) 1.67 hrs , e ) 2.67 hrs	c
15,068	physics	a train running at the speed of 60 km / hr crosses a pole in 12 sec . what is the length of the train ?	"speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 12 = 200 m answer : a"	a ) 200 m , b ) 178 m , c ) 186 m , d ) 168 m , e ) 150 m	a
15,069	gain	julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 126 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?	"$ 120 for 2 years = $ 60 per year . extra $ 6 yearned with the compound interest is the percent yearned on percent . so , $ 6 is yearned on $ 60 , which means that the interest = 10 % . this on the other hand means that half of the savings = 60 * 10 = $ 600 . twice of that = $ 1,200 . answer : d ."	a ) 600 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1440	d
15,070	general	a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability q that a + b is prime ?	"total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes q = 15 / 36 . answer : c ."	a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9	c
15,071	gain	mr . tom invested in fund x and fund y . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund y paid 17 % . the interest earned in fund y was exactly $ 200 greater than the interest earned in fund x . how much did ms . tom invest in fund x ?	x + y = 100000 0.17 y = 0.23 a + 200 take away decimals first : 17 y = 23 x + 20000 isolate first equation to solve for x ( your goal ) : y = 100000 - y plug in for b : 17 ( 100000 - x ) = 23 x + 20000 1 , 700000 - 17 x = 23 x + 20000 1 , 680000 = 40 x 1 , 680000 / 40 = x x = 42000 = answer choice c	a ) $ 32000 , b ) $ 36000 , c ) $ 42000 , d ) $ 44000 , e ) $ 45000	c
15,072	gain	on a certain transatlantic crossing , 20 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 40 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?	"0.20 p = rt + c 0.4 ( rt ) = no c = > 0.60 ( rt ) had c 0.20 p = 0.60 ( rt ) rt / p = 1 / 3 = 33 % answer - a"	a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %	a
15,073	physics	two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 200 m , in what time will they cross other travelling in opposite direction ?	"speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 200 + 200 ) / 20 = 20 sec . answer : e"	a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 20 sec	e
15,074	geometry	how many diagonals does a polygon with 23 sides have , if one of its vertices does not connect to any diagonal ?	"if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 23 - 1 then 22 * ( 22 - 3 ) / 2 = 209 correct option : e"	a ) 201 , b ) 159 , c ) 179 , d ) 189 , e ) 209	e
15,075	physics	a train moves at average speed of 60 kmph reaches its destination on time . what its average speed becomes 50 kmph , then it reaches its destination 15 late . find the length of the journey ?	"difference between timings = 15 min = 1 / 4 hr let the length of the journey be x km . then x / 50 - x / 60 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer ( b )"	a ) 4.86 km , b ) 2.5 km , c ) 6.86 km , d ) 5.867 km , e ) 3.25 km	b
15,076	general	how many points ( x , y ) lie on the line segment between ( 32 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?	"slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 32 ) = - 1 / 5 y = mx + b = > 12 2 / 3 = - 22 / 3 + b = > b = 19 y = - x / 5 + 19 only integer values work , and the only multiples of 5 between 7 and 32 for x values are 10 , 15 , 20 , 25 and 30 , thus 5 points . c"	a ) one , b ) 4 , c ) 5 , d ) 8 , e ) 9	c
15,077	physics	a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 72 km / hr . what is the length of the platform ?	"speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 20 = 400 m . let the length of the platform be x m . then , ( x + 400 ) / 36 = 20 = > x = 320 m . answer : e"	a ) 229 , b ) 240 , c ) 288 , d ) 277 , e ) 320	e
15,078	general	the difference between a number and its two - fifth is 510 . what is 50 % of that number ?	"let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 50 % of 850 = 425 . answer : b"	a ) 426 , b ) 425 , c ) 427 , d ) 428 , e ) 429	b
15,079	gain	15 % of 75 is the same as vx % of 450 . find x .	15 % of 75 = 11.25 450 * x / 100 = 11.25 x = 2.5 answer : b	a ) 1 , b ) 2.5 , c ) 3 , d ) 4 , e ) 5	b
15,080	general	marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 25 % . what percent of the projected revenue was the actual revenue ?	"last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 120 . actual / projected * 100 = 75 / 120 * 100 = 62.5 % . answer : c"	a ) 53 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %	c
15,081	physics	5 / 8 th of a job is completed in 10 days . if a person works at the same pace , how many days will he take to complete the job ?	explanation : solution : it is given that 5 / 8 th of the work is completed in 10 days . = > remaining work = 3 / 8 th of total applying unitary method : total work will be completed in 10 * 8 / 5 days = > it takes 16 days to complete total work = > hence , remaining work days = 16 - 10 = 6 days answer : c	a ) 8 , b ) 9 , c ) 6 , d ) 2 , e ) 1	c

14,982

general

a tank holds x gallons of a saltwater solution that is 20 % salt by volume . one fourth of the water is evaporated , leaving all of the salt . when 5 gallons of water and 10 gallons of salt are added , the resulting mixture is 33 1 / 3 % salt by volume . what is the value of x ?

"nope , 150 . i can only get it by following pr ' s backsolving explanation . i hate that . original mixture has 20 % salt and 80 % water . total = x out of which salt = 0.2 x and water = 0.8 x now , 1 / 4 water evaporates and all salt remains . so what remains is 0.2 x salt and 0.6 x water . now 10 gallons salt is added and 5 gallons of water is added . so salt now becomes - > ( 0.2 x + 10 ) and water - - > ( 0.6 x + 5 ) amount of salt is 33.33 % of total . so amount of water is 66.66 % . so salt is half of the volume of water . so ( 0.2 x + 10 ) = ( 0.6 x + 5 ) / 2 = 0.4 x + 20 = 0.6 x + 5 = > 0.2 x = 15 solving , x = 75 answer : b"

a ) 37.5 , b ) 75 , c ) 100 , d ) 150 , e ) 175

b

14,983

physics

two trains of equal lengths take 15 sec and 20 sec respectively to cross a telegraph post . if the length of each train be 120 m , in what time will they cross other travelling in opposite direction ?

"speed of the first train = 120 / 15 = 8 m / sec . speed of the second train = 120 / 20 = 6 m / sec . relative speed = 8 + 6 = 14 m / sec . required time = ( 120 + 120 ) / 14 = 17 sec . answer : c"

a ) 16 sec , b ) 12 sec , c ) 17 sec , d ) 21 sec , e ) 23 sec

c

14,984

gain

the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 13 percent , what was the annual interest rate last year ?

13 = 1.1 * x x = 11.81 % answer d )

a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 11.81 % , e ) 11.50 %

d

14,985

gain

the area of a circle is increased by 300 % . by what percent has the radius of the circle increased ?

"the area of the circle is increased by 300 % , thus the area is increased 4 times . the area of a circle it proportional to the square of the radius ( area = π r ^ 2 ) , therefore the radius must increase 2 times ( diameter increase 2 times = area increase 4 times ) , which is increase by 100 % . answer : c"

a ) 400 % , b ) 200 % , c ) 100 % , d ) 600 % , e ) 800 %

c

14,986

general

562 ã — 99 = ?

"562 ã — ( 100 - 1 ) 56200 - 562 = 55638 answer c"

a ) 55684 , b ) 55432 , c ) 55638 , d ) 44530 , e ) 44538

c

14,987

physics

angelina walked 150 meters from her home to the grocery at a constant speed . she then walked 200 meters to the gym at double the speed . she spent 10 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?

let the speed be x . . . so time taken from home to grocery = 150 / x . . the speed to gym = 2 x . . so time taken = 200 / 2 x = 100 / x . . its given 150 / x - 100 / x = 10 50 / x = 10 x = 5 m / secs . . so grocery to gym = 2 * 5 = 10 m / s . . . answer : d

a ) 2 , b ) 3 , c ) 4 , d ) 10 , e ) 12

d

14,988

geometry

find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 5 cm and 4 cm ?

"1 / 2 * 20 ( 5 + 4 ) = 90 cm 2 answer : e"

a ) 189 cm 2 , b ) 150 cm 2 , c ) 127 cm 2 , d ) 177 cm 2 , e ) 90 cm 2

e

14,989

general

there are 200 female managers in a certain company . find the total number y of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .

"{ managers } = { female managers } + { male managers } ; we are told that the total number of managers in the company is 2 / 5 of all the employees , thus { managers } = 2 / 5 ( m + f ) , where m and f are number of female and male employees , respectively . also , we know that 2 / 5 of all male employees are managers : { male managers } = 2 / 5 * mas well as there are total of 200 female managers : { female managers } = 200 ; thus : 2 / 5 ( m + f ) = 200 + 2 / 5 * m - - > f = 500 . answer : c ."

a ) 300 , b ) y = 400 , c ) y = 500 , d ) y = 600 , e ) none of these

c

14,990

general

find large number from below question the difference of two numbers is 2500 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder

"let the smaller number be x . then larger number = ( x + 1365 ) . x + 2500 = 6 x + 15 5 x = 2485 x = 497 large number = 497 + 1365 = 2997 d"

a ) 3345 , b ) 1250 , c ) 1540 , d ) 2997 , e ) 1635

d

14,991

general

here is a simple arithmetical puzzle in his own flowery , poetical language . if one - fifth of a hive of bees flew to the badamba flower , one - third flew to the slandbara , 3 times the difference of these two numbers flew to an arbour , and one bee continued to fly about , attracted on each side by the fragrant ketaki and malati , what was the total number of bees ?

b 15 the number of bees was 15

a ) 11 , b ) 15 , c ) 18 , d ) 17 , e ) 19

b

14,992

general

what is the range of all the roots of | x ^ 2 - 1 | = x ?

we get 2 quadratic equations here . . 1 ) x ^ 2 - x - 1 = 0 . . . . . . . roots 2 , - 1 2 ) x ^ 2 + x - 1 = 0 . . . . . . . . roots - 2 , 1 inserting each root in given equation , it can be seen that - 1 and - 2 do not satisfy the equations . so value of x for given equation . . . . x = 2 or x = 1 i guess range is 2 - 1 = 1 d

a ) 4 , b ) 3 , c ) 2 , d ) 1 , e ) 0

d

14,993

geometry

the radius of a sphere is increased by 50 % . the increase in surface area of the sphere is :

"explanation : take radius 100 . then surface area is 4 × π π × 100 × 100 . after increase radius by 50 % the radius becomes 100 + 50 % of 100 = 150 then new surface area is 4 × π π × 150 × 150 then put the values into formula of percentage = 4 π 1502 − 4 π 10024 π 1002 × 1004 π 1502 − 4 π 10024 π 1002 × 100 = 125 % answer : b"

a ) 168 , b ) 125 , c ) 186 , d ) 197 , e ) 191

b

14,994

other

a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . what is the greatest two digit prime saturated integer ?

"clearly d a number is said to be prime saturated if the product of all the different positive prime factors of a is less than the square root of a . 96 has more number of smaller prime factor thats the clue ! ! = d"

a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95

d

14,995

gain

if x is invested in a bank at a rate of simple interest of y % p . a . for two years , then the interest earned is 900 . if x is invested at y % p . a . , for two years when the interest is compounded annually , the interest is 922.50 . what is the value of x ?

simple way to solve this question is to use options . from si , we know that x * y = 45,000 . now , put the value of x = 9000 , we will have y = 5 % to calculate ci , now , we know 1 st year amount = 9000 + 5 % of 9000 = 9450 . 2 nd year , amount = 9450 + 5 % of 9450 = 9922.50 . we can see after 2 years interest = 9922.50 - 9000 = 922.50 . hence , it satisfies the question . hence a is the correct answer

a ) 9000 , b ) 6000 , c ) 5000 , d ) 4000 , e ) 3000

a

14,996

general

in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 17 to the thrice of the remainder . the dividend is

"divisor = ( 6 * 3 ) + 17 = 35 5 * quotient = 35 quotient = 7 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 7 ) + 6 = 146 . b )"

a ) 74 , b ) 146 , c ) 86 , d ) 92 , e ) 98

b

14,997

gain

the sale price of a trolley bag including the sale tax is rs . 280 . the rate of sale tax is 12 % . if the shopkeeper has made a profit of 25 % , the cost price of the trolley bag is :

"explanation : 112 % of s . p . = 280 s . p . = rs . ( 280 x 100 / 112 ) = rs . 250 . c . p . = rs ( 100 / 125 x 250 ) = rs 200 answer : a"

a ) rs 200 , b ) rs 220 , c ) rs 260 , d ) rs 280 , e ) none of these

a

14,998

physics

walking with 4 / 5 of my usual speed , i miss the bus by 3 minutes . what is my usual time ?

speed ratio = 1 : 4 / 5 = 5 : 4 time ratio = 4 : 51 - - - - - - - - 3 4 - - - - - - - - - ? è 12 answer : e

a ) 16 min , b ) 26 min , c ) 34 min , d ) 20 min , e ) 12 min

e

14,999

gain

if c is 20 % of a and 10 % of b , what percent of a is b ?

answer = e 20 a / 100 = 10 b / 100 b = 20 a / 10 = 200 a / 100 = 200 %

a ) 2.5 % , b ) 15 % , c ) 25 % , d ) 35 % , e ) 200 %

e

15,000

gain

a 18 % stock yielding 12 % is quoted at :

"income of rs 12 on investment of rs 100 income of rs 18 on investment of ? = ( 18 * 100 ) / 12 = 150 answer : e"

a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 120 , e ) s . 150

e

15,001

other

find the number of zeroes at the end of 50 !

"calculate division by 5 and 25 50 / 5 = 10 50 / 25 = 2 total = 12 answer : c"

a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14

c

15,002

gain

at a certain university , 68 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?

total women = 68 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 22 % but question wants to know the percent of men that are tenured 22 % / 40 % = 55 % c

a ) 25 , b ) 37.5 , c ) 55 , d ) 62.5 , e ) 75

c

15,003

physics

a man can row upstream at 25 kmph and downstream at 65 kmph , and then find the speed of the man in still water ?

"us = 25 ds = 65 m = ( 65 + 25 ) / 2 = 45 answer : a"

a ) 45 , b ) 86 , c ) 30 , d ) 78 , e ) 38

a

15,004

gain

a furniture dealer purchased a desk for $ 150 and then set the selling price equal to the purchase price plus a markup that was 50 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?

"anyway , in this question , there is no discount but the mark up is given as 50 % of the selling price . so it is not 50 % of $ 150 but instead , 50 % of selling price which is obtained by adding mark up to $ 150 . so if selling price is s , 150 + 50 % of s = s s = 300 profit = 150 which is calculated on cost price in % terms . so 150 / 150 * 100 = 100 % is profit . c"

a ) 60 % , b ) 70 % , c ) 100 % , d ) 90 % , e ) 80 %

c

15,005

general

sally has a gold credit card with a certain spending limit , and a platinum card with twice the spending limit of the gold card . currently , she has a balance on her gold card that is 1 / 3 of the spending limit on that card , and she has a balance on her platinum card that is 1 / 8 of the spending limit on that card . if sally transfers the entire balance on her gold card to her platinum card , what portion of her limit on the platinum card will remain unspent ?

let s assume the platinum card spending limit = x gold card spending limit will be = x / 2 balance on gold card is = x / 2 * 1 / 3 = x / 6 platinum card unspent limit is = x - 1 / 8 x = 7 / 8 x so if gold card balance is transferred then the rest unspent will be 7 / 8 x - x / 6 = 17 / 24 x so the ans is c

a ) 11 / 30 , b ) 29 / 60 , c ) 17 / 24 , d ) 19 / 30 , e ) 11 / 15

c

15,006

other

two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 9 : 17 . the first number is :

"( 3 x - 9 ) : ( 5 x - 9 ) = 9 : 17 x = 12 = > 3 x = 36 answer : a"

a ) 36 , b ) 77 , c ) 88 , d ) 55 , e ) 221

a

15,007

gain

in a particular state , 70 % of the counties received some rain on monday , and 55 % of the counties received some rain on tuesday . no rain fell either day in 35 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?

70 + 55 + 35 = 160 % the number is 60 % above 100 % because 60 % of the counties were counted twice . the answer is d .

a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %

d

15,008

gain

the effective annual rate of interest corresponding to a nominal rate of 6 % per annum payable half yearly is

"solution amount of rs . 100 for 1 year when compounded half yearly = rs . [ 100 x ( 1 + 3 / 100 ) 2 ] = rs . 106.09 % . effective rate = ( 106.09 - 100 ) % = rs . 6.09 % . answer d"

a ) 6.06 % , b ) 6.07 % , c ) 6.08 % , d ) 6.09 % , e ) none

d

15,009

gain

a 340 - liter solution of kola is made from 80 % water , 6 % concentrated kola and the rest is made from sugar . if 3.2 liters of sugar , 10 liter of water and 6.8 liters of concentrated kola were added to the solution , what percent of the solution is made from sugar ?

denominator : 340 + 10 + 3.2 + 6.8 = 360 numerator : 340 ( 1 - . 80 - . 06 ) + 3.2 340 ( 0.14 ) + 3.2 47.6 + 3.2 50.8 ratio : 50.8 / 360 = 0.14 answer : e

a ) 6 % . , b ) 7.5 % . , c ) 9.2 % . , d ) 10.5 % . , e ) 14 % .

e

15,010

physics

a man ' s regular pay is $ 3 per hour up to 40 hours . overtime is twice the payment for regular time . if he was paid $ 198 , how many hours overtime did he work ?

"at $ 3 per hour up to 40 hours , regular pay = $ 3 x 40 = $ 120 if total pay = $ 168 , overtime pay = $ 198 - $ 120 = $ 78 overtime rate ( twice regular ) = 2 x $ 3 = $ 6 per hour = > number of overtime hours = $ 78 / $ 6 = 13 ans is e"

a ) 8 , b ) 5 , c ) 9 , d ) 6 , e ) 13

e

15,011

physics

there are 24 stations between ernakulam and chennai . how many second class tickets have to be printed , so that a passenger can travel from one station to any other station ?

"the total number of stations = 26 from 26 stations we have to choose any two stations and the direction of travel ( ernakulam to chennai is different from chennai to ernakulam ) in 26 p 2 ways . 26 p 2 = 26 * 25 = 650 answer : c"

a ) 800 , b ) 820 , c ) 650 , d ) 870 , e ) 900

c

15,012

gain

fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.64 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?

let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.64 9.9 - 45 x + 36 x = 8.64 9 x = 1.26 x = 0.14 the answer is e .

a ) 8 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 14 %

e

15,013

physics

a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 5 days . in how many days can they complete the remaining work ?

"work done by a in 5 days = 5 / 10 = 1 / 2 remaining work = 1 / 2 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 1 / 2 * 6 / 1 = 3 days . answer : e"

a ) 6 days , b ) 2 days , c ) 8 days , d ) 4 days , e ) 3 days

e

15,014

general

a bag contains an equal number of one rupee , 50 paise and 25 paise coins respectively . if the total value is 70 , how many coins of each type are there ?

"let number of each type of coin = x . then , 1 × x + . 50 × x + . 25 x = 70 ⇒ 1.75 x = 70 ⇒ x = 40 coins answer c"

a ) 20 coins , b ) 30 coins , c ) 40 coins , d ) 25 coins , e ) none of these

c

15,015

general

the product of two numbers is 120 and the sum of their squares is 289 . the sum of the number is ?

let the numbers be x and y . then , xy = 120 and x 2 + y 2 = 289 . ( x + y ) 2 = x 2 + y 2 + 2 xy = 289 + ( 2 x 120 ) = 529 x + y = 529 = 23 . option a

a ) 23 , b ) 25 , c ) 27 , d ) 31 , e ) 35

a

15,016

general

one millisecond is 0.001 of a second . the costs for a single run of a computer program are $ 1.07 for operating - system overhead , $ 0.023 per millisecond of computer time , and $ 5.35 for the mounting of a data tape . what is the total of these 3 costs for 1 run of a program that requires 1.5 seconds of computer time ?

operating system overhead for 1 run = 1.07 $ mounting of data tape = 5.35 $ cost per 1 millisecond of computer time = . 023 $ total cost of 1 run of a program that requires 1.5 seconds of computer time = 1.07 + ( . 023 * 1500 ) + 5.35 = 1.07 + 34.5 + 5.35 = 40.92 $ answer e

a ) $ 7.15 , b ) $ 8.87 , c ) $ 28.96 , d ) $ 35.57 , e ) $ 40.92

e

15,017

physics

the length of a room is 5.5 m and width is 3.75 m . what is the cost of paying the floor by slabs at the rate of rs . 800 per sq . meter .

"explanation : area = 5.5 × 3.75 sq . metre . cost for 11 sq . metre . = rs . 800 hence , total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : option d"

a ) rs . 12000 , b ) rs . 19500 , c ) rs . 18000 , d ) rs . 16500 , e ) rs . 17500

d

15,018

physics

by travelling at 50 kmph , a person reaches his destination on time . he covered two - third the total distance in one - third of the total time . what speed should he maintain for the remaining distance to reach his destination on time ?

"let the time taken to reach the destination be 3 x hours . total distance = 50 * 3 x = 150 x km he covered 2 / 3 * 150 x = 100 x km in 1 / 3 * 3 x = x hours so , the remaining 50 x km , he has to cover in 2 x hours . required speed = 50 x / 2 x = 25 kmph . answer : c"

a ) 23 kmph , b ) 24 kmph , c ) 25 kmph , d ) 26 kmph , e ) 27 kmph

c

15,019

general

5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 60 only . men â € ™ s wages are ?

"5 m = xw = 8 b 5 m + xw + 8 b - - - - - 60 rs . 5 m + 5 m + 5 m - - - - - 60 rs . 15 m - - - - - - 60 rs . = > 1 m = 4 rs . answer : c"

a ) 6 rs , b ) 2 rs , c ) 4 rs , d ) 9 rs , e ) 3 rs

c

15,020

general

what least value should be replaced by * in 483 * 4312 so the number become divisible by 6

"explanation : trick : number is divisible by 6 , if sum of all digits is divisible by 3 and 2 , last digit is 2 so it is dividable by 2 so ( 4 + 8 + 3 + * + 4 + 3 + 1 + 2 ) = 25 + * should be divisible by 6 , 15 + will be divisible by , so that least number is 2 . answer : option d"

a ) 3 , b ) 4 , c ) 5 , d ) 2 , e ) 7

d

15,021

general

line q has the equation 5 y – 3 x = 90 . if line s is perpendicular to q , has an integer for its y - intercept , and intersects q in the second quadrant , then how many possible line s ’ s exist ? ( note : intersections on one of the axes do not count . )

5 y - 3 x = 90 and so y = 3 x / 5 + 18 when x = 0 , then y = 18 . when y = 0 , then x = - 30 the slope is 3 / 5 , so the slope of line s is - 5 / 3 . through the point ( - 30 , 0 ) , 0 = - 5 ( - 30 ) / 3 + c the y - intercept is c = - 50 . thus the perpendicular line s can have y - intercepts from - 49 up to 17 . the number of possible lines is 49 + 17 + 1 = 67 the answer is d .

a ) 58 , b ) 61 , c ) 64 , d ) 67 , e ) 70

d

15,022

gain

the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 275 , then the mean profit for the last 15 days would be

"average would be : 350 = ( 275 + x ) / 2 on solving , x = 425 . answer : d"

a ) rs . 200 , b ) rs . 350 , c ) rs . 275 , d ) rs . 425 , e ) none of these

d

15,023

gain

100 liter solution of cool - drink is made from 10 % jasmine water . if 5 liters of jasmine and 10 liters of water were added to the solution , what percent of the solution is jasmine ?

denominator 100 + 5 + 10 115 numerator 100 * 0.1 = 10 - - - > jasmine water 10 + 5 = 15 - - - > new content of jasmine water in new solution ratio 3 / 23 answer is b

a ) 1 / 13 , b ) 2 / 23 , c ) 3 / 31 , d ) 4 / 15 , e ) 2 / 3

b

15,024

general

in 1990 the budgets for projects q and v were $ 700,000 and $ 780,000 , respectively . in each of the next 10 years , the budget for q was increased by $ 30,000 and the budget for v was decreased by $ 10,000 . in which year was the budget for q equal to the budget for v ?

"let the no of years it takes is x . 700 + 30 x = 780 - 10 x - - > 40 x = 80 and x = 2 . thus , it happens in 1992 . a ."

a ) 1992 , b ) 1993 , c ) 1994 , d ) 1995 , e ) 1996

a

15,025

gain

a person buys an article at rs . 350 . at what price should he sell the article so as to make a profit of 30 % ?

"cost price = rs . 350 profit = 30 % of 350 = rs . 105 selling price = cost price + profit = 350 + 105 = 455 answer : a"

a ) 455 , b ) 277 , c ) 269 , d ) 261 , e ) 281

a

15,026

physics

working together , wayne and his son can shovel the entire driveway in three hours . if wayne can shovel four times as fast as his son can , how many hours would it take for his son to shovel the entire driveway on his own ?

"w : the time for wyane to do the job s : the time for his son to do the job we have 1 / w + 1 / s = 1 / 4 and w = 4 s then we have 1 / ( 4 * s ) + 1 / s = 1 / 4 < = > 5 / ( 4 * s ) = 1 / 4 < = > s = 5 ans : c"

a ) 4 , b ) 6 , c ) 5 , d ) 9 , e ) 12

c

15,027

other

thomas ' s age and matt ' s age are in the ratio 3 : 5 . two years ago the ratio of their ages was 5 : 9 . find the ratio of their ages 4 years hence ?

let ages of thomas and matt be x and y respectively . x / y = 3 / 5 = > x = 3 / 5 y ( x - 2 ) / ( y - 2 ) = 5 / 9 = > 9 x - 18 = 5 y - 10 = > 9 x = 5 y + 8 but x = 3 / 5 y 9 * 3 / 5 y = 5 y + 8 27 y = 25 y + 40 = > y = 20 years = > x = 3 * 20 / 5 = > 12 years ratio of their ages four years hence , ( 12 + 4 ) / ( 20 + 4 ) = 16 / 24 . = > 2 : 3 answer : b

a ) 1 : 2 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) 5 : 6

b

15,028

general

the average of first 11 prime numbers is ?

"sum of 11 prime no . = 160 average = 160 / 11 = 14.55 answer : a"

a ) 14.55 , b ) 11.11 , c ) 12.11 , d ) 13.11 , e ) 14.11

a

15,029

gain

if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 50 , what is the compound interest on the same at the same rate and for the same time ?

"simple interest for 2 years = rs . 50 ie . for 1 years rs . 25 . . in the first year the s . i and c . i are same ie . rs . 25 . so in the 2 nd year in c . i calculated for 1 years interest also . so in second years for rs . 25 interest is 25 * 5 / 100 = 1.25 . so total c . p = 51.25 . answer : b"

a ) rs . 52 , b ) rs . 51.25 , c ) rs . 54.25 , d ) rs . 60 , e ) rs . 70

b

15,030

general

exactly 3 / 8 of the people in the room are under the age of 21 , and exactly 5 / 12 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?

"the total number of the people in the room must be a multiple of both 8 and 12 ( in order 3 / 7 and 5 / 13 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 8 and 12 , which is 96 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 96 people in the room . therefore there are 3 / 8 * 96 = 36 people in the room under the age of 21 . answer : b ."

a ) 21 , b ) 36 , c ) 39 , d ) 60 , e ) 65

b

15,031

general

a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 40 marks . the maximum marks are :

"explanation : given that the student got 125 marks and still he failed by 40 marks = > the minimum pass mark = 125 + 40 = 165 given that minimum pass mark = 33 % of the total mark answer : a ) 500"

a ) 500 , b ) 387 , c ) 298 , d ) 267 , e ) 191

a

15,032

general

the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 148 , what is the difference between the ages of patrick and monica ?

"ages of p and mi = 3 x + 5 x ages of mi and mo = 3 x : 5 x rationalizing their ages . ratio of their ages will be 9 x : 15 x : 25 x sum = 47 x = 148 x = 3 difference if ages of pa and mo = 25 x - 9 x = 16 x = 16 * 3 = 48 answer b"

a ) 27 , b ) 48 , c ) 45 , d ) 72 , e ) 18

b

15,033

physics

a train 360 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 340 m long ?

"speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 360 + 340 = 700 m required time = 700 * 2 / 25 = 56 sec answer : a"

a ) 56 sec , b ) 42 sec , c ) 45 sec , d ) 48 sec , e ) 50 sec

a

15,034

general

a motorist travels to a place 150 km away at an average speed of 50 km / hr and returns at 30 km / hr . his average speed for the whole journey in km / hr is ?

explanation : average speed = ( 2 xy ) / ( x + y ) km / hr = ( 2 * 50 * 30 ) / ( 50 + 30 ) km / hr . 37.5 km / hr . answer : c

a ) 37.9 , b ) 37.53 , c ) 37.5 , d ) 37.1 , e ) 37.4

c

15,035

general

48.95 - 32.006 = ?

"48.950 - 32.006 - - - - - - - - - 16.944 answer is d"

a ) 16.089 , b ) 16.35 , c ) 16.89 , d ) 16.944 , e ) none of them

d

15,036

general

the average age of 20 persons in a office is 15 years . out of these , the average age of 5 of them is 14 years and that of the other 9 persons is 16 years . the age of the 15 th person is ?

"age of the 15 th student = 20 * 15 - ( 14 * 5 + 16 * 9 ) = 300 - 214 = 86 years answer is b"

a ) 79 , b ) 86 , c ) 95 , d ) 72 , e ) 80

b

15,037

general

a vessel of capacity 2 litre has 30 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?

"30 % of 2 litres = 0.6 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 3.0 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 30 % answer : a"

a ) 30 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .

a

15,038

general

what is the 4 digit no . in which the 1 st digit is 1 / 3 of the second , the 3 rd is the sum of the 1 st and 2 nd , and the last is 3 times the second ?

first digit is 1 / 3 second digit = > the numbers can be 1 & 3 , 2 & 6 , 3 & 9 . first + second = third = > we can eliminate 3 & 9 since 3 + 9 = 12 . last is 3 times the second = > we can eliminate option 2 & 6 since 3 * 6 = 18 . hence the number is 1349 c

a ) 1123 , b ) 1234 , c ) 1349 , d ) 1455 , e ) 1567

c

15,039

physics

the distance between two cities a and b is 1410 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?

"explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 1410 . therefore , 60 x + 75 ( x - 1 ) = 1410 . = > x = 3 . so , they meet at ( 8 + 11 ) i . e , 7 pm . answer : b"

a ) 09 pm , b ) 07 pm , c ) 11 pm , d ) 05 am , e ) 03 am

b

15,040

physics

a train running at the speed of 30 km / hr crosses a pole in 9 sec . what is the length of the train ?

"speed = 30 * 5 / 18 = 25 / 3 m / sec length of the train = speed * time = 25 / 3 * 9 = 75 m answer : a"

a ) 75 m , b ) 180 m , c ) 324 m , d ) can not be determined , e ) none of these

a

15,041

physics

how long does a train 120 m long running at the speed of 70 km / hr takes to cross a bridge 150 m length ?

"speed = 70 * 5 / 18 = 19.4 m / sec total distance covered = 120 + 150 = 270 m . required time = 270 / 19.4 ' = 13.9 sec . answer : b"

a ) 12.7 sec , b ) 13.9 sec , c ) 18.1 sec , d ) 17.1 sec , e ) 19.7 sec

b

15,042

general

for any integer k greater than 1 , the symbol k * denotes the product of all integers between 1 and k , inclusive . if k * is a multiple of 3,675 , what is the least possible value of k ?

"we basically need 5,5 , 3,7 and 7 in the number . 14 ! , has 3 , 5 , 7 , 10 , 14 now 10 = 2 x 5 14 = 2 x 7 cross check : k ! = 3675 * m ( m is a positive integer ) k ! = 3 * 5 * 5 * 7 * 7 14 ! has all the numbers above . . therefore b . . ! answer : b"

a ) 12 , b ) 14 , c ) 15 , d ) 21 , e ) 25

b

15,043

general

if 2 ^ ( 2 w ) = 8 ^ ( w − 6 ) , what is the value of w ?

"2 ^ ( 2 w ) = 8 ^ ( w − 6 ) 2 ^ ( 2 w ) = 2 ^ ( 3 * ( w − 6 ) ) 2 ^ ( 2 w ) = 2 ^ ( 3 w - 18 ) let ' s equate the exponents as the bases are equal . 2 w = 3 w - 18 w = 18 the answer is c ."

a ) 12 , b ) 15 , c ) 18 , d ) 21 , e ) 24

c

15,044

general

5 friends visited a fruit stall , and everyone decided to contribute equally to the total bill of $ 100 . if one of the friends had a coupon for 6 % off the total bill , and if each friend still contributed equally after the coupon was applied to the bill , how much did each friend pay ?

at the non - discounted price , each friend would pay $ 20 , as $ 100 divided by 5 friends is $ 20 per friend . but if the bill is 6 % off , then each friend would pay 6 % less . 6 % of $ 20 is $ 1.2 , so each friend saves $ 1.2 and pays the remaining 18.8 correct option : option b

a ) 18 , b ) 18.8 , c ) 19 , d ) 17.8 , e ) 17.9

b

15,045

physics

dan ’ s car gets 32 miles per gallon . if gas costs $ 4 / gallon , then how many miles can dan ’ s car go on $ 46 of gas ?

"46 / 4 = 11.5 gallons 11.5 * 32 = 368 miles the answer is c ."

a ) 124 , b ) 256 , c ) 368 , d ) 424 , e ) 512

c

15,046

gain

at what price must an book costing $ 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?

"c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 95 / 100 ) = 59.375 mp = 62.5"

a ) 72.5 , b ) 55.5 , c ) 62.5 , d ) 82.5 , e ) 60.5

c

15,047

other

a certain bag contains 60 balls — 22 white , 10 green , 7 yellow , 15 red , and 6 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?

"according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 10 + 17 ) / 60 = 39 / 60 = 0.65 . answer : b ."

a ) 0.09 , b ) 0.65 , c ) 0.54 , d ) 0.85 , e ) 0.91

b

15,048

general

solution for 1.35 + . 123 + . 321

"1.35 + . 123 + . 321 = 0 0 = 0 - 1.35 - 0.123 - 0.321 0 = - 1.794 answer : b"

a ) 2.91 , b ) 1.794 , c ) 1.338 , d ) 1.986 , e ) 1.999

b

15,049

geometry

carol and jordan draw rectangles of equal area . if carol ' s rectangle measures 12 inches by 15 inches and jordan ' s rectangle is 9 inches long , how wide is jordan ' s rectangle , in inches ?

"area of first rectangle is 12 * 15 = 180 hence area of second would be 9 x = 180 x x = 20 answer is d"

a ) 17 , b ) 18 , c ) 19 , d ) 20 , e ) 21

d

15,050

gain

a , b and c start a business each investing 20000 . after 5 months a withdrew 10000 , b withdrew 15000 and c invests 5000 more . at the end of the year , a total profit of 58000 was recorded . find the share of b .

ratio of the capitals of a , b and c = 20000 ã — 5 + 10000 ã — 7 : 20000 ã — 5 + 5000 ã — 7 : 20000 ã — 5 + 25000 ã — 7 = 170000 : 135000 : 275000 = 170 : 135 : 275 . b â € ™ s share = ( 58000 ã — 135 â „ 580 ) = 13500 answer d

a ) 20,000 , b ) 21,200 , c ) 28,200 , d ) 13,500 , e ) none of these

d

15,051

general

a two digit number is 18 less than the square of the sum of its digits . how many such numbers are there ?

option 2 take n = 10 a + b . given that , ( 10 a + b ) + 18 = k 2 = ( a + b ) 2 given number = k 2 - 18 = ( 10 a + b ) that means , when we add 18 to the given number it should be a perfect square . so k 2 takes the following values . 1 , 4 , 9 , 16 , 25 , 36 , 49 , 64 , 81 , 100 , 121 , . . . . 1 to 16 are ruled out as if we subtract 18 from them , the resulting number is a single digit number . now 25 - 18 = 7 36 - 18 = 18 49 - 18 = 31 64 - 18 = 46 81 - 18 = 63 100 - 18 = 82 121 - 18 = 103 now 63 , 82 satisfies . answer : d

a ) 2233 , b ) 2222 , c ) 2211 , d ) 6382 , e ) 23,17

d

15,052

physics

a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 380 m long platform ?

"let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 380 ) / 36 * 5 / 18 = 50 min . answer : a"

a ) 50 , b ) 27 , c ) 29 , d ) 47 , e ) 28

a

15,053

general

a corporation that had $ 10 billion in profits for the year paid out $ 500 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )

"required answer = [ employee benefit / profit ] * 100 = [ ( 500 million ) / ( 10 billion ) ] * 100 = [ ( 500 * 10 ^ 6 ) / ( 10 * 10 ^ 9 ) ] * 100 = ( 50 / 1000 ) * 100 = 5 % so answer is ( c )"

a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 %

c

15,054

physics

if 24 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?

"if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 24 lines is 24 c 2 = 276 the answer is a ."

a ) 276 , b ) 350 , c ) 425 , d ) 512 , e ) 648

a

15,055

general

a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2490 ?

"let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 a ' s share in the profit of rs . 2490 = 20 ( 2490 / 60 ) = rs . 830 . answer : b"

a ) rs . 832 , b ) rs . 830 , c ) rs . 822 , d ) rs . 812 , e ) rs . 810

b

15,056

physics

a car takes 6 hours to cover a distance of 144 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?

"time = 6 distence = 144 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 144 / 9 = 16 kmph d )"

a ) 50 kmph , b ) 60 kmph , c ) 65 kmph , d ) 16 kmph , e ) none

d

15,057

general

when jessica withdrew $ 200 from her bank account , her account balance decreased by 2 / 5 . if she deposits an amount equal to 2 / 3 of the remaining balance , what will be the final balance in her bank account ?

"as per the question 200 = 2 a / 5 thus - a which is the total amount = 500 the amount thus left = 300 she then deposited 2 / 3 of 300 = 200 total amount in her account = 500 answer d"

a ) 300 , b ) 375 , c ) 400 , d ) 500 , e ) 575

d

15,058

general

on a certain date , pat invested $ 6,000 at x percent annual interest , compounded annually . if the total value of the investment plus interest at the end of 10 years will be $ 24,000 , in how many years total will the total value of the investment plus interest increase to $ 48,000 ?

"24,000 = 6,000 ( 1 + x ) ^ 10 4 = ( 1 + x ) ^ 10 = 2 ^ 2 ( 1 + x ) ^ 10 = ( ( 1 + x ) ^ 5 ) ^ 2 = 2 ^ 2 therefore , ( 1 + x ) ^ 5 = 2 48,000 = 6000 ( 1 + x ) ^ n ( 1 + x ) ^ n = 8 ( 1 + x ) ^ n = 2 ^ 3 ( 1 + x ) ^ n = ( ( 1 + x ) ^ 5 ) ^ 3 = ( 1 + x ) ^ 15 therefore , n = 15 . the answer is a ."

a ) 15 , b ) 16 , c ) 18 , d ) 20 , e ) 24

a

15,059

physics

a mobile battery in 1 hour charges to 20 percent . how much time ( in minute ) will it require more to charge to 40 percent .

1 hr = 20 percent . thus 15 min = 5 percent . now to charge 40 percent 120 min . answer : a

a ) 120 , b ) 150 , c ) 175 , d ) 160 , e ) 130

a

15,060

general

a train starts full of passengers at the first station it drops 1 / 3 of the passengers and takes 280 more at the second station it drops one half the new total and takes 12 more . on arriving at the third station it is found to have 242 passengers . find the no of passengers in the beginning ?

let no of passengers in the beginning be x after first station no passengers = ( x - x / 3 ) + 280 = 2 x / 3 + 280 after second station no passengers = 1 / 2 ( 2 x / 3 + 280 ) + 12 1 / 2 ( 2 x / 3 + 280 ) + 12 = 242 2 x / 3 + 280 = 2 * 230 = 460 - 280 = 180 2 x / 3 = 180 x = 270 . so the answer is option b ) 270 .

a ) 292 , b ) 270 , c ) 192 , d ) 144 , e ) 168

b

15,061

geometry

a specialized type of sand consists of 40 % mineral x by volume and 60 % mineral y by volume . if mineral x weighs 4 grams per cubic centimeter and mineral y weighs 3 grams per cubic centimeter , how many grams does a cubic meter of specialized sand combination weigh ? ( 1 meter = 100 centimeters )

let the volume be 1 m ^ 3 = 1 m * 1 m * 1 m = 100 cm * 100 cm * 100 cm = 1 , 000,000 cm ^ 3 by volume 40 % is x = 400,000 cm ^ 3 60 % is y = 600,000 cm ^ 3 by weight , in 1 cm ^ 3 , x is 4 gms in 400,000 cm ^ 3 , x = 4 * 400,000 = 1 , 600,000 grams in 1 cm ^ 3 , y is 3 gms in 600,000 cm ^ 3 , y = 3 * 600,000 = 1 , 800,000 gms total gms in 1 m ^ 3 = 1 , 600,000 + 1 , 800,000 = 2 , 400,000 answer : b

['a ) 5 , 500,000', 'b ) 2 , 400,000', 'c ) 55,000', 'd ) 28,000', 'e ) 280']

b

15,062

general

a retailer bought a coat at wholesale and marked it up 90 % to its initial price of $ 76 . by how many more dollars does he need to increase the price to achieve a 100 % markup ?

let x be the wholesale price . then 1.9 x = 76 and x = 76 / 1.9 = 40 . to achieve a 100 % markup , the price needs to be $ 80 . the retailer needs to increase the price by $ 4 more . the answer is b .

a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10

b

15,063

other

the hcf of two numbers is 40 and the other two factors of their lcm are 11 and 12 . what is the largest number .

"explanation : hcf of the two numbers = 40 hcf will be always a factor of lcm 40 is factor of lcm other two factors are 11 & 12 then the numbers are ( 40 * 11 ) and ( 40 x 12 ) = 440 and 480 answer : option d"

a ) 462 , b ) 450 , c ) 488 , d ) 480 , e ) 555

d

15,064

physics

in 110 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :

"distance covered by b in 9 sec . = 110 / 45 x 9 m = 22 m . a beats b by 20 metres . answer : option c"

a ) 20 m , b ) 25 m , c ) 22 m , d ) 9 m , e ) 12 m

c

15,065

geometry

three interviewers , a , b , and c are interviewing 50 applicants . only with three interviewers ' admission can an applicant be admitted . if interviewer a admitted 20 applicants , b admitted 22 applicants , and c admitted 20 applicants , at least how many applicants get the admission ?

"if a admitted 20 are overlapping with b admission of 22 but c does not overlap with anybody . then no student will get nod from all the 3 . hence 0 student will get admission . answer : b"

a ) 4 , b ) 0 , c ) 6 , d ) 8 , e ) 12

b

15,066

general

there are 408 boys and 288 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .

explanation : hcf ( 408 , 288 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 288 / 24 = 17 + 12 = 29 answer : e

a ) 31 , b ) 32 , c ) 35 , d ) 30 , e ) 29

e

15,067

physics

walking at 6 / 7 th of his usual speed , a man is 25 mins too late . his usual time is

"as the distance is same s * t = 6 / 7 s * ( t + 25 ) solving this we get t = 150 sec 150 / 60 = 2.5 hrs answer : c"

a ) 7.5 hrs , b ) 1.5 hrs , c ) 2.5 hrs , d ) 1.67 hrs , e ) 2.67 hrs

c

15,068

physics

a train running at the speed of 60 km / hr crosses a pole in 12 sec . what is the length of the train ?

"speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 12 = 200 m answer : a"

a ) 200 m , b ) 178 m , c ) 186 m , d ) 168 m , e ) 150 m

a

15,069

gain

julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest . after two years she earned $ 120 and $ 126 from the simple interest account and the compound interest account respectively . if the interest rates for both accounts were the same , what was the amount of julie ' s initial savings ?

"$ 120 for 2 years = $ 60 per year . extra $ 6 yearned with the compound interest is the percent yearned on percent . so , $ 6 is yearned on $ 60 , which means that the interest = 10 % . this on the other hand means that half of the savings = 60 * 10 = $ 600 . twice of that = $ 1,200 . answer : d ."

a ) 600 , b ) 720 , c ) 1080 , d ) 1200 , e ) 1440

d

15,070

general

a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability q that a + b is prime ?

"total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes q = 15 / 36 . answer : c ."

a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9

c

15,071

gain

mr . tom invested in fund x and fund y . the total amount she invested , in both funds combined , was $ 100000 . in one year , fund x paid 23 % and fund y paid 17 % . the interest earned in fund y was exactly $ 200 greater than the interest earned in fund x . how much did ms . tom invest in fund x ?

x + y = 100000 0.17 y = 0.23 a + 200 take away decimals first : 17 y = 23 x + 20000 isolate first equation to solve for x ( your goal ) : y = 100000 - y plug in for b : 17 ( 100000 - x ) = 23 x + 20000 1 , 700000 - 17 x = 23 x + 20000 1 , 680000 = 40 x 1 , 680000 / 40 = x x = 42000 = answer choice c

a ) $ 32000 , b ) $ 36000 , c ) $ 42000 , d ) $ 44000 , e ) $ 45000

c

15,072

gain

on a certain transatlantic crossing , 20 percent of a ship ' s passengers held round - trip tickets and also took their cars abroad the ship . if 40 percent of the passengers with round - trip tickets did not take their cars abroad the ship , what percent of the ship ' s passengers held round - trip tickets ?

"0.20 p = rt + c 0.4 ( rt ) = no c = > 0.60 ( rt ) had c 0.20 p = 0.60 ( rt ) rt / p = 1 / 3 = 33 % answer - a"

a ) 33.3 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 66.6 %

a

15,073

physics

two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post . if the length of each train be 200 m , in what time will they cross other travelling in opposite direction ?

"speed of the first train = 120 / 10 = 12 m / sec . speed of the second train = 120 / 5 = 8 m / sec . relative speed = 12 + 8 = 20 m / sec . required time = ( 200 + 200 ) / 20 = 20 sec . answer : e"

a ) 17 sec , b ) 12 sec , c ) 16 sec , d ) 15 sec , e ) 20 sec

e

15,074

geometry

how many diagonals does a polygon with 23 sides have , if one of its vertices does not connect to any diagonal ?

"if i calculate it using the formulae , # diagonals = n ( n - 3 ) / 2 each vertex sends of n - 3 diagonals n = 23 - 1 then 22 * ( 22 - 3 ) / 2 = 209 correct option : e"

a ) 201 , b ) 159 , c ) 179 , d ) 189 , e ) 209

e

15,075

physics

a train moves at average speed of 60 kmph reaches its destination on time . what its average speed becomes 50 kmph , then it reaches its destination 15 late . find the length of the journey ?

"difference between timings = 15 min = 1 / 4 hr let the length of the journey be x km . then x / 50 - x / 60 = 1 / 4 x / 10 = 1 / 4 x = 2.5 km answer ( b )"

a ) 4.86 km , b ) 2.5 km , c ) 6.86 km , d ) 5.867 km , e ) 3.25 km

b

15,076

general

how many points ( x , y ) lie on the line segment between ( 32 , 12 2 / 3 ) and ( 7 , 17 2 / 3 ) such that x and y are both integers ?

"slope = ( 17 2 / 3 - 12 2 / 3 ) / ( 7 - 32 ) = - 1 / 5 y = mx + b = > 12 2 / 3 = - 22 / 3 + b = > b = 19 y = - x / 5 + 19 only integer values work , and the only multiples of 5 between 7 and 32 for x values are 10 , 15 , 20 , 25 and 30 , thus 5 points . c"

a ) one , b ) 4 , c ) 5 , d ) 8 , e ) 9

c

15,077

physics

a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 72 km / hr . what is the length of the platform ?

"speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 20 = 400 m . let the length of the platform be x m . then , ( x + 400 ) / 36 = 20 = > x = 320 m . answer : e"

a ) 229 , b ) 240 , c ) 288 , d ) 277 , e ) 320

e

15,078

general

the difference between a number and its two - fifth is 510 . what is 50 % of that number ?

"let the number be x . then , x - 2 / 5 x = 510 x = ( 510 * 5 ) / 3 = 850 50 % of 850 = 425 . answer : b"

a ) 426 , b ) 425 , c ) 427 , d ) 428 , e ) 429

b

15,079

gain

15 % of 75 is the same as vx % of 450 . find x .

15 % of 75 = 11.25 450 * x / 100 = 11.25 x = 2.5 answer : b

a ) 1 , b ) 2.5 , c ) 3 , d ) 4 , e ) 5

b

15,080

general

marketing executives for a certain chewing gum company projected a 20 percent increase in revenue this year over that of last year , but revenue this year actually decreased by 25 % . what percent of the projected revenue was the actual revenue ?

"last year revenue = 100 ( assume ) ; this year revenue = 75 ; projected revenue = 120 . actual / projected * 100 = 75 / 120 * 100 = 62.5 % . answer : c"

a ) 53 % , b ) 58 % , c ) 62.5 % , d ) 64 % , e ) 75 %

c

15,081

physics

5 / 8 th of a job is completed in 10 days . if a person works at the same pace , how many days will he take to complete the job ?

explanation : solution : it is given that 5 / 8 th of the work is completed in 10 days . = > remaining work = 3 / 8 th of total applying unitary method : total work will be completed in 10 * 8 / 5 days = > it takes 16 days to complete total work = > hence , remaining work days = 16 - 10 = 6 days answer : c

a ) 8 , b ) 9 , c ) 6 , d ) 2 , e ) 1

c