id
int64 14.8k
60.8k
| category
stringclasses 15
values | diagramRef
stringclasses 314
values | Problem
stringlengths 5
4.31k
| Rationale
stringlengths 0
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stringlengths 0
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15,182 |
physics
|
a is twice as good a work man as b and together they finish the work in 14 days . in how many days a alone can finish the work ?
|
"wc = 2 : 1 2 x + x = 1 / 14 = > x = 1 / 42 2 x = 1 / 21 a can do the work in 21 days . answer : b"
|
a ) 12 , b ) 21 , c ) 77 , d ) 99 , e ) 22
|
b
|
|
15,183 |
general
|
if 3 < x < 6 < y < 8 , then what is the greatest possible positive integer difference of x and y ?
|
3 < x < 6 < y < 8 ; 3 < x y < 8 3 + y < x + 8 y - x < 5 . positive integer difference is 4 ( for example y = 7.5 and x = 3.5 ) answer : b .
|
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
|
b
|
|
15,184 |
general
|
a lemonade stand sold only small and large cups of lemonade on tuesday . 2 / 5 of the cups sold were small and the rest were large . if the large cups were sold for 7 / 6 as much as the small cups , what fraction of tuesday ' s total revenue was from the sale of large cups ?
|
"a simpler way i guess would be to think that in total 5 cups were sold . out of which 2 are small and 3 are large . now let the small ones cost $ 6 . so the large ones would cost $ 7 . so , 2 * 6 = 12 and 3 * 7 = 21 . total revenue was 12 + 21 = 33 and large cup sales as found above is 21 therefore answer is 21 / 33 i . e 7 / 11 b"
|
a ) ( a ) 7 / 16 , b ) ( b ) 7 / 11 , c ) ( c ) 10 / 21 , d ) ( d ) 17 / 35 , e ) ( e ) 1 / 2
|
b
|
|
15,185 |
physics
|
x does a work in 15 days . y does the same work in 45 days . in how many days they together will do the same work ?
|
"x ' s 1 day ' s work = 1 / 15 y ' s 1 day ' s work = 1 / 45 ( x + y ) ' s 1 day ' s work = ( 1 / 15 + 1 / 45 ) = 1 / 11.25 both together will finish the work in 11.25 days . correct option is d"
|
a ) 10 , b ) 12 , c ) 20 , d ) 11.25 , e ) 15
|
d
|
|
15,186 |
general
|
a person is saving money to purchase a car . he earns Γ’ Β£ 4000 per month and saves Γ’ Β£ 500 to buy the car . if he needs Γ’ Β£ 45000 to buy his dream car . how much money he will earn , before he saves enough money to buy the car ?
|
he is saving Γ’ Β£ 500 per month . he needs Γ’ Β£ 45000 and it takes Γ’ Β£ 45000 / Γ’ Β£ 500 = 90 months to save the money . in 90 months , he earns 90 * Γ’ Β£ 4000 = Γ’ Β£ 36000 . answer : c
|
a ) a - 352000 , b ) b - 356000 , c ) c - 360000 , d ) d - 348000 , e ) e - 340000
|
c
|
|
15,187 |
gain
|
there is 60 % increase in an amount in 6 years at s . i . what will be the c . i . of rs . 12,000 after 3 years at the same rate ?
|
"explanation : let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = ( 100 * 60 ) / ( 100 * 6 ) = 10 % p . a . now , p = rs . 12000 , t = 3 years and r = 10 % p . a . c . i . = [ 12000 * { ( 1 + 10 / 100 ) 3 - 1 } ] = 12000 * 331 / 1000 = rs . 3972 answer : option c"
|
a ) rs . 3932 , b ) rs . 3972 , c ) rs . 3372 , d ) rs . 3942 , e ) rs . 3772
|
c
|
|
15,188 |
physics
|
mariah has decided to hire three workers . to determine whom she will hire , she has selected a group of 14 candidates . she plans to have one working interview with 3 of the 14 candidates every day to see how well they work together . how many days will it take her to have working interviews with all the different combinations of job candidates ?
|
"333 . answer e"
|
a ) 720 , b ) 120 , c ) 300 , d ) 30 , e ) 333
|
e
|
|
15,189 |
physics
|
how many seconds will a train 110 meters long take to cross a railway platform 165 meters long if the speed of the train is 132 kmph ?
|
"d = 110 + 165 = 275 s = 132 * 5 / 18 = 110 / 3 mps t = 275 * 3 / 110 = 7.5 sec b ) 7.5 sec"
|
a ) 6 sec , b ) 7.5 sec , c ) 8 sec , d ) 3 sec , e ) 10 sec
|
b
|
|
15,190 |
gain
|
a 16 % stock yielding 8 % is quoted at ?
|
"assume that face value = rs . 100 as it is not given to earn rs . 8 , money invested = rs . 100 to earn rs . 16 , money invested = 100 Γ 16 / 8 = rs . 175 ie , market value of the stock = rs . 200 answer is e ."
|
a ) 165 , b ) 170 , c ) 175 , d ) 180 , e ) 200
|
e
|
|
15,191 |
general
|
let a , b , c be distinct digits . consider a two - digit number β ab β and a 3 - digit number β ccb β , both defined under the usual decimal number system , if ( ab ) 2 = ccb > 300 , then the value of b is
|
explanation : given , ( ab ) 2 = ccb . [ only 1 , 5 and 6 on squaring will result with same digits in units place . ] taking a = 2 , b = 1 , = > ( 21 ) ^ 2 = 441 > 300 . hence , the required value of b = 1 answer : a
|
a ) 1 , b ) 0 , c ) 5 , d ) 6 , e ) 7
|
a
|
|
15,192 |
general
|
john ' s marks wrongly entered as 82 instead of 62 . due to that the average marks for the class got increased by half ( 1 / 2 ) . the number of john in the class is ?
|
otal increase in marks = x x 1 = x 2 2 x / 2 = ( 82 - 62 ) x / 2 = 40 x = 80 . c
|
a ) 70 , b ) 78 , c ) 80 , d ) 84 , e ) 90
|
c
|
|
15,193 |
physics
|
gary β s gas station serves an average of 12 cars per hour on saturdays , 10 cars per hour on sundays , and 9 cars per hour on all other days of the week . if the station is open from 6 a . m . to 10 p . m . every day , how many cars does gary β s station serve over the course of a typical week ?
|
"6 a . m . to 10 p . m . = 16 hours number of cars serviced on weekdays = ( 16 * 9 * 5 ) number of cars serviced on saturday = ( 16 * 12 ) number of cars serviced on sunday = ( 16 * 10 ) number of cars served in a week = 16 ( 45 + 12 + 10 ) = 16 * 67 = 1072 answer : a"
|
a ) 1,072 , b ) 1,200 , c ) 1,240 , d ) 1,280 , e ) 1,320
|
a
|
|
15,194 |
general
|
each digit 1 through 5 is used exactly once to create a 5 - digit integer . if the 1 and the 2 can not be adjacent digits in the integer , how many 5 - digit integers are possible ?
|
"number of arrangements using 5 distinct digits = 5 ! number of arrangements in which 1 and 2 are adjacent - consider 1 and 2 together as one group . now you have 4 numbers / groups to arrange which can be done in 4 ! ways . in each of these arrangements , 1 and 2 can be arranged as 12 or 21 . number of arrangements in which 3 and 4 are not adjacent = 5 ! - 2 * 4 ! = 72 answer : c"
|
a ) 48 , b ) 66 , c ) none of these , d ) 78 , e ) 90
|
c
|
|
15,195 |
general
|
in a room filled with 7 people , 2 people have exactly 1 sibling in the room and 5 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
|
"there are suppose a b c d e f g members in the room 4 people who have exactly one sibling . . . . a b c d . . . . ( a is bs β sssibl β g β ssand β ssviceversa ) β ss ( c β ssis β ssds β sssibl β g β ssand β ssviceversa ) β ss ( c β ssis β ssdssibl β gandviceversa ) ( cisds sibling and viceversa ) ( c is ds sibling and viceversa ) . . . now remaning efg are 5 people who have exactly 2 siblings . . . . ( e has f and g as his / her sibling and so on . . ) there are now 3 different set of siblings ( a and b ) ( c and d ) ; ( efg ) now first selecting 2 people out of 7 is 7 c 2 = 21 first sibling pair - - - - ( a and b ) - - selecting 2 people - - 2 c 2 = 1 second sibling pair ( c and d ) - - selecting 2 people - - 2 c 2 = 1 third sibling pair ( e f g ) - - selecting 2 out of 5 - - 5 c 2 = 10 total = 1 + 1 + 10 = 12 but , a / c to formula p ( success ) - 1 - p ( fail ) here , p ( failure ) is selecting 2 people who are siblings = 12 / 21 ( 21 is 7 c 2 ) = 1 - 12 / 21 = 9 / 21 = 3 / 7 ans b"
|
a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 21
|
b
|
|
15,196 |
general
|
sum of the squares of 3 no . ' s is 267 and the sum of their products taken two at a time is 131 . find the sum ?
|
"( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 267 + 2 * 131 a + b + c = β 529 = 23 d"
|
a ) 20 , b ) 24 , c ) 26 , d ) 23 , e ) 30
|
d
|
|
15,197 |
general
|
a number whose fifth part increased by 2 is equal to its fourth part diminished by 2 is ?
|
"answer let the number be n . then , ( n / 5 ) + 2 = ( n / 4 ) - 2 Γ’ β‘ β ( n / 4 ) - ( n / 5 ) = 4 Γ’ β‘ β ( 5 n - 4 n ) / 20 = 4 Γ’ Λ Β΄ n = 80 option : b"
|
a ) 160 , b ) 80 , c ) 200 , d ) 220 , e ) none
|
b
|
|
15,198 |
general
|
how many diagonals does a 63 - sided convex polygon have ?
|
"a 63 - sided convex polygon has 63 vertices . if we examine a single vertex , we can see that we can connect it with 60 other vertices to create a diagonal . note : there are 60 options because we ca n ' t connect the vertex to itself , and we ca n ' t connect it to its adjacent vertices , since this would not create a diagonal . if each of the 63 vertices can be connected with 60 vertices to create a diagonal then . . . . . . the total number of diagonals = ( 63 ) ( 60 ) = 3780 however , before we select answer choice c , we must recognize that we have counted every diagonal twice . for example , we might connect vertex a with vertex f and count that as 1 diagonal , and at the same time we connect vertex f with vertex a and count that as 1 diagonal . of course these diagonals are the same . to account for counting each diagonal twice , we must divide 3780 by 2 to get : 1890 answer : a"
|
a ) 1890 , b ) 1953 , c ) 3780 , d ) 3843 , e ) 3906
|
a
|
|
15,199 |
probability
|
three unbiased coins are tossed , what is the probability of getting at least 2 tails ?
|
"total cases are = 2 ^ 3 = 8 favoured cases = [ tth , tht , htt , ttt ] = 4 probability = 4 / 8 = 1 / 2 answer d"
|
a ) 1 / 5 , b ) 1 / 7 , c ) 1 / 8 , d ) 1 / 2 , e ) 1 / 10
|
d
|
|
15,200 |
probability
|
if a coin is flipped , the probability that the coin will land tails is 1 / 2 . if the coin is flipped 4 times , what is the probability that it will land tails up on the first 2 flips and not on the last 2 flips ?
|
( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) * ( 1 / 2 ) = 1 / 16 answer : d
|
a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 2 , d ) 1 / 16 , e ) 1 / 32
|
d
|
|
15,201 |
physics
|
a train 180 m long running at 70 kmph crosses a platform in 20 sec . what is the length of the platform ?
|
"d = 70 * 5 / 18 = 20 = 388 β 180 = 208 answer : a"
|
a ) 208 , b ) 277 , c ) 350 , d ) 881 , e ) 271
|
a
|
|
15,202 |
physics
|
a sum of 25 was paid for a work which a can do in 32 days , b in 20 days , b and c in 12 days and d in 24 days . how much did c receive if all the 4 work together ?
|
a ' s one day ' s work = 1 β 32 b ' s one day ' s work = 1 β 20 ( b + c ) ' s one day ' s work = 1 β 12 β΄ c ' s one day ' s work = 1 β 12 - 1 β 20 = 1 β 30 d ' s one day ' s work = 1 β 24 β΄ ( a + b + c + d ) ' s one day ' s work 1 / 32 + 1 / 20 + 1 / 30 + 1 / 24 = 75 + 120 + 80 + 100 / 2400 = 375 β 2400 = 15 β 96 = 5 β 32 β΄ out of 5 β 32 of work done 1 β 30 of the work is done by c . β out of 25 paid for the work , c will receive 1 / 30 / 5 / 32 Γ 25 , i . e , 1 β 30 Γ 32 β 5 Γ 25 , i . e , 16 β 3 answer b
|
a ) 14 β 3 , b ) 16 β 3 , c ) 15 β 3 , d ) 17 β 3 , e ) none of these
|
b
|
|
15,203 |
physics
|
a train 120 m long crosses a platform with a speed of 60 kmph in 15 sec ; find the length of the platform ?
|
d = 120 + x t = 15 s = 120 + x / 15 * 18 / 5 = 60 kmph . = > ( 120 + x ) * 18 = 4500 = > 120 + x = 250 = > x = 130 m answer : b
|
a ) 110 , b ) 130 , c ) 120 , d ) 125 , e ) 135
|
b
|
|
15,204 |
physics
|
a train running at the speed of 142 km / hr crosses a pole in 12 seconds . find the length of the train .
|
"speed = 162 * ( 5 / 18 ) m / sec = 45 m / sec length of train ( distance ) = speed * time 45 * 12 = 540 meter answer : a"
|
a ) 540 , b ) 288 , c ) 200 , d ) 340 , e ) 712
|
a
|
|
15,205 |
geometry
|
a certain cube floating in a bucket of water has between 80 and 85 percent of its volume below the surface of the water . if between 8 and 15 cubic centimeters of the cube ' s volume is above the surface of the water , then the length of a side of the cube is approximately
|
"if sides are 7 , vol = 7 ^ 3 = 343 80 % = 274.4 , 85 % = 291.55 so vol above water , between 68.6 and 51.45 - - > too big if side are 4 , vol = 64 80 % = 51.2 , 85 % = 54.4 vol above water between 12.8 and 9.6 so 4 should be the answer . check option c , if sides are 5 , vol = 125 80 % = 100 , . 85 % = 106.25 vol above water between 18.75 - 25 ( sides are 4 cubic centimeters ) b"
|
a ) 3 , b ) 4 , c ) 7 , d ) 8 , e ) 9
|
b
|
|
15,206 |
general
|
in the floor of a particular kitchen owned by an abstract artist , each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left . if there are 9 rows in all and a total of 405 tiles in the floor , how many tiles does the leftmost row contain ?
|
this question can be solved in a variety of ways : with algebra , by testing the answers and by using a great number property shortcut involving consecutive integers . we ' re given a few facts to work with : 1 ) there are 9 rows of tiles . 2 ) when going from ' left to right ' , each row contains two fewer tiles than the one next to it . 3 ) there are a total of 405 tiles we ' re asked how many tiles the left - most most row holds ( meaning the one with the most tiles ) . to start , 405 is divisible by 9 , so we can figure out the average number of tiles per row . that is 405 / 9 = 45 . since we ' re dealing with a set of 9 consecutive integers that differ by 2 each , we know that the ' 5 th row ' will have 45 tiles ( the average ) . then we just have to ' add 2 s ' until we get to the first row . . . 45 + 2 + 2 + 2 + 2 = 53 . final answer : a
|
a ) 53 , b ) 56 , c ) 60 , d ) 64 , e ) 68
|
a
|
|
15,207 |
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 145 , 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 = 145 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
|
|
15,208 |
general
|
bill made a profit of 10 % by selling a product . if he had purchased that product for 10 % less and sold it at a profit of 30 % , he would have received $ 70 more . what was his original selling price ?
|
"let the original purchase price be x so original selling price at 10 % profit = 1.1 x if product is purchased at 10 % less of original = 0.9 x profit of 30 % on this price = 1.3 ( 0.9 x ) he would have received $ 70 more in second scenario = > 1.3 ( 0.9 x ) - 1.1 x = 70 = > 0.07 x = 70 = > x = $ 1000 original purchase price = $ 1000 hence , original selling price ( at 10 % of profit ) = 1.1 ( 1000 ) = $ 1100 option d"
|
a ) $ 770 , b ) $ 660 , c ) $ 700 , d ) $ 1100 , e ) $ 840
|
d
|
|
15,209 |
general
|
if the product of 10 integers is negative , at most how many of the integers can be negative ?
|
"the product of 10 integers is negative thus an odd number of integers need to be negative to have a negative product we are asked at most how many are required . so , the highest odd integer before 6 , i . e . 9 correct option : d"
|
a ) 2 , b ) 3 , c ) 4 , d ) 9 , e ) 6
|
d
|
|
15,210 |
physics
|
the sum of 11 consecutive integers is 1111 . what is the greatest integer in the set ?
|
"let x be the first integer in the set , then x + 10 is the largest integer . the sum is : x + ( x + 1 ) + ( x + 2 ) + . . . + ( x + 10 ) = 11 x + 10 * 11 / 2 = 11 ( x + 5 ) then x + 5 = 101 x = 96 the largest integer in the set is 96 + 10 = 106 the answer is d ."
|
a ) 100 , b ) 102 , c ) 104 , d ) 106 , e ) 108
|
d
|
|
15,211 |
gain
|
a discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price . if , during a special sale , an additional 20 percent were to be deducted from the discount price , what would be the lowest possible price of an item costing $ 200 before any discount ?
|
"since the question is essentially just about multiplication , you can do the various mathstepsin a variety of ways ( depending on whichever method you find easiest ) . we ' re told that the first discount is 10 % to 30 % , inclusive . we ' re told that the next discount is 20 % off of the discounted price . . . . we ' re told to maximize the discount ( thus , 30 % off the original price and then 20 % off of the discounted price ) . thatmathcan be written in a number of different ways ( fractions , decimals , etc . ) : 30 % off = ( 1 - . 3 ) = ( 1 - 30 / 100 ) = ( . 7 ) and the same can be done with the 20 % additional discount . . . the final price of an item that originally cost $ 200 would be . . . . . ( $ 200 ) ( . 7 ) ( . 8 ) = ( $ 200 ) ( . 56 ) = 112 final answer : a"
|
a ) $ 112.00 , b ) $ 145.60 , c ) $ 163.80 , d ) $ 182.00 , e ) $ 100.00
|
a
|
|
15,212 |
gain
|
in town x , 90 percent of the population are employed , and 20 percent of the population are employed males . what percent of the employed people in town x are females ?
|
"total employed people 90 % , out of which 20 are employed males , hence 70 % are employed females . ( employed females ) / ( total employed people ) = 70 / 90 = 7 / 9 = 77 % answer : c ."
|
a ) 16 % , b ) 66 % , c ) 77 % , d ) 88 % , e ) 52 %
|
c
|
|
15,213 |
physics
|
two pipes can fill the cistern in 10 hr and 12 hr respectively , while the third empty it in 20 hr . if all pipes are opened simultaneously , then the cistern will be filled in
|
"solution : work done by all the tanks working together in 1 hour . 1 / 10 + 1 / 12 β 1 / 20 = 2 / 15 hence , tank will be filled in 15 / 2 = 7.5 hour option ( a )"
|
a ) 7.5 hr , b ) 8 hr , c ) 8.5 hr , d ) 10 hr , e ) none of these
|
a
|
|
15,214 |
general
|
there are 12 teams in a certain league and each team plays each of the other teams exactly once . what is the total number of games played ?
|
"12 c 2 = 66 the answer is b ."
|
a ) 55 , b ) 66 , c ) 77 , d ) 88 , e ) 99
|
b
|
|
15,215 |
gain
|
by selling 18 pencils for a rupee a man loses 15 % . how many for a rupee should he sell in order to gain 15 % ?
|
"85 % - - - 18 115 % - - - ? 85 / 115 * 18 = 13 answer : b"
|
a ) 8 , b ) 9 , c ) 10 , d ) 89 , e ) 81
|
b
|
|
15,216 |
general
|
the jogging track in a sports complex is 1000 meters in circumference . deepak and his wife start from the same point and walk in opposite directions at 20 km / hr and 12 km / hr respectively . they will meet for the first time in ?
|
"clearly , the two will meet when they are 1000 m apart to be 20 + 12 = 32 km apart , they take 1 hour to be 1000 m apart , they take 32 * 1000 / 1000 = 32 min . answer is a"
|
a ) 32 min , b ) 40 min , c ) 35 min , d ) 25 min , e ) 20 min
|
a
|
|
15,217 |
general
|
in a box of 8 pens , a total of 2 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
|
"p ( neither pen is defective ) = 6 / 8 * 5 / 7 = 15 / 28 the answer is e ."
|
a ) 6 / 11 , b ) 8 / 15 , c ) 9 / 20 , d ) 11 / 25 , e ) 15 / 28
|
e
|
|
15,218 |
gain
|
a trader bought a car at 20 % discount on its original price . he sold it at a 60 % increase on the price he bought it . what percent of profit did he make on the original price ?
|
"original price = 100 cp = 80 s = 80 * ( 160 / 100 ) = 128 100 - 128 = 28 % answer : a"
|
a ) 28 % , b ) 72 % , c ) 12 % , d ) 82 % , e ) 16 %
|
a
|
|
15,219 |
gain
|
mary works in a restaurant a maximum of 40 hours . for the first 20 hours , she is paid $ 8 per hour . for each overtime hour , she is paid at a rate which is 25 % higher than her regular rate . how much mary can earn in a week ?
|
"mary receives $ 8 ( 20 ) = $ 160 for the first 20 hours . for the 20 overtime hours , she receives $ 8 ( 0.25 ) + $ 8 = $ 10 per hour , that is $ 10 ( 20 ) = $ 200 . the total amount is $ 160 + $ 200 = $ 360 answer c 360 ."
|
a ) 300 , b ) 420 , c ) 360 , d ) 320 , e ) 400
|
c
|
|
15,220 |
general
|
if jake loses 8 pounds , he will weigh twice as much as his sister . together they now weigh 278 pounds . what is jake β s present weight , in pounds ?
|
"consider sister weight now as x jakes weight ( 2 times + 8 ) = 2 x + 8 ( 2 x + 8 ) + ( x ) = 278 x = 90 jake ' s weight is . . . . 188 correct answer is e"
|
a ) 131 , b ) 135 , c ) 139 , d ) 147 , e ) 188
|
e
|
|
15,221 |
general
|
arjun started a business with rs . 20,000 and is joined afterwards by anoop with rs . 40 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
|
suppose anoop joined after 3 months . then , 20000 * 12 = 40000 * ( 12 β x ) = > = > x = 6 . answer : d
|
a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
|
d
|
|
15,222 |
general
|
cereal a is 10 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
|
"ratio of a / ratio of b = ( average wt of mixture - wt of b ) / ( wt of a - average wt of mixture ) = > ratio of a / ratio of b = ( 4 - 2 ) / ( 10 - 4 ) = 2 / 6 = 1 / 3 so they should be mixed in the ratio 1 : 3 answer - e"
|
a ) 2 : 9 , b ) 2 : 7 , c ) 1 : 6 , d ) 1 : 4 , e ) 1 : 3
|
e
|
|
15,223 |
general
|
a man goes to shopkeeper and says that if u give me as much as i have , i will spend rs . 10 / - on ur shop . shopkeeper agrees and man moves to another shopkeeper ans asked same . at 3 rd shop after all the transaction , he was left with no money . find the initial amount with the man
|
man has rs . x he leaves - 1 st shop wid rs . ( 2 x - 10 ) 2 nd shop wid rs . [ 2 ( 2 x - 10 ) - 10 ] 3 rd shop wid rs . { 2 [ 2 ( 2 x - 10 ) - 10 ] - 10 } = 0 ( since he has no money left ) so solving the eqn x = 8.75 answer : d
|
a ) 5.75 , b ) 6.75 , c ) 7.75 , d ) 8.75 , e ) 9.75
|
d
|
|
15,224 |
gain
|
find the compound interest on $ 26,000 at 20 % per annum for 9 months , compounded quarterly
|
"principal = $ 26000 ; time = 9 months = 3 quarters ; rate = 20 % per annum = 5 % per quarter . amount = $ [ 26000 x ( 1 + ( 5 / 100 ) ) ^ 3 ] = $ 30098.25 ci . = $ ( 30098.25 - 26000 ) = $ 4098.25 answer d ."
|
a ) 2532.93 , b ) 2552.26 , c ) 2524.23 , d ) 4098.25 , e ) 2512.23
|
d
|
|
15,225 |
general
|
if x / y = 7 / 3 , then ( x + y ) / ( x - y ) = ?
|
"any x and y satisfying x / y = 7 / 3 should give the same value for ( x + y ) / ( x - y ) . say x = 7 and y = 3 , then ( x + y ) / ( x - y ) = ( 7 + 3 ) / ( 7 - 3 ) = 5 / 2 . answer : b ."
|
a ) 5 , b ) 5 / 2 , c ) - 1 / 6 , d ) - 1 / 5 , e ) - 5
|
b
|
|
15,226 |
general
|
3889 + 12.952 β ? = 3854.002
|
explanation let 3889 + 12.952 β x = 3854.002 . then x = ( 3889 + 12.952 ) β 3854.002 = 3901.952 β 3854.002 = 47.95 . answer d
|
a ) 47.095 , b ) 47.752 , c ) 47.932 , d ) 47.95 , e ) none
|
d
|
|
15,227 |
general
|
in the new budget the price of milk rose by 10 % . by how much percent must a person reduce his consumption so that his expenditure on it does not increase ?
|
"reduce in consumption = r / ( 100 + r ) * 100 % = 10 / 110 * 100 = 9.1 % answer is c"
|
a ) 7.5 % , b ) 9.1 % , c ) 10.9 % , d ) 12.6 % , e ) 15 %
|
c
|
|
15,228 |
general
|
brindavan express leave chennai central station every day at 07.50 am and goes to bangalore city railway station . this train is very popular among the travelers . on 25 th july 2012 number of passengers traveling by i class and ii class was in the ratio 1 : 4 . the fare for this travel is in the ratio 3 : 1 . the total fare collected was rs . 224000 / . ( rs . two lakhs 20 4 1000 only ) . what was the fare collected from i class passengers on that day ?
|
solution : let the number of passenger traveling by first class be x . then , number of passenger traveling by second class will be 4 x . but the fare is in the ratio 3 : 1 in other words , if 3 y fare is collected per i class passenger , y would be collected per ii class passenger . fares of i class passengers : fares of ii class passengers = x * 3 y : 4 x * y = 3 : 4 the above ratio can be interpreted as follows . if total fare is 3 + 4 = 7 , then i class passengers should pay rs . 3 similarly , we can calculate the fare of i class passengers when total was 224000 total fare i class fare 7 3 224000 ? = 224000 * ( 3 / 7 ) = rs . 96000 . answer : option b
|
a ) rs . 32000 , b ) rs . 96000 , c ) rs . 128000 , d ) rs . 500000 , e ) none of these
|
b
|
|
15,229 |
gain
|
a candidate appearing for an examination has to secure 35 % marks to pass paper i . but he secured only 42 marks and failed by 23 marks . what is the maximum mark for paper i ?
|
"he secured 42 marks nd fail by 23 marks so total marks for pass the examinatn = 65 let toal marks x x * 35 / 100 = 65 x = 186 answer : c"
|
a ) 110 , b ) 120 , c ) 186 , d ) 140 , e ) 150
|
c
|
|
15,230 |
gain
|
15 litres of mixture contains 20 % alcohol and the rest water . if 3 litres of water be mixed with it , the percentage of alcohol in the new mixture would be ?
|
"alcohol in the 15 litres of mix . = 20 % of 15 litres = ( 20 * 15 / 100 ) = 3 litres water in it = 15 - 3 = 12 litres new quantity of mix . = 15 + 3 = 18 litres quantity of alcohol in it = 3 litres percentage of alcohol in new mix . = 3 * 100 / 18 = 50 / 3 = 16.67 % answer is a"
|
a ) 16.67 % , b ) 23 % , c ) 18.3 % , d ) 19.75 % , e ) 21.23 %
|
a
|
|
15,231 |
physics
|
during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 210 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
|
"easy 560 is the answer . 3 / 4 ( x / 2 ) = 210 x = 210 * 8 / 3 = 560 . answer e"
|
a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 560
|
e
|
|
15,232 |
physics
|
the ratio between the length and the breadth of a rectangular park is 3 : 2 . if a man cycling along the boundary of the park at the speed of 12 km / hr completes one round in 10 minutes , then the area of the park ( in sq . m ) is
|
"perimeter = distance covered in 10 min . = 12000 x 10 m = 2000 m . 60 let length = 3 x metres and breadth = 2 x metres . then , 2 ( 3 x + 2 x ) = 2000 or x = 200 . length = 600 m and breadth = 400 m . area = ( 600 x 400 ) m 2 = 240000 m 2 . b"
|
a ) 153200 , b ) 240000 , c ) 153600 , d ) 154000 , e ) 154200
|
b
|
|
15,233 |
general
|
if | 5 x - 5 | = 150 , what is the sum of all the possible values of x ?
|
"there will be two cases 5 x - 5 = 150 or 5 x - 5 = - 150 = > x = 31 or x = - 29 sum of both the values will be - 29 + 31 = 2 answer is a"
|
a ) 2 , b ) - 2 , c ) 6 , d ) - 3 , e ) 5
|
a
|
|
15,234 |
general
|
in a class of 27 students in an examination in maths 5 students scored 95 marks each , 3 get zero each and the average of the rest was 45 . what is the average of the whole class ?
|
explanation : total marks obtained by a class of 25 students = 5 * 95 + 3 * 0 + 19 * 45 = 1330 average marks of whole class = 1330 / 27 = 49.3 answer : option e
|
a ) a ) 47 , b ) b ) 45.6 , c ) c ) 44 , d ) d ) 48 , e ) e ) 49.3
|
e
|
|
15,235 |
probability
|
a bag contains 6 black and 3 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
|
"let number of balls = ( 6 + 3 ) = 9 . number of white balls = 3 . p ( drawing a white ball ) = 3 / 9 = 1 / 3 . option b ."
|
a ) 3 / 4 , b ) 1 / 3 , c ) 1 / 7 , d ) 1 / 8 , e ) 4 / 3
|
b
|
|
15,236 |
other
|
the ratio of three numbers is 1 : 2 : 4 and the sum of their squares is 1701 . the sum of the numbers is ?
|
"let the numbers be x , 2 x , 4 x then , x ^ 2 + 4 x ^ 2 + 16 x ^ 2 = 1701 21 x ^ 2 = 1701 x ^ 2 = 81 x = 9 answer is e"
|
a ) a ) 10 , b ) b ) 12 , c ) c ) 15 , d ) d ) 14 , e ) e ) 9
|
e
|
|
15,237 |
general
|
a person saved $ 10 in buying an item on sale . if he spent $ 100 for the item , approximately how much percent he saved in the transaction ?
|
actual price = 100 + 10 = $ 110 saving = 10 / 110 * 100 = 100 / 11 = 10 % approximately answer is b
|
a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 %
|
b
|
|
15,238 |
general
|
an amount of money is to be divided between p , q and r in the ratio of 3 : 7 : 12 . if the difference between the shares of p and q is rs . 2800 , what will be the difference between q and r ' s share ?
|
"4 - - - 2800 5 - - - ? = > 3500 answer : b"
|
a ) 2788 , b ) 3500 , c ) 7282 , d ) 2782 , e ) 2729
|
b
|
|
15,239 |
general
|
suraj has a certain average of runs for 8 innings . in the 9 th innings he scores 90 runs thereby increasing his average by 6 runs . what is his average after the 9 th innings ?
|
"to improve his average by 6 runs per innings he has to contribute 8 x 6 = 48 runs for the previous 8 innings . thus , the average after the 9 th innings = 90 - 48 = 42 . answer : a"
|
a ) 42 , b ) 64 , c ) 36 , d ) 72 , e ) 27
|
a
|
|
15,240 |
physics
|
if the speed of a man is 66 km per hour , then what is the distance traveled by him in 30 seconds ?
|
"the distance traveled in 30 sec = 66 * ( 5 / 18 ) * 30 = 550 m answer : a"
|
a ) 550 m , b ) 500 m , c ) 375 m , d ) 420 m , e ) 440 m
|
a
|
|
15,241 |
gain
|
what percent is 70 of 280 ?
|
"70 / 280 = 1 / 4 1 / 4 Γ 100 = 25 % b"
|
a ) 12 % , b ) 25 % , c ) 26 % , d ) 27 % , e ) 28 %
|
b
|
|
15,242 |
other
|
in what ratio must tea at rs . 64 per kg be mixed with tea at rs . 74 per kg so that the mixture must be worth rs . 69 per kg ?
|
"required ratio = 500 : 500 = 1 : 1 answer a"
|
a ) 1 : 1 , b ) 3 : 2 , c ) 4 : 3 , d ) 5 : 3 , e ) none
|
a
|
|
15,243 |
general
|
the number of singles that a baseball player hit increased 5 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 2 percent . if the total number of singles and doubles that she hit increased 2 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
|
"soln : - 1.05 s + 0.98 d = 1.02 [ s + d ] 0.03 s = 0.04 d s / d = 4 / 3 answer : a"
|
a ) 4 : 3 , b ) 9 : 11 , c ) 3 : 1 , d ) 2 : 1 , e ) 11 : 3
|
a
|
|
15,244 |
general
|
a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 90,000 . the 75 associates have an average salary of $ 30,000 . what is the average salary for the company ?
|
another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 3 a * 1 + a * 5 ) / 6 = 8 a / 6 = 40000 answer is b . $ 40,000
|
a ) $ 35,000 , b ) $ 40,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
|
b
|
|
15,245 |
physics
|
a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 5 km / hr , find the time taken by the boat to go 70 km downstream .
|
"speed of boat in still water = 13 km / hr speed of the stream = 5 km / hr speed downstream = ( 13 + 5 ) = 18 km / hr time taken to travel 70 km downstream = 70 Γ’ Β β 18 = 3.8 hours answer is b"
|
a ) 4.25 hr , b ) 3.8 hr , c ) 8.25 hr , d ) 2.25 hr , e ) 2.50 hr
|
b
|
|
15,246 |
general
|
a man has 1044 candles . after burning , he can make a new candle from 9 stubs left behind . find the maximum number of candles that can be made .
|
explanation : since , 1 candle is made from 9 stubs . therefore , from 1044 stubs , 1044 / 9 i . e 116 candles will be made . now , from 116 stubs , 116 / 9 i . e 12 candles can be made and 8 stubs will be left . thus , total stubs left is ( 12 + 8 ) = 20 out of which 20 / 9 i . e 2 candles can be made and 2 stubs will be left . thus , maximum number of candles that can be made is 130 ( 116 + 12 + 2 ) . answer : c
|
a ) 116 , b ) 120 , c ) 130 , d ) 140 , e ) none
|
c
|
|
15,247 |
general
|
if n is an integer , f ( n ) = f ( n - 1 ) - n and f ( 4 ) = 12 . what is the value of f ( 6 ) ?
|
"since f ( n ) = f ( n - 1 ) - n then : f ( 6 ) = f ( 5 ) - 6 and f ( 5 ) = f ( 4 ) - 5 . as given that f ( 4 ) = 12 then f ( 5 ) = 12 - 5 = 7 - - > substitute the value of f ( 5 ) back into the first equation : f ( 6 ) = f ( 5 ) - 6 = 7 - 6 = 1 . answer : a . questions on funtions to practice :"
|
a ) 1 , b ) 0 , c ) - 1 , d ) 2 , e ) 4
|
a
|
|
15,248 |
gain
|
if a and b get profits of rs . 6000 and rs . 4000 respectively at the end of year the ratio of their investments are ?
|
"profit = investment * time so , 6000 = i 1 * 1 = 6000 4000 = i 2 * 1 = 4000 i 1 / i 2 = 6000 / 4000 = 3 / 2 answer : b"
|
a ) 1 : 4 , b ) 3 : 2 , c ) 2 : 3 , d ) 2 : 5 , e ) none of these
|
b
|
|
15,249 |
general
|
of the total amount that jill spent on a shopping trip , excluding taxes , she spent 60 percent on clothing , 10 percent on food , and 30 percent on other items . if jill paid a 4 percent tax on the clothing , no tax on the food , and an 8 percent tax on all other items , then the total tax that she paid was what percent of the total amount that she spent , excluding taxes ?
|
"let amount spent by jill = 100 clothing = 50 , food = 20 , others = 30 tax on clothing = 2.4 tax on others = 2.4 percentage = 4.8 / 100 = 4.8 % answer : e"
|
a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 4.8 %
|
e
|
|
15,250 |
physics
|
a 900 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
|
"speed = 900 / 18 = 50 / 1 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 39 = 50 / 1 = > x = 1950 m . l = 1950 - 900 = 1050 answer : option b"
|
a ) 1000 , b ) 1050 , c ) 1060 , d ) 370 , e ) 380
|
b
|
|
15,251 |
general
|
what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 3 ?
|
"explanatory answer step 1 : identify the series the smallest 3 digit number that will leave a remainder of 2 when divided by 3 is 101 . the next couple of numbers that will leave a remainder of 2 when divided by 3 are 104 and 107 . the largest 3 digit number that will leave a remainder of 2 when divided by 3 is 998 . it is evident that any number in the sequence will be a 3 digit positive integer of the form ( 3 n + 2 ) . so , the given numbers are in an arithmetic sequence with the first term being 101 and the last term being 998 and the common difference being 3 . step 2 : compute the sum sum of an arithmetic progression ( ap ) = [ first term + last term / 2 ] n we know the first term : 101 we know the last term : 998 . the only unknown is the number of terms , n . in an a . p . , the nth term an = a 1 + ( n - 1 ) * d in this case , therefore , 998 = 101 + ( n - 1 ) * 3 or 897 = ( n - 1 ) * 3 ( n - 1 ) = 299 or n = 300 . sum of the ap will therefore , be [ 101 + 998 / 2 ] β 300 = 164,850 choice b is the correct answer ."
|
a ) 897 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720
|
b
|
|
15,252 |
general
|
what is the remainder when 10 ^ 49 + 2 is divided by 11 ?
|
"with exponent - based problems and huge numbers , it ' s often helpful to try to establish a pattern using small numbers . on this problem , while 1049 + 2 is a massive number that you ' d never want to try to perform calculations with , you can start by using smaller numbers to get a feel for what it would look like : 10 ^ 2 + 2 = 102 , which when divided by 11 produces a remainder of 3 ( as 9 * 11 = 99 , leaving 3 left over ) 10 ^ 3 + 2 = 1002 , which when divided by 11 produces a remainder of 1 ( as 9 * 110 = 990 , and when you add one more 11 to that you get to 1001 , leaving one left ) 10 ^ 4 + 2 = 10002 , which when divided by 11 produces a remainder of 3 ( as you can get to 9999 as a multiple of 11 , which would leave 3 left over ) 10 ^ 5 + 2 = 100002 , which when divided by 11 produces a remainder of 1 ( as you can get to 99990 and then add 11 more , bringing you to 100001 leaving one left over ) . by this point , you should see that the pattern will repeat , meaning that when 10 has an even exponent the remainder is 3 and when it has an odd exponent the remainder is 1 . therefore , since 10 has an odd exponent in the problem , the remainder will be 1 . answer is a"
|
a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 7
|
a
|
|
15,253 |
gain
|
john makes $ 65 a week from his job . he earns a raise andnow makes $ 70 a week . what is the % increase ?
|
"increase = ( 5 / 65 ) * 100 = ( 1 / 13 ) * 100 = 7.69 % . a"
|
a ) 7.69 % , b ) 16.66 % , c ) 17.8 % , d ) 19 % , e ) 21 %
|
a
|
|
15,254 |
gain
|
if 40 % of a certain number is 160 , then what is 20 % of that number ?
|
"explanation : 40 % = 40 * 4 = 160 20 % = 20 * 4 = 80 answer : option e"
|
a ) 75 , b ) 100 , c ) 120 , d ) 30 , e ) 80
|
e
|
|
15,255 |
general
|
if the sum of two positive integers is 12 and the difference of their squares is 48 , what is the product of the two integers ?
|
"let the 2 positive numbers x and y x + y = 12 - - 1 x ^ 2 - y ^ 2 = 48 = > ( x + y ) ( x - y ) = 48 - - 2 using equation 1 in 2 , we get = > x - y = 4 - - 3 solving equation 1 and 3 , we get x = 8 y = 4 product = 8 * 4 = 32 answer a"
|
a ) 32 , b ) 119 , c ) 128 , d ) 135 , e ) 143
|
a
|
|
15,256 |
other
|
three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 276 . what is their h . c . f . ?
|
"let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 276 x = 23 hcf of 2 x , 3 x and 4 x = x = 23 the answer is b ."
|
a ) 18 , b ) 23 , c ) 28 , d ) 32 , e ) 36
|
b
|
|
15,257 |
general
|
a grocer has a sale of rs . 3435 , rs . 3927 , rs . 3855 , rs . 4230 and rs . 3562 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 3500 ?
|
"explanation : total sale for 5 months = rs . ( 3435 + 3927 + 3855 + 4230 + 3562 ) = rs . 19009 . required sale = rs . [ ( 3500 x 6 ) Γ’ β¬ β 19009 ] = rs . ( 21000 Γ’ β¬ β 19009 ) = rs . 1991 . answer a"
|
a ) s . 1991 , b ) s . 2991 , c ) s . 3991 , d ) s . 4991 , e ) s . 5991
|
a
|
|
15,258 |
geometry
|
what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 55 ?
|
"let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 55 = rs . 3740 . answer : e"
|
a ) s . 3944 , b ) s . 3948 , c ) s . 3942 , d ) s . 3965 , e ) s . 3740
|
e
|
|
15,259 |
geometry
|
d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 25 : 144 and bc = 13 cm , then find the length of de .
|
"abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 169 / 25 side of abc / side of ade = 13 / 5 so the length of de = 5 answer - b"
|
a ) 12 , b ) 5 , c ) 14 , d ) 11 , e ) 15
|
b
|
|
15,260 |
general
|
chris mixed 3 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 4 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
|
"1 lbs of raisin = $ 1 3 lbs of raisin = $ 3 1 lbs of nuts = $ 4 4 lbs of nuts = $ 16 total value of mixture = 16 + 3 = 19 fraction of the value of raisin = 3 / 19 ans : e"
|
a ) 1 / 7 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 19
|
e
|
|
15,261 |
general
|
a wildlife preserve is being planned for 8000 rhinoceroses . the preserve is to contain a total of 10000 acres of watering area , plus 100 acres of grazing area for each rhinoceros . if the number of rhinoceroses is expected to increase by 10 percent , how many 1000 acres should the preserve have in order to provide for the increased population ?
|
number of rhinos = 8000 watering area = 10,000 acres number of rhino to increase by 10 percent , then number of rhino = 8800 grazing area for a rhino = 100 total grazing area for 8800 rhinos = 8800 * 100 = 8 , 80,000 total area required for the wildlife preserve = 8 , 80,000 + 10,000 = 8 , 90,000 = 890 * 1000 answer e
|
a ) 340 , b ) 330 , c ) 320 , d ) 310 , e ) 890
|
e
|
|
15,262 |
general
|
a certain number when divided by 65 leaves a remainder 25 , what is the remainder if the same no . be divided by 15 ?
|
"explanation : 65 + 25 = 90 / 15 = 6 ( remainder ) c"
|
a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
|
c
|
|
15,263 |
physics
|
a , b and c can do a piece of work in 24 , 30 and 40 days respectively . they start the work together but c leaves 4 days before the completion of the work . in how many days is the work done ?
|
x / 24 + x / 30 + x / 40 = 1 x = 11 days answer : d
|
a ) 11 , b ) 5 , c ) 70 , d ) 11 , e ) 13
|
d
|
|
15,264 |
general
|
find the least number which when divided by 20 , 25,35 and 40 leaves remainders 14 , 19,29 and 34 respectively .
|
"here , ( 20 - 14 ) = 6 , ( 25 β 19 ) = 6 , ( 35 - 29 ) = 6 and ( 40 - 34 ) = 6 . therefore , required number = ( l . c . m . of 20,25 , 35,40 ) β 6 = 1394 . answer is a ."
|
a ) 1394 , b ) 1294 , c ) 1194 , d ) 1094 , e ) none of them
|
a
|
|
15,265 |
general
|
a gambler bought $ 4,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
|
"in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 4,000 - $ 880 = $ 3,120 . answer : d"
|
a ) $ 2,040 , b ) $ 2,120 , c ) $ 1,960 , d ) $ 3,120 , e ) $ 1,400
|
d
|
|
15,266 |
physics
|
what is the maximum number of pieces of birthday cake of size 10 β by 10 β that can be cut from a cake 20 β by 20 β ?
|
"the prompt is essentially asking for the maximum number of 10 x 10 squares that can be cut from a larger 20 by 20 square . since each ' row ' and each ' column ' of the larger square can be sub - divided into 2 ' pieces ' each , we have ( 2 ) ( 2 ) = 4 total smaller squares ( at maximum ) . a"
|
a ) 4 , b ) 10 , c ) 16 , d ) 20 , e ) 25
|
a
|
|
15,267 |
geometry
|
the perimeter of an equilateral triangle is 60 . if one of the sides of the equilateral triangle is the side of an isosceles triangle of perimeter 65 , then how long is the base of isosceles triangle ?
|
the base of the isosceles triangle is 65 - 20 - 20 = 25 units the answer is d .
|
['a ) 10', 'b ) 15', 'c ) 20', 'd ) 25', 'e ) 30']
|
d
|
|
15,268 |
physics
|
while driving from a - ville to b - town , harriet drove at a constant speed of 105 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 145 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
|
"5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . e . t = 174 min * leg a - b - - - > d = 105.174 / 60 = 18270 / 60 * leg b - a - - - - > d = 145 * 126 / 60 = 18270 / 60 so the correct ans . ise"
|
a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 174
|
e
|
|
15,269 |
general
|
what number times ( 1 β 2 ) ^ 2 will give the value of 2 ^ 3 ?
|
x * ( 1 / 2 ) ^ 2 = 2 ^ 3 x = 2 ^ 2 * 2 ^ 3 = 2 ^ 5 = 32 the answer is e .
|
a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 32
|
e
|
|
15,270 |
gain
|
a sum of money at simple interest amounts to rs . 815 in 3 years and to rs . 864 in 4 years . the sum is :
|
"s . i . for 1 year = rs . ( 864 - 815 ) = rs . 49 . s . i . for 3 years = rs . ( 49 x 3 ) = rs . 147 . principal = rs . ( 815 - 147 ) = rs . 668 . answer : option c"
|
a ) s . 650 , b ) s . 690 , c ) s . 668 , d ) s . 700 , e ) s . 760
|
c
|
|
15,271 |
gain
|
the value of a machine depreciates at 22 % per annum . if its present value is $ 1 , 50,000 , at what price should it be sold after two years such that a profit of $ 24,000 is made ?
|
"the value of the machine after two years = 0.78 * 0.78 * 1 , 50,000 = $ 91,260 sp such that a profit of $ 24,000 is made = 91,260 + 24,000 = $ 1 , 15,260 d"
|
a ) $ 255260 , b ) $ 435260 , c ) $ 125260 , d ) $ 115260 , e ) $ 155260
|
d
|
|
15,272 |
general
|
8 liters of a 25 percent solution of alcohol in water are mixed with 2 liters of a 12 percent alcohol in water solution . what is the percentage of alcohol in the new solution ?
|
the total amount of alcohol is 0.25 ( 8 ) + 0.12 ( 2 ) = 2.24 liters . the percentage is 2.24 / 10 = 22.4 / 100 which is 22.4 % the answer is d .
|
a ) 21.2 % , b ) 21.6 % , c ) 22.0 % , d ) 22.4 % , e ) 22.8 %
|
d
|
|
15,273 |
general
|
find a two digit number , given that the sum of the digits is 13 and the difference of the digits is 5 . ?
|
"using elimination method find which of the options fit the description of the number . . . from the option only 94 meets this description sum of digits - - - 9 + 4 = 13 difference of digits - - - 9 - 4 = 5 answer e ."
|
a ) 74 , b ) 82 , c ) 95 , d ) 76 , e ) 94
|
e
|
|
15,274 |
geometry
|
the diagonals of a rhombus are 14 cm and 18 cm . find its area ?
|
"1 / 2 * 14 * 18 = 126 answer : d"
|
a ) 176 , b ) 190 , c ) 150 , d ) 126 , e ) 292
|
d
|
|
15,275 |
general
|
if a and b are positive numbers , and a ^ 3 + b ^ 3 = 140 , then the greatest possible value of a is between :
|
if a = 5.1 and b is a bit less than 2 , then a ^ 3 + b ^ 3 can equal 140 . if a > 8 , then a ^ 3 + b ^ 3 > 140 . the answer is e .
|
a ) 0 and 2 , b ) 2 and 3 , c ) 3 and 4 , d ) 4 and 5 , e ) 5 and 8
|
e
|
|
15,276 |
other
|
in a certain state , the ratio of registered republicans to registered democrats is 3 to 2 , and every registered voter is either a republican or a democrat . if 80 percent of the republicans and 25 percent of the democrats are expected to vote for candidate x , and everyone else is expected to vote for candidate y , by what percent is candidate x expected to win the election ?
|
"since we were expected to find a percentage figure - it thought that it might be easier to pick a ' smart number ' to represent the total number of voters ( republicans and democrats ) . therefore , i picked 100 ( as the total number of voters ) and thus 30 : 20 represents the number ratio of republicans : democrats . if 80 % of republicans ( which is ( 60 * 0.8 ) = 48 ) and 25 % of democrats ( 40 * 0.25 = 10 ) voted for candidate x , means that out of total of 100 voters ; 58 ( 48 + 10 ) voters voted for candidate x and 42 voted for candidate y . thus we can infer that candidate x is expected to win the election by 16 ( 58 - 42 ) votes . therefore candidate x is expected to win the election by ( 16 / 100 ) votes which is equivalent to 16 % . i think the answer is c ."
|
a ) 2 % , b ) 5 % , c ) 16 % , d ) 20 % , e ) 25 %
|
c
|
|
15,277 |
gain
|
rs 70000 is divided into two parts one part is given to a person with 10 % interest and another part is given to a person with 20 % interest . at the end of first year he gets profit 8000 find money given by 10 % ?
|
"let first parrt is x and second part is y then x + y = 70000 - - - - - - - - - - eq 1 total profit = profit on x + profit on y 8000 = ( x * 10 * 1 ) / 100 + ( y * 20 * 1 ) / 100 80000 = x + 2 y - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - eq 2 80000 = 70000 + y so y = 10000 then x = 70000 - 10000 = 60000 first part = 60000 answer : d"
|
a ) 30000 , b ) 40000 , c ) 50000 , d ) 60000 , e ) 70000
|
d
|
|
15,278 |
general
|
a sum of money is to be distributed among a , b , c , d in the proportion of 5 : 2 : 4 : 3 . if c gets rs . 700 more than d , what is b ' s share ?
|
"let the shares of a , b , c and d be rs . 5 x , rs . 2 x , rs . 4 x and rs . 3 x respectively . then , 4 x - 3 x = 700 x = 700 . b ' s share = rs . 2 x = rs . ( 2 x 700 ) = rs . 1400 . answer = b"
|
a ) rs . 500 , b ) rs . 1400 , c ) rs . 2000 , d ) rs . 2500 , e ) none of the above
|
b
|
|
15,279 |
physics
|
trapezoid jklm in the x - y plane has coordinates j = ( β 2 , β 4 ) , k = ( β 2 , 2 ) , l = ( 6 , 8 ) , and m = ( 6 , β 4 ) . what is its perimeter ?
|
"jk = 6 lm = 12 kl = using distance formula 10 jm = using distance formula 8 sum of all is 36 b"
|
a ) 34 , b ) 36 , c ) 38 , d ) 40 , e ) ( f ) 42
|
b
|
|
15,280 |
general
|
the average weight of 4 persons increases by 1.5 kg . if a person weighing 65 kg is replaced by a new person , what could be the weight of the new person ?
|
"total weight increases = 4 Γ 1.5 = 6 kg so the weight of new person = 65 + 6 = 71 kg answer a"
|
a ) 71 kg , b ) 77 kg , c ) 76.5 kg , d ) data inadequate , e ) none of these
|
a
|
|
15,281 |
gain
|
rs 3500 is divided into two parts such that one part is put out at 3 % and the other at 5 % . if the annual interest earned from both the investments be rs 144 , find the first part .
|
"explanation : average rate = ( 144 / 3500 ) * 100 = 4.11 ratio = 8.85 : 11.14 so , first part = ( 8.85 / 20 ) * 3500 = rs 1550 . answer : e"
|
a ) s 4000 , b ) s 2800 , c ) s 1800 , d ) s 1500 , e ) s 1550
|
e
|
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