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15,082
general
of the goose eggs laid at a certain pond , 1 / 2 hatched and 3 / 4 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
"let x be the number of eggs that were laid . ( 2 / 5 ) ( 3 / 4 ) ( 1 / 2 ) x = 120 ( 6 / 40 ) x = 120 x = 800 the answer is a ."
a ) 800 , b ) 840 , c ) 880 , d ) 920 , e ) 960
a
15,083
other
the ratio between the present ages of a and b is 4 : 3 respectively . the ratio between a ' s age 4 years ago and b ' s age 4 years hence is 1 : 1 . what is the ratio between a ' s age 4 years hence and b ' s age 4 years ago ?
let the present ages of a and b be 4 x and 3 x years respectively . then , ( 4 x - 4 ) / ( 3 x + 4 ) = 1 / 1 1 x = 8 = > x = 8 required ratio = ( 4 x + 4 ) : ( 3 x - 4 ) = 36 : 20 = 9 : 5 . answer : e
a ) 3 : 4 , b ) 3 : 0 , c ) 3 : 1 , d ) 3 : 2 , e ) 9 : 5
e
15,084
general
in the storage room of a certain bakery , the ratio of sugar to flour is 5 to 2 , and the ratio of flour to baking soda is 10 to 1 . if there were 60 more pounds of baking soda in the room , the ratio of flour to baking soda would be 8 to 1 . how many pounds of sugar are stored in the room ?
"sugar : flour = 5 : 2 = 25 : 10 ; flour : soda = 10 : 1 = 10 : 1 ; thus we have that sugar : flour : soda = 25 x : 10 x : 1 x . also given that 10 x / ( 1 x + 60 ) = 8 / 1 - - > x = 240 - - > sugar = 25 x = 6000 answer : e ."
a ) 600 , b ) 1200 , c ) 1500 , d ) 3600 , e ) 6000
e
15,085
general
robert ' s salary was decreased by 60 % and subsequently increased by 60 % . how much percentage does he lose ?
let original salary be $ 100 salary after decreasing 60 % = 100 - 100 x 60 / 100 = $ 40 salary after increasing 60 % on $ 40 = 40 + 40 x 60 / 100 = $ 64 percentage of loss = 100 - 64 = 36 % answer : d
a ) 10 % , b ) 20 % , c ) 25 % , d ) 36 % , e ) 50 %
d
15,086
gain
if the simple interest on $ 1500 increase by $ 20 , when the time increase by 2 years . find the rate percent per annum .
applying the above formula , we have 20 = 1500 * r * 2 / 100 r = 20 * 100 / 1500 * 2 = 0.7 % . answer is e
a ) 0.6 % , b ) 0.5 % , c ) 0.1 % , d ) 0.2 % , e ) 0.7 %
e
15,087
general
if the least common multiple of two prime numbers x and y is 10 , where x > y , then the value of 2 x + y is
lcm of two prime numbers will basically be multiple of those numbers . lcm = 10 = 2 * 5 , both of which are prime . now we know x > y , so x = 5 and y = 2 . 2 x + y = 2 * 5 + 2 = 10 + 2 = 12 . answer : d
a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 21
d
15,088
physics
a train is 360 meter long is running at a speed of 56 km / hour . in what time will it pass a bridge of 140 meter length .
"explanation : speed = 56 km / hr = 56 * ( 5 / 18 ) m / sec = 140 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 / 140 / 9 = 32.14 seconds answer : d"
a ) 20.14 seconds , b ) 12.14 seconds , c ) 22.14 seconds , d ) 32.14 seconds , e ) none of these
d
15,089
probability
if two integers x , y ( x > y ) are selected from - 10 to 10 ( inclusive ) , how many possible cases are there ?
"if two integers x , y ( x > y ) are selected from - 10 to 9 ( inclusive ) , how many possible cases are there ? a . 150 b . 180 c . 190 d . 210 e . 240 - - > 21 c 2 = 21 * 20 / 2 = 210 . therefore , the answer is d"
a ) 150 , b ) 180 , c ) 190 , d ) 210 , e ) 240
d
15,090
other
two family reunions are happening at the same hotel , the oates reunion and the yellow reunion . all 100 guests at the hotel attend at least one of the reunions . if 42 people attend the oates reunion and 65 people attend the yellow reunion , how many people attend both reunions ?
no of people in oates reunion = 42 no of people in yellow reunion = 65 attending both = x all guests attend at least one . therefore , 100 = 42 + 65 - ( both ) both = 7 answer b
a ) 2 , b ) 7 , c ) 10 , d ) 16 , e ) 22
b
15,091
other
there are 190 items that are members of set u . of these items , 49 are members of set b , 59 are not members of either of set a or set b , and 23 are members of both sets a and b . how many of the members of set u are members of set a ?
"you had the answer almost right . the x = 82 refers to only set a . however what ' s being asked is how many members are part of set a . this will include : 1 . only set a 2 . set a and set b so the answer is set a = 82 + set ab = 82 + 23 = 105 d"
a ) 72 , b ) 85 , c ) 94 , d ) 105 , e ) 108
d
15,092
general
1,2 , 3,2 , 4,6 , 4,8 , _____
"divide the series : 1 , 2,3 2 , 4,6 4,8 , ? so it is 12 answer : c"
a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
c
15,093
general
if a person walks at 14 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance travelled by him is :
"let the actual distance travelled be x km . then , x / 10 = ( x + 20 ) / 14 14 x = 10 x + 200 4 x = 200 x = 50 km . answer : a"
a ) 50 km , b ) 56 km , c ) 70 km , d ) 80 km , e ) 46 km
a
15,094
gain
by investing rs . 1620 in 8 % stock , michael earns rs . 135 . the stock is then quoted at :
michel earns rs 135 by investing rs 1620 to earn rs 8 how much he have to invest ? = ( 8 * 1620 ) / 135 = rs 96 answer : b
a ) rs . 80 , b ) rs . 96 , c ) rs . 106 , d ) rs . 108 , e ) rs . 118
b
15,095
gain
in a certain company 20 % of the men and 40 % of the women attended the annual company picnic . if 35 % of all the employees are men . what % of all the employee went to the picnic ?
total men in company 35 % means total women in company 65 % ( assume total people in company 100 % ) no of men emplyess attended picnic = 35 x ( 20 / 100 ) = 7 no of women empolyees attened picnin = 65 x ( 40 / 100 ) = 26 total percentage of empolyess attened the picnic = 7 + 26 = 33 % answer : a
a ) 33 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37 %
a
15,096
other
set x consists of the integers from 10 to 15 , inclusive , while set y consists of the integers from 5 to 10 , inclusive . how many distinct integers do belong to the both sets at the same time ?
"x = { 10 , 11 , 12,13 , 14,15 } y = { 5,6 , 7 , 8 , 9 , 10 } common elements = { 10 } = 1 element answer : option d ."
a ) 5 , b ) 8 , c ) 4 , d ) 1 , e ) 9
d
15,097
general
if the average ( arithmetic mean ) of 7 consecutive integers is 20 , then the product of the greatest and least integer is
n = smallest number n + 6 = largest number ( n + n + 6 ) / 2 = 20 = > ( 2 n + 6 ) / 2 = 20 = > n + 3 = 20 = > n = 17 so product of n and n + 6 = ( 17 ) ( 23 ) = 391 answer - d
a ) 343 , b ) 393 , c ) 363 , d ) 391 , e ) 409
d
15,098
physics
a boatman goes 4 km against the current of the stream in 4 hour and goes 1 km along the current in 20 minutes . how long will it take to go 6 km in stationary water ?
speed upstream = 4 / 4 = 1 km / hr speed downstream = 1 / ( 20 / 60 ) = 3 km / hr speed in still water = 1 / 2 ( 3 + 1 ) = 2 km / hr time taken to travel 6 km in still water = 6 / 2 = 3 hours answer : c
a ) 5 hours , b ) 1 hours , c ) 3 hours , d ) 2 hours , e ) 4 hours
c
15,099
gain
if the cost price of 35 chocolates is equal to the selling price of 21 chocolates , the gain percent is :
"explanation : solution : let c . p . of each chocolate be re . 1 . then , c . p . of 21 chocolates = rs . 21 ; s . p . of 21 chocolates = rs . 35 . . ' . gain % = 14 * 100 / 21 = 66.66 % answer : b"
a ) 66.55 % , b ) 66.66 % , c ) 66 % , d ) 55 % , e ) 66.33 %
b
15,100
general
a , b , c subscribe rs . 50000 for a business . a subscribes rs . 4000 more than b and b rs . 5000 more than c . out of a total profit of rs . 35000 a receives :
"let c = x . then b = x + 5000 and a + x + 5000 + 4000 = x + 9000 therefore , x + x + 5000 + x + 9000 = 50000 û x = 12000 . therefore , a : b : c = 21000 : 17000 : 12000 = 21 : 17 : 12 therefore , a ’ s share = rs ( 35000 * 21 / 50 ) = rs . 14700 answer : c"
a ) rs . 11900 , b ) rs . 8400 , c ) rs . 14700 , d ) rs . 13600 , e ) rs . 14600
c
15,101
general
i have only 1 $ and 2 $ note . i want to give 95 $ to john . how many maximum number of 2 $ note i need ?
check whether 95 is divisible by 2 then that is maximum no of 2 $ note else check next maximum term before 95 so 94 / 2 = 47 ans is c
a ) 39 , b ) 95 , c ) 47 , d ) 55 , e ) 76
c
15,102
general
3 , 5 , 7 , 11 , 13 , 17 , 19 , ____
"the sequence is a series of prime numbers , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 . . . . answer : c ."
a ) 25 , b ) 36 , c ) 23 , d ) 49 , e ) 27
c
15,103
geometry
mr . loyd wants to fence his square shaped land of 150 sqft each side . if a pole is laid every 10 ft how many poles do he need ?
"if each side is 120 feet . . then total perimeter is 150 * 4 = 600 poles every 10 feet hence no of poles = 600 / 10 = 60 answer : d"
a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 65
d
15,104
physics
the speed of a car is 10 km in the first hour and 60 km in the second hour . what is the average speed of the car ?
"s = ( 10 + 60 ) / 2 = 35 kmph answer : c"
a ) 79 kmph , b ) 85 kmph , c ) 35 kmph , d ) 23 kmph , e ) 14 kmph
c
15,105
physics
the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 30 kms . what was the total distance traveled in 12 hours ?
"explanation : total distance travelled in 12 hours = ( 30 + 32 + 34 + . . . . . upto 12 terms ) this is an a . p with first term , a = 30 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 30 + { 12 - 1 ) x 2 ] = 6 ( 82 ) = 492 kms . answer : c"
a ) 252 kms , b ) 152 kms , c ) 492 kms , d ) 752 kms , e ) 152 kms
c
15,106
general
a basket contains 5 apples , of which 1 is spoiled and the rest are good . if henry is to select 2 apples from the basket simultaneously and at random , what is the possibility that the 2 apples selected will include the spoiled apple ?
"p ( both apples are not spoiled ) = 4 c 2 / 5 c 2 = 4 * 3 / 5 * 4 = 3 / 5 p ( one of the apple spoiled ) = 1 - 3 / 5 = 2 / 5 answer is c ."
a ) 1 / 5 , b ) 3 / 10 , c ) 2 / 5 , d ) 1 / 2 , e ) 3 / 5
c
15,107
physics
the length of minute hand of a clock is 5.4 cm . what is the area covered by this in 5 minutes
"area of circle is pi * r ^ 2 but in 5 minutes area covered is ( 5 / 60 ) * 360 = 30 degree so formula is pi * r ^ 2 * ( angle / 360 ) = 3.14 * ( 5.4 ^ 2 ) * ( 30 / 360 ) = 7.63 cm ^ 2 answer : e"
a ) 15.27 , b ) 16.27 , c ) 17.27 , d ) 7.27 , e ) 7.63
e
15,108
general
if q = ( x – 5 ) ^ 2 + ( x + 1 ) ^ 2 – 6 , then y is least when x =
let us transform the formula : q = ( x – 5 ) ² + ( x + 1 ) ² – 6 = x ² – 10 x + 25 + x ² + 2 x + 1 – 6 = 2 x ² – 8 x + 20 = 2 × ( x ² – 4 x + 10 ) = 2 × ( ( x ² – 4 x + 4 ) + 6 ) = 2 × ( ( x – 2 ) ² + 6 ) any square is greater or equal 0 . therefore the formula possess the least value when ( x – 2 ) ² = 0 . x – 2 = 0 x = 2 the correct answer is choice ( d ) .
a ) - 2 , b ) - 1 , c ) 0 , d ) 2 , e ) none of the above
d
15,109
other
among 400 students , 56 % study sociology , 44 % study mathematics and 40 % study biology . if 42 % of students study both mathematics and sociology , what is the largest possible number of students who study biology but do not study either mathematics or sociology ?
"i would just like to add a bit of explanation after the step where you calculate that the number of students studying both m and s = 168 using your analysis : we see that the total number of students who study either maths or sociology = 176 + 224 - 168 = 232 so , in the image we know that the number of students in the zone with the black boundary = 232 let ' s assume the number of students who studyonlybiology to beb ( this is the number that we have to maximize ) and , let ' s assume the number of students who study none of the three subjects , that is the number of students in the white space = w since the total number of students = 400 , we can write : 232 + b + w = 400 or , b + w = 400 - 232 = 168 that is , b = 168 - w so , the maximum value ofbwill happen forw = 0 this is how we get , the maximum value ofb = 168 d"
a ) 30 , b ) 90 , c ) 120 , d ) 168 , e ) 188
d
15,110
physics
10 machines , each working at the same constant rate , together can complete a certain job in 12 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 8 days ?
"another solution which is faster is since each machine works at a constant rate . the time needs to bought down from 12 to 8 . so the new time is 2 / 3 of the original time . thus to achieve this we need the rate to be 3 / 2 of original . so 3 / 2 * 10 = 15 so we need 15 - 10 = 5 more machines . answer : d"
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 8
d
15,111
physics
express a speed of 42 kmph in meters per second ?
"42 * 5 / 18 = 12 mps answer : e"
a ) 10 mps , b ) 18 mps , c ) 19 mps , d ) 17 mps , e ) 12 mps
e
15,112
general
average of money that group of 4 friends pay for rent each month is $ 800 . after one persons rent is increased by 20 % the new mean is $ 870 . what was original rent of friend whose rent is increased ?
"0.2 x = 4 ( 870 - 800 ) 0.2 x = 280 x = 1400 answer b"
a ) 800 , b ) 1400 , c ) 1000 , d ) 1100 , e ) 1200
b
15,113
geometry
how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 17 inches than that of a rectangular sheet of paper measuring 8.5 inches by 11 inches ?
"area of sheet a = 11 * 17 area of sheet b = 11 * 8.5 difference in area = 11 * 8.5 required % = ( 11 * 8.5 ) * 100 / ( 11 * 8.5 ) % = 100 % answer : c"
a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %
c
15,114
general
carina has 70 ounces of coffee divided into 5 - and 10 - ounce packages . if she has 2 more 5 - ounce packages than 10 - ounce packages , how many 10 - ounce packages does she have ?
"lets say 5 and 10 ounce packages be x and y respectively . given that , 5 x + 10 y = 70 and x = y + 2 . what is the value of y . substituting the x in first equation , 5 y + 10 + 10 y = 70 - > y = 60 / 15 . = 4 c"
a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
c
15,115
physics
a room of 5 m 44 cm long and 3 m 74 cm broad is to be paved with squre tiles . find the least number of squre tiles required to cover the floor .
"explanation : area of the room = 544 * 374 sq cm size of largest square tile = h . c . f of 544 cm and 374 cm = 34 cm area of 1 tile = 34 * 34 sq cm no . of tiles required = ( 544 * 374 ) / ( 34 * 34 ) = 176 answer : d ) 176"
a ) 233 , b ) 877 , c ) 279 , d ) 176 , e ) 291
d
15,116
other
he ratio between the sale price and the cost price of an article is 7 : 5 . what is the ratio between the profit and the cost price of that article ?
"let c . p . = rs . 5 x and s . p . = rs . 7 x . then , gain = rs . 2 x required ratio = 2 x : 5 x = 2 : 5 . answer : e"
a ) 2 : 6 , b ) 2 : 9 , c ) 2 : 4 , d ) 2 : 1 , e ) 2 : 5
e
15,117
gain
in an exam ashley secured 332 marks . if she secured 83 % makes , find the maximum marks
let the maximum marks be m . ashley ’ s marks = 83 % of m ashley secured 332 marks therefore , 83 % of m = 332 ⇒ 83 / 100 × m = 332 ⇒ m = ( 332 × 100 ) / 83 ⇒ m = 33200 / 83 ⇒ m = 400 therefore , ashley got 332 marks out of 400 marks . answer : d
a ) 133 , b ) 376 , c ) 377 , d ) 400 , e ) 377
d
15,118
general
an amount of rs . 3120 was divided among a , b and c , in the ratio 1 / 2 : 1 / 3 : 1 / 4 . find the share of a ?
"let the shares of a , b and c be a , b and c respectively . a : b : c = 1 / 2 : 1 / 3 : 1 / 4 let us express each term with a common denominator which is the last number divisible by the denominators of each term i . e . , 12 . a : b : c = 6 / 12 : 4 / 12 : 3 / 12 = 6 : 4 : 3 . share of a = 6 / 13 * 3120 = rs . 1440 answer : d"
a ) 1320 , b ) 1196 , c ) 1210 , d ) 1440 , e ) 1050
d
15,119
general
how many different values of positive integer x , for which | x + 9 | < x , are there ?
"answer c i opted to put the random value option . i used 0 , 9 , - 9 and the the extreme of 10 and - 10 . . i was able to solve it in 1 : 09 c"
a ) 0 , b ) 2 , c ) 3 , d ) 8 , e ) 16
c
15,120
gain
the salary of a typist was at first raised by 10 % and then the same was reduced by 5 % . if he presently draws rs . 5225 . what was his original salary ?
"x * ( 110 / 100 ) * ( 95 / 100 ) = 5225 x * ( 11 / 10 ) * ( 1 / 100 ) = 55 x = 5000 answer : b"
a ) 2277 , b ) 5000 , c ) 1000 , d ) 2651 , e ) 1971
b
15,121
other
3 numbers are in the ratio 3 : 5 : 7 . the largest number is 56 . what is the difference between smallest and largest number ?
the three numbers are 3 x , 5 x , and 7 x . the largest number is 56 = 7 * 8 , so x = 8 . the smallest number is 3 * 8 = 24 . 56 - 24 = 32 the answer is d .
a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
d
15,122
geometry
a rectangular field is to be fenced on three sides leaving a side of 8 feet uncovered . if the area of the field is 680 sq . ft , how many feet of fencing will be required ?
"given that length and area , so we can find the breadth . length x breadth = area 8 x breadth = 680 breadth = 85 feet area to be fenced = 2 b + l = 2 ( 85 ) + 8 = 178 feet answer : d ) 178 ft"
a ) 244 ft , b ) 88 ft , c ) 122 ft , d ) 178 ft , e ) 66 ft
d
15,123
gain
a cricket bat is sold for $ 900 , making a profit of $ 225 . the profit percentage would be
"225 / ( 900 - 225 ) = 33.33 % . answer : c"
a ) 24 % , b ) 25.5 % , c ) 33.33 % , d ) 36.3 % , e ) 40 %
c
15,124
other
initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many r women are currently in the room ?
"the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
d
15,125
general
instead of multiplying a number by 2 , the number is divided by 10 . what is the percentage of error obtained ?
let the number be x the right number is 2 x the wrong number is x / 10 error is ( 2 x - x / 10 ) = 19 x / 10 percentage of error is ( ( 19 x / 10 ) / 2 x ) * 100 = 95 % answer : c
a ) 94 % , b ) 92 % , c ) 95 % , d ) 93 % , e ) 97 %
c
15,126
physics
a train 710 m long is running at a speed of 78 km / hr . if it crosses a tunnel in 1 min , then the length of the tunnel is ?
"speed = 78 * 5 / 18 = 65 / 3 m / sec . time = 1 min = 60 sec . let the length of the train be x meters . then , ( 710 + x ) / 60 = 65 / 3 x = 590 m . answer : e"
a ) 2898 , b ) 277 , c ) 500 , d ) 297 , e ) 590
e
15,127
gain
find the annual income derived by investing $ 6800 in 30 % stock at 136 .
by investing $ 136 , income obtained = $ 30 . by investing $ 6800 , income obtained = $ [ ( 30 / 136 ) * 6800 ] = $ 1500 . answer b .
a ) 550 , b ) 1500 , c ) 250 , d ) 1300 , e ) 400
b
15,128
geometry
the ratio of the volumes of two cubes is 729 : 1331 . what is the ratio of their total surface areas ?
"ratio of the sides = ³ √ 729 : ³ √ 1331 = 9 : 11 ratio of surface areas = 92 : 112 = 81 : 121 answer : a"
a ) 81 : 121 , b ) 81 : 126 , c ) 81 : 189 , d ) 81 : 176 , e ) 81 : 117
a
15,129
gain
if the cost price of 50 articles is equal to the selling price of 46 articles , then the gain or loss percent is ?
given that , cost price of 50 article is equal to selling price of 46 articles . let cost price of one article = rs . 1 selling price of 46 articles = rs . 50 but cost price of 46 articles = rs . 46 therefore , the trader made profit . \ percentage of profit = 4 / 46 * 100 = 8.69 % answer : e
a ) 22 , b ) 65 , c ) 78 , d ) 33 , e ) 8.69
e
15,130
gain
two years ago , ram put $ 1,000 into a savings account . at the end of the first year , his account had accrued $ 100 in interest bringing his total balance to $ 1,100 . the next year , his account balance increased by 20 % . at the end of the two years , by what percent has sam ' s account balance increased from his initial deposit of $ 1,000 ?
"investment 1000 dollars 1 st year total gained = 100 total amount end of first year = 1100 second year account increased by 20 % = 1100 * 0.2 = 220 therefore total amount by second year end = 1320 so total percentage increase in money = ( 1320 - 1000 ) * 100 / 1000 = 32 % correct answer e = 32 %"
a ) 40 % , b ) 25 % , c ) 35 % , d ) 30 % , e ) 32 %
e
15,131
physics
city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 4 : 20 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
"train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 4 : 20 pm + 2 hrs = 6 : 20 pm answer : d . 6 : 20"
a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 20 , e ) 7 : 00
d
15,132
general
if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 6.2 ] + [ - 3.4 ] + [ 12.7 ] ?
"you are asked what the closest lesser integer value to [ x ] is . [ - 6.2 ] = - 7.0 [ - 3.4 ] = - 4.0 [ 12.7 ] = 12.0 therefore , answer is : - 7.0 - 4.0 + 12.0 = - 1.0 option a ."
a ) - 1 , b ) 0 , c ) 1 , d ) 2 , e ) 3
a
15,133
general
of the total amount that jill spent on a shopping trip , excluding taxes , she spent 50 percent on clothing , 10 percent on food , and 40 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 = 10 , others = 40 tax on clothing = 2 tax on others = 3.2 percentage = 5.2 / 100 = 5.2 % answer : d"
a ) 2.8 % , b ) 3.6 % , c ) 4.4 % , d ) 5.2 % , e ) 6.0 %
d
15,134
gain
indu gave bindu rs . 3750 on compound interest for 2 years at 4 % per annum . how much loss would indu has suffered had she given it to bindu for 2 years at 4 % per annum simple interest ?
"3750 = d ( 100 / 4 ) 2 d = 6 answer : c"
a ) 1 , b ) 2 , c ) 6 , d ) 4 , e ) 9
c
15,135
other
how many integers from 1 to 100 ( both inclusive ) have odd number of factors ?
all perfect squares have odd # of factors . squaring integers 1 - 10 produces 1 , 4 , 9 , 16 , . . . 100 which all have odd # of factors . answer is d
a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) greater than 10
d
15,136
gain
company p had 15 percent more employees in december than it had in january . if company p had 460 employees in december , how many employees did it have in january ?
given : january * 1.15 = december - - > january * 1.15 = 460 - - > january = 460 / 1.15 = 400 . answer : b .
a ) 391 , b ) 400 , c ) 410 , d ) 423 , e ) 445
b
15,137
general
if rs . 10 be allowed as true discount on a bill of rs . 110 at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is
"explanation : present worth = amount - truediscount = 110 - 10 = rs . 100 si on rs . 100 for a certain time = rs . 10 si on rs . 100 for doube the time = rs . 20 truediscount on rs . 120 = 120 - 100 = rs . 20 truediscount on rs . 110 = ( 110 x 20 / 120 ) = rs . 18.33 answer : b"
a ) 18.20 , b ) 18.33 , c ) 18 , d ) 18.3 , e ) none of these
b
15,138
physics
an outlet pipe can empty 2 / 3 of a cistern in 16 minutes . in 4 minutes , what part of the cistern will be emptied ?
"4 / 16 * 2 / 3 = 1 / 6 the answer is d ."
a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 4 , d ) 1 / 6 , e ) 1 / 8
d
15,139
general
s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits y are in s ( 99 ) ?
"focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b"
a ) y = 350 , b ) y = 353 , c ) y = 354 , d ) y = 356 , e ) y = 357
b
15,140
other
in a primary school , the ratio of the number of girls to boys is 5 : 8 . if there are 160 girls , the total number of students in the college is :
let the number of girls and boys be 5 x and 8 x . total number of students = 13 x = 13 x 32 = 416 . answer : d
a ) 100 , b ) 250 , c ) 260 , d ) 300 , e ) 350
d
15,141
gain
20 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
"20 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 20 ) * 100 = 180 square feet answer : option b"
a ) 14.4 , b ) 180 , c ) 50.4 , d ) 60 , e ) 90
b
15,142
general
a certain fraction is equivalent to 2 / 5 . if the numerator of the fraction is increased by 3 and the denominator is doubled , the new fraction is equivalent to 1 / 3 . what is the sum of the numerator and denominator of the original fraction ?
x / y = 2 / 5 - > 1 ( x + 3 ) / 2 y = 1 / 3 - > 2 divide 1 by 2 : = > 2 x / ( x + 3 ) = 6 / 5 = > 10 x = 6 x + 18 = > x = 3 / 2 = > y = 5 / 2 * 3 / 2 = 15 / 4 so x + y = 21 / 4 the answer is a
a ) 21 / 4 , b ) 35 , c ) 28 , d ) 26 , e ) 21
a
15,143
other
a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 7 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
"ans : 147 7 c 1 * 7 c 2 answer c )"
a ) 42 , b ) 70 , c ) 147 , d ) 165 , e ) 315
c
15,144
general
find the sum of first 30 natural numbers
"explanation : sum of n natural numbers = n ( n + 1 ) 2 = 30 ( 30 + 1 ) 2 = 30 ( 31 ) 2 = 465 answer : option c"
a ) 470 , b ) 468 , c ) 465 , d ) 463 , e ) 485
c
15,145
general
the average age of students of a class is 15.8 years . the average age of boys in the class is 16.4 years and that of the girls is 15.3 years . the ration of the number of boys to the number of girls in the class is ?
"let the ratio be k : 1 . then , k * 16.4 + 1 * 15.3 = ( k + 1 ) * 15.8 = ( 16.4 - 15.8 ) k = ( 15.8 - 15.3 ) = k = 0.5 / 0.6 = 5 / 6 required ratio = 5 / 6 : 1 = 5 : 6 . answer : a"
a ) 5 : 6 , b ) 2 : 3 , c ) 2 : 5 , d ) 2 : 1 , e ) 2 : 4
a
15,146
physics
car a runs at the speed of 50 km / hr and reaches its destination in 8 hours . car b runs at the speed of 70 km / h and reaches its destination in 4 hours . what is the ratio of distances covered by car a and car b ?
"car a travels 50 × 8 = 400 km car b travels 70 × 4 = 280 km the ratio is 400 : 280 = 40 : 28 = 10 : 7 the answer is c ."
a ) 3 : 7 , b ) 4 : 9 , c ) 10 : 7 , d ) 5 : 7 , e ) 6 : 11
c
15,147
general
. the price of commodity p increases by 40 paise every year , while the price of commodity q increases by 15 paise every year . if in 2001 , the price of commodity p was rs . 4.20 and that of q was rs . 6.30 , in which year commodity p will cost 40 paise more than the commodity q ?
explanation : let the commodity p costs 40 paise more than the commodity q after n years price of the commodity p in 2001 = rs . 4.20 since the price of the commodity p increases by rs 0.40 every year , price of the commodity p after n years from 2001 = rs . 4.20 + ( n × . 40 ) price of the commodity q in 2001 = rs . 6.30 since the price of the commodity q increases by rs 0.15 every year , price of the commodity q after n years from 2001 = rs . 6.30 + ( n × . 15 ) since the commodity p costs rs . 0.40 more that the commodity q after n years from 2001 , 4.20 + ( n × . 40 ) = 6.30 + ( n × . 15 ) + 0.40 = > ( 40 n - . 15 n ) = 6.30 - 4.20 + 0.40 = 2.5 = > . 25 n = 2.5 ⇒ n = 2.5 / . 25 = 250 / 25 = 101.15 ¯ = > commodity p costs rs . 0.40 more that the commodity q after 10 years from 2001 . i . e . , in 2011 . answer : option d
a ) 2008 , b ) 2009 , c ) 2010 , d ) 2011 , e ) none of these
d
15,148
general
david obtained 70 , 60 , 78 , 60 and 65 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology what are his average marks ?
"explanation : average = ( 70 + 60 + 78 + 60 + 65 ) / 5 = 333 / 5 = 66.6 . answer : c"
a ) 75 , b ) 27.6 , c ) 66.6 , d ) 16.5 , e ) 11
c
15,149
geometry
the circumferences of two circles are 264 meters and 352 meters . find the difference between the areas of the larger and the smaller circles .
"let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 264 and 2 ∏ l = 352 s = 264 / 2 ∏ and l = 352 / 2 ∏ difference between the areas = ∏ l 2 - ∏ s 2 = ∏ { 1762 / ∏ 2 - 1322 / ∏ 2 } = 1762 / ∏ - 1322 / ∏ = ( 176 - 132 ) ( 176 + 132 ) / ∏ = ( 44 ) ( 308 ) / ( 22 / 7 ) = ( 2 ) ( 308 ) ( 7 ) = 4312 sq m answer : c"
a ) 3312 , b ) 2888 , c ) 4312 , d ) 2881 , e ) 1221
c
15,150
physics
find the cost of fencing around a circular field of diameter 30 m at the rate of rs . 5 a meter ?
"2 * 22 / 7 * 15 = 94.25 94.25 * 5 = rs . 471.25 answer : e"
a ) 288 , b ) 132 , c ) 772 , d ) 592 , e ) 471.25
e
15,151
geometry
a hall is 24 meters long and 12 meters wide . if the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls , what is the volume of the hall ( in cubic meters ) ?
2 hl + 2 hw = 2 lw h = lw / ( l + w ) volume = lwh = ( lw ) ^ 2 / ( l + w ) = 2304 the answer is d .
['a ) 1896', 'b ) 1912', 'c ) 2108', 'd ) 2304', 'e ) 2524']
d
15,152
general
if 15 students in a class average 70 % on an exam and 10 students average 95 % on the same exam , what is the average in percent for all 25 students ?
"( 15 * 70 + 10 * 95 ) / 25 = 80 % the answer is d ."
a ) 77 % , b ) 78 % , c ) 79 % , d ) 80 % , e ) 81 %
d
15,153
general
on dividing a number by 8 , we get 8 as quotient and 0 as remainder . on dividing the same number by 5 , what will be the remainder ?
"number = 8 * 8 + 0 = 64 5 ) 64 ( 12 60 - - - - - - - - 4 required number = 4 . answer : b"
a ) 10 , b ) 4 , c ) 8 , d ) 6 , e ) 5
b
15,154
physics
a dog travelled for 2 hours . he covered the first half of the distance at 10 kmph and remaining half of the distance at 5 kmph . find the distance travelled by the dog ?
let the distance travelled be x km . total time = ( x / 2 ) / 10 + ( x / 2 ) / 5 = 2 = > x / 20 + x / 10 = 2 = > ( 1 x + 2 x ) / 20 = 2 = > x = 20 km answer : a
a ) 20 km , b ) 16 km , c ) 6 km , d ) 3 km , e ) 61 km
a
15,155
gain
the owner of a furniture shop charges his customer 30 % more than the cost price . if a customer paid rs . 8450 for a computer table , then what was the cost price of the computer table ?
"cp = sp * ( 100 / ( 100 + profit % ) ) = 8450 ( 100 / 130 ) = rs . 6500 . answer : d"
a ) rs . 5725 , b ) rs . 5275 , c ) rs . 6275 , d ) rs . 6500 , e ) none of these
d
15,156
general
the difference of two numbers is 1355 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
"let the smaller number be x . then larger number = ( x + 1355 ) . x + 1355 = 6 x + 15 5 x = 1340 x = 268 smaller number = 270 . answer d"
a ) 240 , b ) 270 , c ) 295 , d ) 268 , e ) 252
d
15,157
gain
weights of two friends ram and shyam are in the ratio 7 : 5 . if ram ' s weight is increased by 10 % and total weight of ram and shyam become 82.8 kg , with an increases of 15 % . by what percent did the weight of shyam has to be increased ?
"solution : given ratio of ram and shayam ' s weight = 7 : 5 hence , ( x - 15 ) / ( 15 - 10 ) = 7 / 5 or , x = 22 % . answer : option c"
a ) 19 % , b ) 10 % , c ) 22 % , d ) 16 % , e ) none
c
15,158
general
a picnic attracts 240 persons . there are 60 more men than women , and 60 more adults than children . how many men are at this picnic ?
"adult + children = 240 let , children = y then , adult = y + 60 i . e . y + ( y + 60 ) = 240 i . e . y = 90 i . e . adult = 90 + 20 = 110 adults include only men and women i . e . men + women = 110 let women , w = x then men , m = x + 60 i . e . x + ( x + 60 ) = 2 x + 60 = 110 i . e . x = 25 i . e . men , m = 25 + 60 = 85 answer : option e"
a ) 240 , b ) 75 , c ) 110 , d ) 130 , e ) 85
e
15,159
geometry
a rectangular rug with side lengths of 2 feet and 7 feet is placed on a square floor that has an area of 64 square feet . if the surface of the rug does not extend beyond the area of the floor , what fraction of the area of the floor is not covered by the rug ?
area of the rectangular rug = 2 * 7 = 14 fraction not covered by the rug = ( total area - rug area ) / total area = ( 64 - 14 ) / 64 = 25 / 32 = d
['a ) a . 3 / 16', 'b ) 1 / 4', 'c ) c . 1 / 2', 'd ) 25 / 32', 'e ) 7 / 8']
d
15,160
gain
at a small company , 58 percent of the employees are women , and 60 percent of the employees are married . if 2 / 3 of the men are single , what fraction of the women are married ?
lets take total employees are 100 . given that , total women = 58 and total married = 60 . total men = 100 - 58 = 42 and single men = 2 / 3 * 42 = 28 . married men = total men - single men = 42 - 28 = 14 . married women = total married - married men = 60 - 14 = 46 . fraction of women are married = married women / total women = 46 / 58 = 23 / 29 . ans c
a ) 5 / 16 , b ) 1 / 3 , c ) 23 / 29 , d ) 7 / 10 , e ) 5 / 7
c
15,161
physics
pipe a can fill a tank in 6 minutes and pipe b cam empty it in 24 minutes . if both the pipes are opened together after how many minutes should pipe b be closed , so that the tank is filled in 30 minutes ?
"let the pipe b be closed after x minutes . 30 / 6 - x / 24 = 1 = > x / 24 = 30 / 6 - 1 = 4 = > x = 4 * 24 = 96 . answer : c"
a ) 18 , b ) 27 , c ) 96 , d ) 27 , e ) 21
c
15,162
general
the present ages of 3 persons are in the proportion of 4 : 7 : 9 . 8 years ago , the sum of their ages was 116 . find their present ages .
let the present ages of three persons be 4 k , 7 k and 9 k respectively . ( 4 k - 8 ) + ( 7 k - 8 ) + ( 9 k - 8 ) = 116 20 k = 140 k = 7 therefore , then present ages are 28 , 49,63 . answer : b
a ) 20 , 35,45 , b ) 28 , 49,63 , c ) 16 , 28,36 , d ) 16 , 28,46 , e ) none of these
b
15,163
geometry
a circular well with a diameter of 4 metres , is dug to a depth of 14 metres . what is the volume of the earth dug out ?
"solution volume = π r 2 h ‹ = › ( 22 / 7 × 2 × 2 × 14 ) m 3 ‹ = › 176 m 3 . answer e"
a ) 32 m 3 , b ) 36 m 3 , c ) 40 m 3 , d ) 44 m 3 , e ) 176 m 3
e
15,164
physics
a can do a job in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is ?
"a ' s 1 day work = 1 / 15 b ' s 1 day work = 1 / 20 a + b 1 day work = 1 / 15 + 1 / 20 = 7 / 60 a + b 5 days work = 7 / 60 * 5 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 answer is d"
a ) 2 / 15 , b ) 8 / 15 , c ) 3 / 11 , d ) 5 / 12 , e ) 6 / 13
d
15,165
general
the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 12 terms of the arithmetic progression ?
"n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 12 . . . we get 12 / 2 [ 2 a + 14 d ] = 15 [ a + 7 d ] = 12 * 10 = 120 . . . answer is b . . ."
a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 270
b
15,166
general
when asked what the time is , a person answered that the amount of time left is 1 / 5 of the time already completed . what is the time .
"a day has 24 hrs . assume x hours have passed . remaining time is ( 24 - x ) 24 − x = 15 x ⇒ x = 2024 − x = 15 x ⇒ x = 20 time is 8 pm answer : d"
a ) 2 , b ) 9 , c ) 3 , d ) 8 , e ) 6
d
15,167
general
a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 340 million , approximately what was the percent increase in sales ?
"new value – old value ) / old value x 100 we are given : february sales this year = 385 million february sales last year = 340 million we need to determine the percent increase between sales from last year to sales this year . thus , the new value = 385 million and the old value = 340 million . let ’ s plug them into our percent change formula . ( new value – old value ) / old value x 100 [ ( 385 – 340 ) / 340 ] x 100 65 / 340 x 100 ≈ 13 % . the answer is e ."
a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 13 %
e
15,168
gain
a reduction of 50 % in the price of apples would enable a man to obtain 80 more for rs . 55 , what is reduced price per dozen ?
c 55 * ( 50 / 100 ) = 28 - - - 64 ? - - - 12 = > rs . 4
a ) 1 , b ) 3 , c ) 4 , d ) 7 , e ) 10
c
15,169
general
the maximum numbers of students among them 781 pens and 710 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is
"olution required number of students . = h . c . f of 781 and 710 . â € ¹ = â € º 71 . answer a"
a ) 71 , b ) 910 , c ) 1001 , d ) 1911 , e ) none
a
15,170
general
if the price of a certain bond on may 1 st was 1 / 2 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
"the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 1 / 2 * 12 = 6 ; the price on july 1 st = 6 * 1.5 = 9 . the average price of the bond on may 1 st and july 1 st = ( 6 + 9 ) / 2 = 7.5 . the price of the bond on june 1 st ( 12 ) is 8 / 5 times ( 160 % ) the average price of the bond on may 1 st and july 1 st . answer : e ."
a ) 50 % , b ) 75 % , c ) 120 % , d ) 133 1 / 3 % , e ) 160 %
e
15,171
physics
a can give b 200 meters start and c 400 meters start in a kilometer race . how much start can b give c in a kilometer race ?
"a runs 1000 m while b runs 800 m and c runs 600 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 600 ) / 800 = 750 m . b can give c = 1000 - 750 = 250 m . answer : b"
a ) 111.12 , b ) 250 , c ) 111.64 , d ) 111.11 , e ) 101.12
b
15,172
physics
in a kilometer race , a beats b by 40 meters or 15 seconds . what time does a take to complete the race ?
"time taken by b run 1000 meters = ( 1000 * 15 ) / 50 = 300 sec . time taken by a = 300 - 15 = 285 sec . answer : b"
a ) 277 sec , b ) 285 sec , c ) 267 sec , d ) 167 sec , e ) 276 sec
b
15,173
other
a number is said to be prime saturated if the product of all the different positive prime factors of r is less than the square root of r . 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 r is less than the square root of r . 96 has more number of smaller prime factor thats the clue ! ! = d
a ) 99 , b ) 98 , c ) 97 , d ) 96 , e ) 95
d
15,174
general
the difference between the place values of two threes in the numerical 40378273 is
"required difference = ( 300000 - 3 ) = 299997 . answer is b"
a ) 29997 , b ) 299997 , c ) 297 , d ) 0 , e ) none of them
b
15,175
general
rahim bought 42 books for rs . 520 from one shop and 22 books for rs . 248 from another . what is the average price he paid per book ?
"average price per book = ( 520 + 248 ) / ( 42 + 22 ) = 768 / 64 = rs . 12 answer : c"
a ) s . 17 , b ) s . 18 , c ) s . 12 , d ) s . 11 , e ) s . 10
c
15,176
physics
a can do a piece of work in 80 days and b in 100 days . they work together for 20 days and then b goes away . in how many days will a finish the remaining work ?
"explanation : in this type of questions we first get the finishing of work in 1 minute for both pipes then we will add them to get the result , as : part finished by a in 1 day = 1 / 80 part finished by b in 1 day = 1 / 100 part finished by ( a + b ) in 1 day = 1 / 80 + 1 / 100 = 9 / 400 so ( a + b ) ' s 20 days work = 20 * 9 / 400 = 9 / 20 remaining work = 1 - 9 / 20 = 11 / 20 . number days to finish the remaining work by a = 80 * 11 / 20 = 44 days . option b"
a ) 33 days , b ) 44 days , c ) 55 days , d ) 42 days , e ) 32 days
b
15,177
general
what is the smallest no . that should be added to 41381 to make it exactly divisible by 9 ?
"if a number is divisible by 9 , the sum of its digits must be a multiple of 9 . here , 4 + 1 + 3 + 8 + 1 = 17 , the next multiple of 9 is 18 . 1 must be added to 41381 to make it divisible by 9 a"
a ) 1 , b ) 3 , c ) 5 , d ) 6 , e ) 9
a
15,178
general
lucia ' s sells kale at x dollar per pound for the first 20 pounds and . 8 x for every subsequent pound . amby ' s price is x per pound for the first 14 pounds and . 9 x for subsequent pounds . what is the minimum number of pounds over 15 for which lucia ' s becomes an equal or better deal ?
for amy ' s deal to be better , the cost has to be less or equal to lucia ' s assuming ' n ' is the number of pounds of kale , the equation is 20 x + ( n - 20 ) ( 0.8 x ) < = 14 x + ( n - 14 ) ( 0.9 x ) resolve it : = = > 20 x + 0.8 nx - 16 x < = 14 x + 0.9 nx - 12.6 x = = > 2.6 x < = 0.1 nx = = > 26 x < = nx = = > x ( n - 26 ) > = 0 as x can not be 0 , = = > n - 26 > = 0 = = > n > = 26 so the minimum value is 26 ' b ' would be the correct answer
a ) 24 , b ) 26 , c ) 25 , d ) 27 , e ) 28
b
15,179
gain
a ladder 30 feet long is leaning against a wall that is perpendicular to level ground . the bottom of the ladder is 10 feet from the base of the wall . if the top of the ladder slips down 5 feet , how many feet will the bottom of the ladder slip ?
30 ^ 2 - 10 ^ 2 = 800 it means that the height is equal to 28.28 . since the top of the ladder slips down 5 feet , then the height of the wall = 28.28 - 5 = 23.28 the bottom = sqrt ( 30 ^ 2 - 23.28 ^ 2 ) = sqrt ( 900 - 541.95 ) = 18.92 ans is c
a ) 14 , b ) 15 , c ) 18.92 , d ) 19 , e ) 25
c
15,180
geometry
triangle xyz is an isosceles right triangle . if side xy is longer than side yz , and the area of the triangle is 25 , what is the measure of side xy ?
"ans a . . 10 . . xy being larger means it is the hyp . . area = ( 1 / 2 ) * ( yz ) ^ 2 = 25 or yz = 5 * \ sqrt { 2 } . . therefore hyp = xy = 10"
a ) 10 , b ) 4 √ 2 , c ) 8 , d ) 8 √ 2 , e ) can not be determined from the information provided
a
15,181
general
p has $ 35 more than what q and r together would have had if both b and c had 1 / 7 of what p has . how much does p have ?
"p = ( 2 / 7 ) * p + 35 ( 5 / 7 ) * p = 35 p = 49 the answer is c ."
a ) $ 45 , b ) $ 47 , c ) $ 49 , d ) $ 51 , e ) $ 53
c