regisss/math_qa huggingface dataset:
Problem: together , 15 type a machines and 7 type b machines can complete a certain job in 4 hours . together 8 type b machines and 15 type c machines can complete the same job in 11 hours . how many hours r would it take one type a machine , one type b machine , and one type c machine working together to complete the job ( assuming constant rates for each machine ) ?
Options: a ) 22 hours , b ) 30 hours , c ) 44 hours , d ) 60 hours , e ) it can not be determined from the information above .
Rationale: "say the rates of machines a , b and c are a , b , and c , respectively . together 15 type a machines and 7 type b machines can complete a certain job in 4 hours - - > 15 a + 7 b = 1 / 4 ; together 8 type b machines and 15 type c machines can complete the same job in 11 hours - - > 8 b + 15 c = 1 / 11 . sum the above : 15 a + 15 b + 15 c = 1 / 4 + 1 / 11 = 15 / 44 - - > reduce by 15 : a + b + c = 1 / 44 - - > so , the combined rate of the three machines is 1 / 44 job / hour - - > time is reciprocal of the rate , thus machines a , b and c can do the job r in 44 hours . answer : c ."
Answer: c
Problem: the cricket team of 11 members is 28 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 25 , e ) 28
Rationale: "let the average age of the whole team be x years . 11 x - ( 28 + 31 ) = 9 ( x - 1 ) = > 11 x - 9 x = 50 = > 2 x = 50 = > x = 25 . so , average age of the team is 25 years . d"
Answer: d
Problem: a , b and c are partners . a receives 2 / 3 of profits , b and c dividing the remainder equally . a ' s income is increased by rs . 400 when the rate to profit rises from 5 to 7 percent . find the capital of b ?
Options: a ) 3999 , b ) 7799 , c ) 2500 , d ) 5000 , e ) 2912
Rationale: "a : b : c = 2 / 3 : 1 / 6 : 1 / 6 = 4 : 1 : 1 x * 2 / 100 * 2 / 3 = 400 b capital = 30000 * 1 / 6 = 5000 . answer : d"
Answer: d
Problem: a reduction of 30 % in the price of apples would enable a man to obtain 54 more for rs . 30 , what is reduced price per dozen ?
Options: a ) 1 , b ) 2 , c ) 6 , d ) 7 , e ) 10
Rationale: "b 30 * ( 30 / 100 ) = 9 - - - 54 ? - - - 12 = > rs . 2"
Answer: b
Problem: a certain psychologist charges $ 35 more for the first hour of therapy than for each additional hour . if the total charge to a patient who receives 5 hours of therapy is $ 350 , what is the total charge to a patient who receives only 2 hours of therapy ?
Options: a ) $ 120 , b ) $ 135 , c ) $ 161 , d ) $ 165 , e ) $ 192
Rationale: "let the charge for first hour = x + 35 then charge for each additional hour = x x + 35 + 4 x = 350 = > 5 x = 315 = > x = 63 total charge for patient for 3 hours of therapy = x + 35 + x = 2 x + 35 = 161 $ answer c"
Answer: c
Problem: the average length of 6 ropes is 80 cm . if the average length of one third of the ropes measure to 70 cm , what is the average of the other ropes ?
Options: a ) 75 . , b ) 85 . , c ) 90 . , d ) 94 . , e ) 100 .
Rationale: edit : given ( x 1 + x 2 . . . + x 6 ) / 6 = 80 ( x 1 + x 2 . . . + x 6 ) = 480 - - > eq 1 . now given avg length of one third ropes is 70 . that means out 6 / 3 = 2 ropes . let the avg length of two ropes be ( x 1 + x 2 ) / 2 = 70 . ( x 1 + x 2 ) = 140 . - - > eq 2 . now we are asked to find the average of the remaining i . e . ( x 3 + x 4 + x 5 + x 6 ) substitute eq 2 in eq 1 then we get 140 + x 3 + x 4 + x 5 + x 6 = 480 = > x 3 + x 4 + x 5 + x 6 = 340 now divide 340 by 4 we get 85 . = > ( x 3 + x 4 + x 5 + x 6 ) / 4 = 85 = avg length of remaining ropes . imo correct option is b .
Answer: b
Problem: x and y are two towns . ganesh covers the distance from x to y at an average speed of 44 km / hr . however , he covers the distance from y to x at an average speed of 36 km / hr . his average speed during the whole journey in km / hr . is :
Options: a ) 39.6 , b ) 43 , c ) 40 , d ) 38 , e ) 29
Rationale: "solution : average speed = 2 xy / x + y = 2 * 44 * 36 / 44 + 36 = 39.6 answer : a"
Answer: a
Problem: if the cost price is 95 % of selling price then what is the profit percentage .
Options: a ) 5.26 , b ) 5.16 , c ) 5.61 , d ) 5.52 , e ) 5
Rationale: "selling price = rs 100 : then cost price = rs 95 : profit = rs 5 . profit = { ( 5 / 95 ) * 100 } % = 5.26 % answer is a ."
Answer: a
Problem: one fourth of a solution that was 10 % sugar by weight was replaced by a second solution resulting in a solution that was 20 percent sugar by weight . the second solution was what percent sugar by weight ?
Options: a ) 65 % , b ) 50 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "say the second solution ( which was 1 / 4 th of total ) was x % sugar , then 3 / 4 * 0.1 + 1 / 4 * x = 1 * 0.20 - - > x = 0.5 . alternately you can consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.1 + 25 * x = 100 * 0.20 - - > x = 0.5 . answer : b ."
Answer: b
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 20 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 80 , c ) 100 , d ) 44 , e ) 250
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 4.8 , so radius is 2.4 new area = 5.76 π increase in area is 1.76 π % increase in area = 1.76 / 4 * 100 so , % increase is 44 % answer will be ( d )"
Answer: d
Problem: what is the perimeter of a square field whose diagonal is 8 √ 2 ?
Options: a ) 82 m , b ) 32 m , c ) 27 m , d ) 26 m , e ) 76 m
Rationale: "4 a = 32 m answer : b"
Answer: b
Problem: in a division sum , the quotient is 120 , the divisor 456 and the remainder 333 , find the dividend ?
Options: a ) 55287 , b ) 29887 , c ) 27768 , d ) 55053 , e ) 17191
Rationale: "explanation : 120 * 456 + 333 = 55053 answer : d"
Answer: d
Problem: what is the remainder when ( 71 ) ( 73 ) is divided by 9 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "( 71 ) ( 73 ) = ( 72 - 1 ) ( 72 + 1 ) = 72 ^ 2 - 1 which is 1 less than a multiple of 9 . then the remainder will be 8 . the answer is e ."
Answer: e
Problem: what is the probability that a number selected from number 1 to 30 is prime number , when each of the given numbers is equally likely to be selected ?
Options: a ) 10 / 30 , b ) 20 / 30 , c ) 1 , d ) 5 / 30 , e ) 15 / 30
Rationale: x = { 2,3 , 5,7 , 11,13 , 17,19 , 23,29 } n ( x ) = 10 n ( s ) = 30 hence required probability = n ( x ) / n ( s ) = 10 / 30 option a is answer
Answer: a
Problem: a grocer purchased a quantity of bananas at 3 pounds for $ 0.50 and sold the entire quantity at 4 pounds for $ 1.00 . how many pounds did the grocer purchase if the profit from selling the bananas was $ 8.00 ?
Options: a ) 40 , b ) 60 , c ) 96 , d ) 120 , e ) 240
Rationale: "cost price of 1 pound of bananas = 0.5 / 3 = 1 / 6 selling price of 1 pound of bananas = 1 / 4 profit per pound = ( 1 / 4 - 1 / 6 ) = ( 1 / 12 ) total profit is given as 8 ( 1 / 12 ) * x = 8 x = 96 answer : c"
Answer: c
Problem: the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 112 ounces , what is the volume , in cubic inches , of 53 ounces of this substance ?
Options: a ) 27 , b ) 36 , c ) 42 , d ) 22 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 53 ounces of a substance has a volume of ( 48 / 112 ) * 53 = 22 cubic inches answer d"
Answer: d
Problem: two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . if they cross each other in 22 seconds , what is the ratio of their speeds ?
Options: a ) 1 : 1 , b ) 3 : 1 , c ) 2 : 3 , d ) 3 : 2 , e ) 3 : 4
Rationale: let the speed of the trains be x and y respectively length of train 1 = 27 x length of train 2 = 17 y relative speed = x + y time taken to cross each other = 22 s = ( 27 x + 17 y ) / ( x + y ) = 22 = ( 27 x + 17 y ) / = 22 ( x + y ) = 5 x = 5 y = x / y = 5 / 5 = 1 / 1 i . e 1 : 1 answer : a
Answer: a
Problem: roses can be purchased individually for $ 5.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 317 , d ) 324 , e ) 325
Rationale: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 5.3 = ~ 5 roses for that amount . total = 312 + 5 = 317 . answer : c ."
Answer: c
Problem: the salaries of a and b together is rs . 14000 . a spend 80 % of his salary and b spends 85 % of his salary . what is the salary of b if their savings are equal ?
Options: a ) rs . 6000 , b ) rs . 8000 , c ) rs . 7500 , d ) rs . 6500 , e ) rs . 8500
Rationale: let the salaries of a and b are x and y respectively x + y = 14000 savings of a = 20 x / 100 = savings of b = 15 y / 100 x = ¾ y 3 / 4 y + y = 14000 , 7 y / 4 = 14000 , y = 8000 answer : b
Answer: b
Problem: how many of the positive divisors q of 120 are also multiples of 4 not including 120 ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 7 . , e ) 8 .
Rationale: "4 , 8,12 , 20,24 , 40,60 . ( 7 ) is the answer other way : factors of 120 = 2 ^ 3 * 3 * 5 separate 2 ^ 2 ( which means 4 ) now , calculate the number of other factors . q = 2 * 3 * 5 = total positive factors are 2 * 2 * 2 = 8 this 8 factors include 120 so subtract 1 from 8 ans is 7 = d"
Answer: d
Problem: how many integers between 323,700 and 458,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 10,030 , c ) 1,353 , d ) 1,352 , e ) 1,349
Rationale: "there is one number in hundred with 1 in the tens digit and 3 in the units digit : 13 , 113 , 213 , 313 , . . . the difference between 323,700 and 458,600 is 458,600 - 323,700 = 134,900 - one number per each hundred gives 134,900 / 100 = 1,349 numbers . answer : e ."
Answer: e
Problem: two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 6 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 12 , c ) 2 / 15 , d ) 1 / 10 , e ) 2 / 10
Rationale: "suppose the water in each jug is l liters cx x ( 1 / 6 ) = l cx = 6 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 6 l = 1 / 12 answer will be b"
Answer: b
Problem: 11 + 12 + 13 + . . . 51 + 52 + 53 = ?
Options: a ) 1361 , b ) 1376 , c ) 1363 , d ) 1364 , e ) 1365
Rationale: "sum = 11 + 12 + 13 + . . . 51 + 52 + 53 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 53 positive integers = 53 * 54 / 2 sum of first 10 positive integers = 11 * 10 / 2 sum = 11 + 12 + 13 + . . . 51 + 52 + 53 = 53 * 54 / 2 - 11 * 10 / 2 = 1376 answer : b"
Answer: b
Problem: a man buys 52 pens at marked price of 46 pens from a whole seller . if he sells these pens giving a discount of 1 % , what is the profit percent ?
Options: a ) 7.6 % , b ) 7.7 % , c ) 11.32 % , d ) 11.91 % , e ) 7.8 %
Rationale: "explanation : let marked price be re . 1 each c . p . of 52 pens = rs . 46 s . p . of 52 pens = 99 % of rs . 52 = rs . 51.48 profit % = ( profit / c . p . ) x 100 profit % = ( 5.48 / 46 ) x 100 = 11.91 % answer : d"
Answer: d
Problem: express 50 mps in kmph ?
Options: a ) 172 , b ) 160 , c ) 150 , d ) 180 , e ) 120
Rationale: "25 * 18 / 5 = 180 kmph answer : d"
Answer: d
Problem: the total price of a kilogram each of shimla apples and red delicious apples is 250 rupees more than the total price of a kilogram each of red delicious apples and fuji apples . fuji apples is how much cheaper than shimla apples ?
Options: a ) 250 , b ) 125 , c ) 500 , d ) 100 , e ) 80
Rationale: ( shimla + red delicious ) - ( red delicious + fuji ) = 250 shimla - fuji = 250 answer : a
Answer: a
Problem: how long does a train 110 m long running at the speed of 72 km / hr takes to cross a bridge 138 m length ?
Options: a ) 82.1 sec . , b ) 12.4 sec , c ) 19.1 sec . , d ) 17.1 sec . , e ) 42.1 sec .
Rationale: speed = 72 * 5 / 18 = 20 m / sec total distance covered = 110 + 138 = 248 m . required time = 248 / 20 = 12.4 sec . answer : b
Answer: b
Problem: what is the 25 th digit to the right of the decimal point in the decimal form of 6 / 11 ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "explanation : to determine the greatest possible number of members , first recognize that each member had to contribute the lowest amount given . build an inequality for the individual contributions and the total amount collected , with n = the number of members in the club , and solve for n . 12 n ≤ 599 n ≤ 49 11 / 12 since n represents individual people it must be a whole number . thus the greatest number of people is 49 . answer : option c"
Answer: c
Problem: a sum of money lent out at s . i . amounts to a total of $ 590 after 2 years and to $ 815 after a further period of 5 years . what was the initial sum of money that was invested ?
Options: a ) $ 490 , b ) $ 500 , c ) $ 510 , d ) $ 520 , e ) $ 530
Rationale: "s . i for 5 years = $ 815 - $ 590 = $ 225 the s . i . is $ 45 / year s . i . for 2 years = $ 90 principal = $ 590 - $ 90 = $ 500 the answer is b ."
Answer: b
Problem: if 5 < x < 9 and y = x + 7 , what is the greatest possible integer value of x + y ?
Options: a ) 21 , b ) 22 , c ) 23 , d ) 24 , e ) 25
Rationale: "x + y = x + x + 7 = 2 x + 7 we need to maximize this value and it needs to be an integer . 2 x is an integer when the decimal of x is . 0 or . 5 the largest such value is 8.5 then x + y = 8.5 + 15.5 = 24 . the answer is d ."
Answer: d
Problem: there are 8 students . 4 of them are men and 4 of them are women . if 4 students are selected from the 8 students . what is the probability that the number of men is equal to that of women ?
Options: a ) 18 / 35 , b ) 16 / 35 , c ) 14 / 35 , d ) 13 / 35 , e ) 12 / 35
Rationale: men = women means 2 men 2 women total such combinations = 4 c 2 * 4 c 2 = 4 ! / 2 ! . 2 ! * 4 ! / 2 ! . 2 ! = 6 * 6 total combinations = 8 c 4 = 8 * 7 * 6 * 5 / 4 * 3 * 2 * 1 = 70 so probability = 36 / 70 = 18 / 35 hence a
Answer: a
Problem: how many seconds will a train 200 meters long running at the rate of 36 kmph take to pass a certain telegraph post ?
Options: a ) 10 sec , b ) 20 sec , c ) 25 sec , d ) 30 sec , e ) 35 sec
Rationale: distance = length of train = 200 meters speed = 36 kmph = 36 * 5 / 18 = 10 m / s required time = 200 / 10 = 20 sec answer is b
Answer: b
Problem: a circular logo is enlarged to fit the lid of a jar . the new diameter is 40 per cent larger than the original . by what percentage has the area of the logo increased ?
Options: a ) 50 , b ) 96 , c ) 100 , d ) 125 , e ) 250
Rationale: "let old diameter be 4 , so radius is 2 old area = 4 π new diameter is 5.6 , so radius is 2.8 new area = 7.84 π increase in area is 3.84 π % increase in area = 3.84 / 4 * 100 so , % increase is 96 % answer will be ( b )"
Answer: b
Problem: a , b and c enter into a partnership by investing $ 11000 , $ 15000 and $ 23000 respectively . at the end of 8 months , b receives $ 3315 as his share . find the share of a .
Options: a ) $ 1865 , b ) $ 2087 , c ) $ 2217 , d ) $ 2431 , e ) $ 2662
Rationale: the ratio of capital of a , b and c = 11000 : 15000 : 23000 = 11 : 15 : 23 a ' s share = ( 11 / 15 ) * 3315 = $ 2431 the answer is d .
Answer: d
Problem: a reduction of 35 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) 42 , b ) 49 , c ) 56 , d ) 63 , e ) 70
Rationale: 800 * ( 35 / 100 ) = 280 - - - - 5 ? - - - - 1 = > rs . 56 answer : c
Answer: c
Problem: water consists of hydrogen and oxygen , and the approximate ratio , by mass , of hydrogen to oxygen is 2 : 16 . approximately how many grams of oxygen are there in 90 grams of water ?
Options: a ) 16 , b ) 90 , c ) 112 , d ) 128 , e ) 142
Rationale: "solution : we are given that the ratio of hydrogen to oxygen in water , by mass , is 2 : 16 . using our ratio multiplier we can re - write this as 2 x : 16 x . we can now use these expressions to determine how much oxygen is in 90 grams of water . 2 x + 16 x = 90 18 x = 90 x = 5 since x is 5 , we know that there are 16 x 5 = 80 grams of oxygen in 90 grams of water . answer b ."
Answer: b
Problem: suppose 3 monkeys take 3 minutes to eat 3 bananas . how many monkeys would it take to eat 6 bananas in 6 minutes ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 3 , e ) 13
Rationale: "one monkey takes 3 min to eat 1 banana , so in 6 mins 1 monkey will eat 2 bananas , so for 6 bananas in 6 min we need 6 / 2 = 3 monkeys answer : d"
Answer: d
Problem: a dessert recipe calls for 50 % melted chocolate and 50 % raspberry puree to make a particular sauce . a chef accidentally makes 15 cups of the sauce with 40 % melted chocolate and 60 % raspberry puree instead . how many cups of the sauce does he need to remove and replace with pure melted chocolate to make the sauce the proper 50 % of each ?
Options: a ) 1.5 , b ) 2.5 , c ) 3 , d ) 4.5 , e ) 5
Rationale: we have 15 cups of sauce with 4040 choc and 6060 rasb cups of choc = 0.4 ∗ 15 = 6 cups of rasb = 0.6 ∗ 15 = 9 now let say we removed x cup of original mix and replaced with x cups of choc . therefore final number of cups of choc = 6 − 0.4 x + x now this number of cup should be 50 % of total = 15 / 2 = 7.5 therefore 6 − 0.4 x + x = 7.5 on solving x = 2.5 answer : b
Answer: b
Problem: if x and y are both odd prime numbers andx < y , then how many different positive integer factors does 2 xyhave ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 12 , e ) 8
Rationale: "x and y are both odd prime numbers - it means either x or y is not 2 and since prime numbers have only two factors - 1 and the number itself x and y each will have ( 1 + 1 ) = 2 factors hence 2 xy will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors e is the answer"
Answer: e
Problem: 1 , 6 , 24 , 60 , 120 , 210 , ___ ?
Options: a ) 336 , b ) 366 , c ) 330 , d ) 660 , e ) 770
Rationale: "it follow the pattern like this . . 2 ^ 3 - 2 = 6 3 ^ 3 - 3 = 24 4 ^ 3 - 4 = 60 5 ^ 3 - 5 = 120 6 ^ 3 - 6 = 210 so . . . 7 ^ 3 - 7 = 336 answer : a"
Answer: a
Problem: there are 30 students in a classroom . the ratio of the # of girls to boys was 1 : 2 , how many boys are there ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: # of girls = x # of boys = 2 x x + 2 x = 30 3 x = 30 x = 30 / 3 = 10 boys = 2 x = 2 * 10 = 20 answer : c
Answer: c
Problem: 99 ! how many zero ' s ?
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: 99 ! = 99 / 5 = 19 = 19 / 5 = 3 so 99 ! has ( 19 + 3 = 22 zeroes ) answer : c
Answer: c
Problem: in a kilometer race , a beats b by 40 meters or 8 seconds . what time does a take to complete the race ?
Options: a ) 221 , b ) 190 , c ) 192 , d ) 191 , e ) 121
Rationale: "time taken by b run 1000 meters = ( 1000 * 8 ) / 40 = 200 sec . time taken by a = 200 - 8 = 192 sec . answer : c"
Answer: c
Problem: the volume of a sphere with radius r is ( 4 / 3 ) * pi * r ^ 3 and the surface area is 4 * pi * r ^ 3 . if a sperical balloon has a volume of 4500 pi cubic centimeters , what is hte surface area of the balloon in square centimeters ?
Options: a ) a . 40 , b ) b . 100 , c ) c . 400 , d ) d . 1,000 , e ) e . 2,000
Rationale: "the surface area is 4 . pi . r ^ 2 ( its area remember not volume ) as 4 / 3 . pi . r ^ 3 = 4500 pi r = 15 so area = 4 . pi . r ^ 2 = 900 . pi = 900 x 3.14 = 2000 ( approx ) e"
Answer: e
Problem: in what time will a train 300 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 9.7 sec , c ) 3.5 sec , d ) 2.9 sec , e ) 7.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 300 / 40 = 7.5 sec . answer : e"
Answer: e
Problem: anand and deepak started a business investing rs . 2250 and rs . 3200 respectively . out of a total profit of rs . 1380 , deepak ' s share is :
Options: a ) 3776 , b ) 810.27 , c ) 815.21 , d ) 688.12 , e ) 267.1
Rationale: ratio of their shares = 2250 : 3200 = 45 : 64 deepak ' s share = 13800 * 64 / 109 = rs . 810.27 . answer : b
Answer: b
Problem: the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 14 cm . find the circumference of a semicircle whose diameter is equal to the side of the square . ( round off your answer to two decimal places )
Options: a ) 77.14 cm , b ) 25.14 cm , c ) 84.92 cm , d ) 94.94 cm , e ) 23.57 cm
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 18 + 14 ) = 64 cm parameter of the square = 64 cm i . e . 4 a = 64 a = 16 diameter of the semicircle = 16 cm circimference of the semicircle = 1 / 2 ( ∏ ) ( 16 ) = 1 / 2 ( 22 / 7 ) ( 16 ) = 352 / 14 = 25.14 cm to two decimal places answer : b"
Answer: b
Problem: find the probability that a leap year selected at random will not have 53 sundays
Options: a ) 6 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 2 / 7
Rationale: "there are 366 days in a leap year : 52 weeks and 2 more days . so , 52 sundays and 2 days . these 2 days can be : { mon , tue } , { tue , wed } , { wed , thu } , { thu , fri } , { fri , sat } , { sat , sun } and { sun , mon } ( 7 cases ) . in order to have 53 sundays we should have either { sat , sun } or { sun , mon } case . the probability of that is 2 / 7 . so , probability of not having 53 sundays is 1 - 2 / 7 = 5 / 7 answer : b ."
Answer: b
Problem: a can do a piece of work in 3 hours ; b and c together can do it in 3 hours , while a and c together can do it in 2 hours . how long will b alone take to do it ?
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 5
Rationale: "a ' s 1 hour ' s work = 1 / 3 ; ( b + c ) ' s 1 hour ' s work = 1 / 3 ; ( a + c ) ' s 1 hour ' s work = 1 / 2 . ( a + b + c ) ' s 1 hour ' s work = ( 1 / 3 + 1 / 3 ) = 2 / 3 . b ' s 1 hour ' s work = ( 2 / 3 - 1 / 2 ) = 1 / 6 . therefore a alone will take 6 hours to do the work . d"
Answer: d
Problem: the area of the floor of a room is 20 m 2 that of a longer wall 15 m 2 and of the shorter wall 12 m 2 , find the edge of the new cube ?
Options: a ) 450 m 3
b ) 100 m 2
c ) 60 m 3
d ) 400 m 3
e ) 500 m 3
Rationale: lb = 20 ; lh = 15 ; fh = 12 ( lbh ) 2 = 20 * 15 * 12 = > lbh = 60 m 3 answer : c
Answer: c
Problem: in a 200 m race , if a gives b a start of 25 metres , then a wins the race by 10 seconds . alternatively , if a gives b a start of 45 metres the race ends in a dead heat . how long does a take to run 200 m ?
Options: a ) 100 seconds , b ) 112.5 seconds , c ) 77.5 seconds , d ) 87.5 seconds , e ) none
Rationale: explanatory answer a gives b a start of 25 metres and still wins the race by 10 seconds . alternatively , if a gives b a start of 45 metres , then the race ends in a dead heat . therefore , the additional 20 metres start given to b compensates for the 10 seconds . i . e . , b runs 20 metres in 10 seconds . hence , b will take 100 seconds to run 200 metres . we know that a gives b a start of 45 metres . b will take 22.5 seconds to run this 45 metres as b runs 20 metres in 10 seconds or at the speed of 2 m / s . hence , a will take 22.5 seconds lesser than b or 100 - 22.5 = 77.5 seconds to complete the race . answer c
Answer: c
Problem: if a farmer wants to plough a farm field on time , he must plough 340 hectares a day . for technical reasons he ploughed only 85 hectares a day , hence he had to plough 2 more days than he planned and he still has 40 hectares left . what is the area of the farm field and how many days the farmer planned to work initially ?
Options: a ) 280 , b ) 490 , c ) 720 , d ) 435 , e ) 679
Rationale: "let x be the number of days in the initial plan . therefore , the whole field is 340 â ‹ … x hectares . the farmer had to work for x + 2 days , and he ploughed 85 ( x + 2 ) hectares , leaving 40 hectares unploughed . then we have the equation : 340 x = 85 ( x + 2 ) + 40 255 x = 210 x = 0.823 so the farmer planned to have the work done in 6 days , and the area of the farm field is 340 ( 0.823 ) = 280 hectares correct answer a"
Answer: a
Problem: p is 60 % more efficient than q . p can complete a work in 26 days . if p and q work together , how many days will it take to complete the same work ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: the work done by p in 1 day = 1 / 26 let work done by q in 1 day = q q × ( 160 / 100 ) = 1 / 26 q = 100 / ( 26 × 160 ) = 10 / ( 26 × 16 ) the work done by p and q in 1 day = 1 / 26 + 10 / ( 26 × 16 ) = 26 / ( 26 × 16 ) = 1 / 16 p and q together can do the work in 16 days . the answer is c .
Answer: c
Problem: if the cost price is 92 % of sp then what is the profit %
Options: a ) 8.70 % , b ) 8.60 % , c ) 8.10 % , d ) 8.30 % , e ) 8.27 %
Rationale: "sol . sp = rs 100 : then cp = rs 92 : profit = rs 8 . profit = { ( 8 / 92 ) * 100 } % = 8.70 % answer is a ."
Answer: a
Problem: a sum was put a simple interest at a certain rate for 7 years . had it been put at 2 % higher rate , it would have fetched rs . 350 more . the sum is :
Options: a ) s . 500 , b ) s . 1000 , c ) s . 1500 , d ) s . 2000 , e ) s . 2500
Rationale: "explanation : let the sub be rs . x and the initial rate be r % . then x ã — ( r + 2 ) ã — 7 / 100 â ˆ ’ x ã — r ã — 7 / 100 = 350 â ‡ ’ x ã — 2 ã — 7 / 100 = 350 â ‡ ’ x ã — 7 / 100 = 175 â ‡ ’ 7 x = 17500 â ‡ ’ x = 2500 answer : option a"
Answer: a
Problem: the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 34 - inch flat - screen television than a square 27 - inch flat - screen television ?
Options: a ) 106.75 , b ) 213.5 , c ) 427 , d ) 729 , e ) 1,156
Rationale: "diagonal of a square = √ 2 * side of square = > side = diagonal / ( √ 2 ) area of square = s * s = ( diagonal ^ 2 ) / 2 difference of both tv ' s = ( 34 ^ 2 - 27 ^ 2 ) / 2 = 427 answer : c"
Answer: c
Problem: â ˆ š 1.5625 = ?
Options: a ) 1.05 , b ) 1.25 , c ) 1.45 , d ) 1.55 , e ) 1.65
Rationale: explanation : 1 | 1.5625 ( 1.25 | 1 | - - - - - - - 22 | 56 | 44 | - - - - - - - 245 | 1225 | 1225 | - - - - - - - | x | - - - - - - - 1.5625 = 1.25 . answer is b
Answer: b
Problem: the tax on a commodity is diminished by 20 % but its consumption is increased by 20 % . find the decrease percent in the revenue derived from it ?
Options: a ) 20 % , b ) 18 % , c ) 4 % , d ) 12 % , e ) 14 %
Rationale: "100 * 100 = 10000 80 * 120 = 9600 10000 - - - - - - - 400 100 - - - - - - - ? = 4 % answer : c"
Answer: c
Problem: three cubes of metal whose edges are 9 , 12 and 18 cm respectively , are melted and one new cube is made . find the edge of the new cube ?
Options: a ) 20.2 , b ) 77 , c ) 66 , d ) 18 , e ) 99
Rationale: "93 + 123 + 183 = a 3 = > a = 20.2 answer : a"
Answer: a
Problem: find ( 7 x + 4 y ) / ( x - 2 y ) if x / 2 y = 3 / 2 ?
Options: a ) 24 , b ) 25 , c ) 26 , d ) 27 , e ) 29
Rationale: "x / 2 y = 3 / 2 = > x = 6 y / 2 = 3 y = > ( 7 x + 4 y ) / ( x - 2 y ) = ( ( 7 * ( 3 y ) ) + 4 y ) / ( 3 y - 2 y ) = > 25 y / y = 25 answer : b"
Answer: b
Problem: the price of lunch for 12 people was $ 207 including a 15 % gratuity for service . what was the average price per person , excluding the gratuity ?
Options: a ) 11.73 , b ) 12 , c ) 13.8 , d ) 14 , e ) 15
Rationale: "clearly e is the answer i used poe here lets consider option ( e ) 12 * 15 = 180 now 180 ( 115 / 100 ) = 207 = > possible answer imo e"
Answer: e
Problem: the banker ' s gain on a sum due 3 years hence at 12 % per annum is rs . 270 . the banker ' s discount is :
Options: a ) rs . 960 , b ) rs . 760 , c ) rs . 840 , d ) rs . 1020 , e ) rs . 1615
Rationale: t . d = ( b . gx 100 ) / ( r / t ) = ( 270 x 100 ) / ( 12 x 3 ) = rs . 750 b . d . = rs . ( 750 + 270 ) = rs . 1020 . answer : d
Answer: d
Problem: a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 26000 , then the share of a is ?
Options: a ) s . 14028 , b ) s . 14000 , c ) s . 14003 , d ) s . 14029 , e ) s . 24029
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 26000 share of b = 7 / 13 ( 26000 ) = rs . 14000 answer : b"
Answer: b
Problem: by selling 150 apples , a fruit - seller gains the selling price of 30 apples . find the gain percent ?
Options: a ) 30 % , b ) 58 % , c ) 25 % , d ) 60 % , e ) 12 %
Rationale: "option c explanation : sp = cp + g 150 sp = 150 cp + 30 sp 120 sp = 150 cp 120 - - - 30 cp 100 - - - ? = > 25 %"
Answer: c
Problem: a certain number of horses and an equal number of men are going somewhere . half of the owners are on their horses ' back while the remaining ones are walking along leading their horses . if the number of legs walking on the ground is 70 , how many horses are there ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "explanation : let number of horses = number of men = x . then , number of legs = 4 x + 2 x ( x / 2 ) = 5 x . so , 5 x = 70 or x = 14 . answer : c"
Answer: c
Problem: 617 x 617 + 583 x 583 = ?
Options: a ) 720578 , b ) 80578 , c ) 80698 , d ) 81268 , e ) none of them
Rationale: "= ( 617 ) ^ 2 + ( 583 ) ^ 2 = ( 600 + 17 ) ^ 2 + ( 600 - 17 ) ^ 2 = 2 [ ( 600 ) ^ 2 + ( 17 ) ^ 2 ] = 2 [ 360000 + 289 ] = 2 x 360289 = 720578 answer is a"
Answer: a
Problem: what positive number , when squared , is equal to the cube of the positive square root of 15 ?
Options: a ) 64 , b ) 32 , c ) 8 , d ) 6 , e ) 2
Rationale: "let the positive number be x x ^ 2 = ( ( 15 ) ^ ( 1 / 2 ) ) ^ 3 = > x ^ 2 = 4 ^ 3 = 36 = > x = 6 answer d"
Answer: d
Problem: a cube with its sides numbered 1 through 6 is rolled twice , first landing on a and then landing on b . if any roll of the cube yields an equal chance of landing on any of the numbers 1 through 6 , what is the probability t that a + b is prime ?
Options: a ) 0 , b ) 1 / 12 , c ) 5 / 12 , d ) 7 / 18 , e ) 4 / 9
Rationale: "total # of outcomes is 6 * 6 = 36 ; favorable outcomes : a - b - - > prime 1 - 1 - - > 2 ; 1 - 2 - - > 3 ; 2 - 1 - - > 3 ; 1 - 4 - - > 5 ; 4 - 1 - - > 5 ; 2 - 3 - - > 5 ; 3 - 2 - - > 5 ; 1 - 6 - - > 7 ; 6 - 1 - - > 7 ; 2 - 5 - - > 7 ; 5 - 2 - - > 7 ; 3 - 4 - - > 7 ; 4 - 3 - - > 7 ; 6 - 5 - - > 11 ; 5 - 6 - - > 11 . total of 15 favorable outcomes t = 15 / 36 . answer : c ."
Answer: c
Problem: a man invested rs . 14400 in rs . 100 shares of a company at 20 % premium . if the company declares 7 % dividend at the end of the year , then how much does he get ?
Options: a ) rs . 500 , b ) rs . 840 , c ) rs . 650 , d ) rs . 720 , e ) none
Rationale: solution number of shares = ( 14400 / 120 ) = 120 . face value = rs . ( 100 x 120 ) = rs . 12000 . annual income = rs . ( 7 / 100 x 12000 ) = rs . 840 . answer b
Answer: b
Problem: a boy standing idle sounds a whistle to his friend at a distance of 1200 m moving away from him in a speeding car at 108 kms / hr . find the duration after which his friend is going to hear him . ( speed of sound = 330 m / sec ) .
Options: a ) 3.6 secs , b ) 4.00 secs , c ) 40 secs , d ) 45 secs , e ) none of these
Rationale: if friend hears sound after t secs , then 330 * t = 1200 + ( 108 * 5 / 18 ) * t 300 t = 1200 t = 4 secs answer : b
Answer: b
Problem: if ' a ' and ' b ' are non - zero numbers such that their sum is 6 times the product , what is the value of 1 / a + 1 / b ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 12
Rationale: a + b = 6 ab 1 / a + 1 / b = ( b + a ) / ( ab ) = 6 . the answer is b .
Answer: b
Problem: two integers are in the ratio of 1 to 4 . if 12 is added to the smaller number , the ratio becomes 1 to 2 . find the larger integer .
Options: a ) 8 , b ) 16 , c ) 32 , d ) 48 , e ) 54
Rationale: one option is to set up the equations and solve : if the ratio of two integers x and y is 1 to 4 , then 4 x = y , where x is the smaller integer . if adding 12 to the smaller integer makes the ratio 1 to 2 , then 2 ( x + 12 ) = y . substituting y = 4 x into the second equation yields 2 x + 24 = 4 x . so , x = 12 ( smaller integer ) and , y = 4 x = 48 ( larger integer ) so d is the correct answer . another option is to test the answer choices . a ) the larger number is 8 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 2 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 2 ) , we get 14 . so , the new ratio is 14 to 8 which is the same as 7 to 4 . no good . we want a resulting ratio of 1 to 2 eliminate a b ) the larger number is 16 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 4 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 4 ) , we get 16 so , the new ratio is 16 to 16 which is 1 to 1 . no good . we want a resulting ratio of 1 to 2 eliminate b c ) the larger number is 32 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 8 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 8 ) , we get 20 so , the new ratio is 20 to 32 which is 5 to 8 . no good . we want a resulting ratio of 1 to 2 eliminate c d ) the larger number is 48 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 12 if 12 is added to the smaller number , the ratio becomes 1 to 2 if we add 12 to the smaller number ( 12 ) , we get 24 so , the new ratio is 24 to 48 . this is the same as the ratio of 1 to 2 therefore ( d ) is correct e ) the larger number is 54 given : the two integers are in the ratio of 1 to 4 so , the smaller number must be 13.5 ( which is not an integer ) since both numbers are integers , the larger number can not be 54 . eliminate e therefore d is the only correct choice .
Answer: d
Problem: if the annual increase in the population of a town is 10 % and the present number of people is 11000 , what will the population be in 2 years ?
Options: a ) 12100 , b ) 15240 , c ) 12456 , d ) 11452 , e ) 13310
Rationale: "the required population is = 11000 ( 1 + 10 / 100 ) ^ 2 = 11000 * 11 / 10 * 11 / 10 = 13310 answer is e"
Answer: e
Problem: shannon and maxine work in the same building and leave work at the same time . shannon lives due north of work and maxine lives due south . the distance between maxine ' s house and shannon ' s house is 60 miles . if they both drive home at the rate 2 r miles per hour , maxine arrives home 30 minutes after shannon . if maxine rider her bike home at the rate of r per hour and shannon still drives at a rate of 2 r miles per hour , shannon arrives home 2 hours before maxine . how far does maxine live from work ?
Options: a ) 20 , b ) 34 , c ) 30 , d ) 40 , e ) 46
Rationale: "nice question + 1 we have that x / 24 - ( 60 - x ) / 2 r = 30 also x / r - ( 60 - x ) / 2 r = 120 so we get that 2 x - 60 = 80 r 3 x - 60 = 240 r get rid of r 120 = 3 x x = 30 hence answer is c"
Answer: c
Problem: the owner of a furniture shop charges his customer 15 % more than the cost price . if a customer paid rs . 6400 for a computer table , then what was the cost price of the computer table ?
Options: a ) rs . 5565 , b ) rs . 6298 , c ) rs . 6290 , d ) rs . 6725 , e ) rs . 6708
Rationale: "cp = sp * ( 100 / ( 100 + profit % ) ) = 6400 ( 100 / 115 ) = rs . 5565 . answer : a"
Answer: a
Problem: a train speeds past a pole in 15 seconds and a platform 140 meters long in 25 seconds . what is the length of the train ( in meters ) ?
Options: a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 230
Rationale: "let the length of the train be x meters . the speed of the train is x / 15 . then , x + 140 = 25 * ( x / 15 ) 10 x = 2100 x = 210 meters the answer is c ."
Answer: c
Problem: it takes 3 workers a total of 15 hours to build a giant machine with each worker working at the same rate . if 5 workers start to build the machine at 11 : 00 am , and one extra worker per hour is added beginning at 1 : 00 pm , at what time will the machine be complete ?
Options: a ) 4 : 30 , b ) 4 : 45 , c ) 5 : 00 , d ) 5 : 15 , e ) 5 : 30
Rationale: "3 workers build 1 / 15 of a machine in one hour . 1 worker builds 1 / 45 of a machine in one hour . in the first 2 hours , 5 workers build 5 * ( 1 / 45 ) * 2 = 10 / 45 of a machine . from 1 : 00 to 2 : 00 , 6 workers build another 6 / 45 . the total is 16 / 45 . from 2 : 00 to 3 : 00 , 7 workers build another 7 / 45 . the total is 23 / 45 . from 3 : 00 to 4 : 00 , 8 workers build another 8 / 45 . the total is 31 / 45 . from 4 : 00 to 5 : 00 , 9 workers build another 9 / 45 . the total is 40 / 45 . to build another 5 / 45 , 10 workers need ( 5 / 10 ) * 60 minutes which is 30 minutes . the machine is complete at 5 : 30 . the answer is e ."
Answer: e
Problem: on the number line , if x is halfway between - 11 and 5 , and if y is halfway between - 3 and 7 , what number is halfway between x and y ?
Options: a ) - 1.5 , b ) - 0.5 , c ) 0.5 , d ) 1.5 , e ) 2.5
Rationale: "x = - 3 and y = 2 . the answer is b ."
Answer: b
Problem: john and david work at a hospital with 4 other workers . for an internal review , 2 of the 4 workers will be randomly chosen to be interviewed . what is the probability that john and david will both be chosen ?
Options: a ) 1 / 14 , b ) 1 / 20 , c ) 1 / 13 , d ) 1 / 7 , e ) 1 / 6
Rationale: "probability that john and david will both be chosen out of 8 workers = ( 2 / 4 ) * ( 1 / 3 ) = 1 / 6 answer e"
Answer: e
Problem: if w / x = 5 / 7 and w / y = 4 / 7 , then ( x + y ) / y =
Options: a ) 1 / 2 , b ) 7 / 3 , c ) 6 / 7 , d ) 1 / 5 , e ) 11 / 13
Rationale: "ratio 1 : 7 w = 5 x ratio 2 : 7 w = 4 y 5 x = 4 y x = 4 y / 3 ( x + y ) / y = ( ( 4 y / 3 ) + y ) / y = y ( 4 / 3 + 1 ) / y = 7 / 3 answer is b"
Answer: b
Problem: a worker ' s take - home pay last year was the same each month , and she saved the same fraction of her take - home pay each month . the total amount of money that she had saved at the end of the year was 6 times the amount of that portion of her monthly take - home pay that she did not save . if all the money that she saved last year was from her take - home pay , what fraction of her take - home pay did she save each month ?
Options: a ) 1 / 6 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 1 / 2
Rationale: "let x be the fraction of her take - home pay that the worker saved . let p be the monthly pay . 12 xp = 6 ( 1 - x ) p 12 xp = 6 p - 6 xp 18 xp = 6 p x = 1 / 3 the answer is d ."
Answer: d
Problem: the product of two numbers is 4107 . if the h . c . f of these numbers is 37 , then the greater number is :
Options: a ) 101 , b ) 107 , c ) 111 , d ) 112 , e ) 113
Rationale: "let the numbers be 37 a and 37 b . then , 37 a * 37 b = 4107 = > ab = 3 now , co - primes with product 3 are ( 1 , 3 ) . so , the required numbers are ( 37 * 1 , 37 * 3 ) i . e . , ( 1 , 111 ) . greater number = 111 . answer : c"
Answer: c
Problem: marts income is 60 percent more than tims income and tims income is 40 percent less than juans income . what percentage of juans income is marts income
Options: a ) 124 % , b ) 120 % , c ) 96 % , d ) 80 % , e ) 64 %
Rationale: "tim = 100 mary ' s income is 60 percent more than tims income ; mary ' s income = t + 0.6 t = 1.6 t = 1.6 * 100 = 160 tims income is 40 percent less than juans income . 100 is 40 % less than juan ' s income 100 = j - 0.4 j 100 = 0.6 j j = 100 / 0.6 = 1000 / 6 what percentage of juans income is marts income ( 160 / ( 1000 / 6 ) ) * 100 = ( 160 * 6 * 100 ) / 1000 = 96 % answer : c"
Answer: c
Problem: on a trip , a cyclist averaged 8 miles per hour for the first 12 miles and 12 miles per hour for the remaining 24 miles . if the cyclist returned immediately via the same route and took a total of 7.5 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?
Options: a ) 9 , b ) 10 , c ) 11 , d ) 12 , e ) 13
Rationale: "the time to go 36 miles was 12 / 8 + 24 / 12 = 1.5 + 2 = 3.5 hours . the average speed for the return trip was 36 miles / 4 hours = 9 mph . the answer is a ."
Answer: a
Problem: the price of a t . v . set worth rs . 20000 is to be paid in 20 installments of rs . 1000 each . if the rate of interest be 6 % per annum , and the first installment be paid at the time of purchase , then the value of the last installment covering the interest as well will be ?
Options: a ) 19002 , b ) 19028 , c ) 27788 , d ) 19000 , e ) 27711
Rationale: "money paid in cash = rs . 1000 balance payment = ( 20000 - 1000 ) = rs . 19000 answer : d"
Answer: d
Problem: working alone , pump a can empty a pool in 4 hours . working alone , pump b can empty the same pool in 6 hours . working together , how many minutes will it take pump a and pump b to empty the pool ?
Options: a ) 132 , b ) 138 , c ) 144 , d ) 150 , e ) 156
Rationale: pump a can empty ( 1 / 4 ) of the pool per hour . pump b can empty ( 1 / 6 ) of the pool per hour . together the pumps can empty 1 / 4 + 1 / 6 = 5 / 12 of the pool per hour . 1 pool / ( 5 / 12 ) pool per hour = 12 / 5 hours = 144 minutes . the answer is c .
Answer: c
Problem: 1704 x 1704 = ?
Options: a ) a ) 3623216 , b ) b ) 2903616 , c ) c ) 3624316 , d ) d ) 3625116 , e ) e ) 3625216
Rationale: "1704 x 1704 = ( 1704 ) 2 = ( 1700 + 4 ) 2 = ( 1700 ) 2 + ( 4 ) 2 + ( 2 x 1700 x 4 ) = 2890000 + 16 + 13600 . = 2903616 . b )"
Answer: b
Problem: the radius of a semi circle is 6.83 cm then its perimeter is ?
Options: a ) 32.52 , b ) 32.47 , c ) 34.97 , d ) 32.92 , e ) 32.33
Rationale: "36 / 7 r = 6.3 = 34.97 answer : c"
Answer: c
Problem: joan took out a mortgage from hel local bank . each monthly mortgage payment she makes must be triple the amount of the previous month ' s payment . if her first payment is $ 100 , and the total amount she must pay back is $ 109300 , how many months will it take joan to pay back her mortgage ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 11 , e ) 13
Rationale: "joan starts off with 100 $ . . which is to be tripled every month her monthly payments look like this : 100 , 300 , 900 , 2700 . . . . . . . . . upto 109300 this can be re written as : 100 x 1 , 100 x 3 , 100 x 9 , 100 x 27 . . . . . . 100 x 1093 so we have 1 , 3 , 9 , 27 . . . . . 109300 in gp we know that a = 1 , and r = 3 ( its easy to figure it out by looking at the question , but regardless of it being mentioned in the question we can still compute the value of r using the formula tn = a 3 ^ n - 1 . . . ) therefore to find the sum of n terms of a gp we use this formula : sn = a ( 1 - r ^ n ) / 1 - r using this and plugging in the information we get . . . 1093 = 1 - 3 ^ n / 1 - 3 ; 1 - 3 ^ n / - 2 cross multiplying we get 1093 x - 2 = 1 - 3 ^ n - 2186 = 1 - 3 ^ n - 2187 = - 3 ^ n 2187 = 3 ^ n ( negatives cancel out ) 2187 can also be re written as 3 ^ 7 therefore ; 3 ^ 7 = 3 ^ n thus n = 7 ( a )"
Answer: a
Problem: jerry began driving from home on a trip averaging 30 miles per hour . how many miles per hour must carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after jerry ?
Options: a ) 35 , b ) 55 , c ) 39 , d ) 40 , e ) 60
Rationale: carla starts 30 minutes later and it takes 3 hr for carla to meet jerry so jerry total time travelled = 3 hr + 30 minutes jerry distance = 30 * ( 3 1 / 2 ) = 105 so carla need to travle 105 to meet jerry in 3 hrs speed of carla = 105 / 3 = 35 miles per hour answer is a
Answer: a
Problem: having scored 97 runs in the 19 th inning , a cricketer increases his average score by 4 . what will be his average score after 19 innings ?
Options: a ) 28 , b ) 27 , c ) 26 , d ) 22 , e ) 25
Rationale: "explanation : let the average score of the first 18 innings be n 18 n + 97 = 19 ( n + 4 ) = > n = 21 so , average score after 19 th innings = x + 4 = 25 . answer : e"
Answer: e
Problem: find the area of a parallelogram with base 22 cm and height 21 cm ?
Options: a ) 462 cm 2 , b ) 478 cm 2 , c ) 490 cm 2 , d ) 268 cm 2 , e ) 668 cm 2
Rationale: "area of a parallelogram = base * height = 22 * 21 = 462 cm 2 answer : a"
Answer: a
Problem: the population of a town increased from 1 , 24,300 to 1 , 62,400 in a decade . the average percent increase of population per year is :
Options: a ) 4.37 % , b ) 4 % , c ) 2.3 % , d ) 3.75 % , e ) none
Rationale: "explanation : increase in 10 years = ( 162400 - 124300 ) = 87500 . increase % = ( 38100 / 162400 x 100 ) % = 23 % . required average = ( 23 / 10 ) % = 2.3 % . answer : option c"
Answer: c
Problem: 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 ?
Options: a ) 5 hours , b ) 1 hours , c ) 3 hours , d ) 2 hours , e ) 4 hours
Rationale: 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
Answer: c
Problem: if z is a multiple of 7899 , what is the remainder when z ^ 2 is divided by 9 ?
Options: a ) 0 , b ) 2 , c ) 3 , d ) 6 , e ) 7
Rationale: the sum of the digits is 7 + 8 + 9 + 9 = 33 . thus 3 is a factor of 7899 , so 3 is a factor of z . then 3 ^ 3 = 9 is a factor of z ^ 2 . then the remainder when z ^ 2 is divided by 9 is 0 . the answer is a .
Answer: a
Problem: working alone , printers x , y , and z can do a certain printing job , consisting of a large number of pages , in 12 , 10 , and 20 hours , respectively . what is the ratio of the time it takes printer x to do the job , working alone at its rate , to the time it takes printers y and z to do the job , working together at their individual rates ?
Options: a ) 5 / 3 , b ) 7 / 4 , c ) 9 / 5 , d ) 11 / 6 , e ) 13 / 7
Rationale: "the time it takes printer x is 12 hours . the combined rate of y and z is 1 / 10 + 1 / 20 = 3 / 20 the time it takes y and z is 20 / 3 the ratio of times is 12 / ( 20 / 3 ) = 3 * 12 / 20 = 9 / 5 the answer is c ."
Answer: c
Problem: the width of a rectangular hall is ½ of its length . if the area of the hall is 288 sq . m , what is the difference between its length and breadth ?
Options: a ) 8 m , b ) 10 m , c ) 12 m , d ) 15 m , e ) 17 m
Rationale: "let the length of the hall be x m breadth of the hall = 1 x / 2 m area of the hall = length * breadth 288 = x * 1 x / 2 x ² = 576 x = 24 difference between the length and breadth of the hall = x - 1 x / 2 = x / 2 = 24 / 2 = 12 m answer : c"
Answer: c
Problem: a can contains a mixture of liquids a and b is the ratio 7 : 5 . when 9 litres of mixture are drawn off and the can is filled with b , the ratio of a and b becomes 7 : 9 . how many liter of liquid a was contained by the can initially ?
Options: a ) 10 , b ) 20 , c ) 21 , d ) 25 , e ) 27
Rationale: using the values here might be the most straightforward way for this question . as a : b : : 7 : 5 - - - > only option c is a multiple of 7 and hence it is a good place to start . also a : b : : 7 : 5 means that , a = ( 712 ) * total and b = ( 5 / 12 ) * total if a = 21 , b = 15 - - - > remove 9 litres - - - > you remove ( 7 / 12 ) * 9 of a - - - > a remaining = 21 - ( 7 / 12 ) * 9 = 63 / 4 similarly , for b , you remove ( 5 / 12 ) * 9 - - - > b remaining = 15 - ( 5 / 12 ) * 9 = 45 / 4 and then add 9 more litres of b - - - > 9 + 45 / 4 = 81 / 4 thus a / b ( final ratio ) = ( 45 / 4 ) / ( 81 / 4 ) = 7 : 9 , the same as the final ratio mentioned in the question . hence c is the correct answer . fyi , the algebraic equations will become : a / b = 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) , where 7 x and 5 x are initial quantities of a and b respectively . thus , 7 / 9 = ( 7 x - ( 7 / 12 ) * 9 ) / ( 5 x - ( 5 / 12 ) * 9 + 9 ) - - - > giving you x = 3 . thus a ( original ) = 7 * 3 = 21 . answer : c
Answer: c
Problem: bert and rebecca were looking at the price of a condominium . the price of the condominium was 25 % more than bert had in savings , and separately , the same price was also 50 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 5 , b ) 2 : 5 , c ) 3 : 5 , d ) 4 : 5 , e ) 1 : 1
Rationale: "suppose bert had 100 so price becomes 125 , this 125 = 1.5 times r ' s saving . . so r ' s saving becomes 250 so required ratio is 100 : 250 = 2 : 5 answer : b"
Answer: b