regisss/math_qa huggingface dataset:
Problem: if the simple interest on a certain sum of money for 4 years is one – fifth of the sum , then the rate of interest per annum is
Options: a ) 4 % , b ) 7 % , c ) 6 % , d ) 5 % , e ) 3 %
Rationale: "explanation : let the principal ( p ) be x then , simple interest ( si ) = x / 5 time ( t ) = 4 years rate of interest per annum ( r ) = ( 100 × si ) / pt = ( 100 × ( x / 5 ) / ( x × 4 ) = 20 / 4 = 5 % answer : option d"
Answer: d
Problem: the average of 11 results is 60 . if the average of first 6 results is 58 and that of the last 6 is 63 , find the sixth result ?
Options: a ) 50 , b ) 52 , c ) 65 , d ) 42 , e ) 66
Rationale: sixth result = 58 * 6 + 63 * 6 - 60 * 11 = 66 answer is e
Answer: e
Problem: if a student loses 5 kilograms , he will weigh twice as much as his sister . together they now weigh 116 kilograms . what is the student ' s present weight in kilograms ?
Options: a ) 76 , b ) 77 , c ) 78 , d ) 79 , e ) 80
Rationale: "let x be the weight of the sister . then the student ' s weight is 2 x + 5 . x + ( 2 x + 5 ) = 116 3 x = 111 x = 37 kg then the student ' s weight is 79 kg . the answer is d ."
Answer: d
Problem: a circular path of 13 m radius has marginal walk 2 m wide all round it . find the cost of leveling the walk at 25 p per m 2 ?
Options: a ) rs . 48 , b ) rs . 64 , c ) rs . 44 , d ) rs . 46 , e ) rs . 34
Rationale: "π ( 152 - 132 ) = 176 176 * 1 / 4 = rs . 44 answer : c"
Answer: c
Problem: tom drives from town q to town b , driving at a constant speed of 60 miles per hour . from town b tom immediately continues to town c . the distance between q and b is twice the distance between b and c . if the average speed of the whole journey was 36 mph , then what is tom ' s speed driving from b to c in miles per hour ?
Options: a ) 12 , b ) 20 , c ) 24 , d ) 30 , e ) 36
Rationale: let ' s assume that it takes 4 hours to go from point q to b . then the distance between them becomes 240 which makes distance between b and c 120 . ( 240 + 120 ) / ( 4 + x ) gives us the average speed which is 36 . you find x = 6 . so the question simplifies itself to 120 / 6 = 20 hence the answer is b .
Answer: b
Problem: a watch was sold at a loss of 10 % . if it was sold for rs . 540 more , there would have been a gain of 8 % . what is the cost price ?
Options: a ) 1000 , b ) 2998 , c ) 3000 , d ) 2788 , e ) 2991
Rationale: "90 % 108 % - - - - - - - - 18 % - - - - 540 100 % - - - - ? = > rs . 3000 answer : c"
Answer: c
Problem: a man took a loan from a bank at the rate of 8 % p . a . simple interest . after 3 years he had to pay rs . 5400 interest only for the period . the principal amount borrowed by him was :
Options: a ) rs . 2000 , b ) rs . 10,500 , c ) rs . 15,500 , d ) rs . 22,500 , e ) none
Rationale: solution principal = rs . ( 100 x 5400 / 8 x 3 ) = rs . 22,500 . answer d
Answer: d
Problem: what is the remainder when the number q = 14 ^ 2 * 15 ^ 8 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 4 , e ) 5
Rationale: 14 ^ 2 has units digit 6 15 ^ 8 has units digit 5 thus q = 14 ^ 2 * 15 ^ 8 has units digit 0 and will be divisible by 5 . the remainder will be zero answer : ( a )
Answer: a
Problem: a jar contains 3 black , 3 white and 1 green balls . if you pick two balls at the same time , what ' s the probability that one ball is black and one is white ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 4 / 7 , d ) 3 / 7 , e ) 1 / 2
Rationale: p ( 1 st black , 2 nd white ) = 3 / 7 * 3 / 6 = 9 / 42 ; p ( 1 st white , 2 nd black ) = 3 / 7 * 3 / 6 = 9 / 42 . p = 9 / 42 + 9 / 42 = 18 / 42 = 3 / 7 . answer : d .
Answer: d
Problem: of the two square fields , the area of the one is 1 hectare , while anothe one is broader by 1 % . there differences in area is :
Options: a ) 201 m ( power ) 2
b ) 220 m ( power ) 2
c ) 211 m ( power ) 2
d ) 219 m ( power ) 2
e ) 205 m ( power ) 2
Rationale: area of one square field = 10000 m ( power ) 2 10000 × 1 = 10000 side of this field = √ 10000 m = 100 m side of another square = 101 m difference of areas = [ 101 ( power ) 2 - 100 ( power ) 2 ] m ( power ) 2 [ 101 + 100 ] [ 101 - 100 ] m ( power ) 2 ( 201 ) ( 1 ) m 2 = 201 m ( power ) 2 answer is a .
Answer: a
Problem: if there are 4 peanuts in a box and mary puts 8 more peanuts inside , how many peanuts are in the box ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: "8 + 4 = 12 correct answer is e ) 12"
Answer: e
Problem: rs . 6000 is lent out in two parts . one part is lent at 5 % p . a simple interest and the other is lent at 10 % p . a simple interest . the total interest at the end of one year was rs . 450 . find the ratio of the amounts lent at the lower rate and higher rate of interest ?
Options: a ) 5 : 1 , b ) 5 : 5 , c ) 5 : 8 , d ) 5 : 4 , e ) 5 : 2
Rationale: let the amount lent at 5 % be rs . x amount lent at 10 % is rs . ( 6000 - x ) total interest for one year on the two sums lent = 5 / 100 x + 10 / 100 ( 6000 - x ) = 600 - 1 x / 20 = > 600 - 1 / 20 x = 450 = > x = 3000 amount lent at 10 % = 3000 required ratio = 3000 : 3000 = 5 : 5 answer : b
Answer: b
Problem: if rs . 1440 / - are divided among a , b and c so that a receives 1 / 3 rd as much as b and b receives 1 / 4 th as much as c . the amount b received is ?
Options: a ) 250 , b ) 270 , c ) 310 , d ) 330 , e ) 350
Rationale: a : b : c = 1 : 3 : 12 total parts = 16 b ' s share is = 3 parts 16 - - - - - > 1440 1 - - - - - > 90 3 - - - - - > 270 ( b ' s share is 270 ) b )
Answer: b
Problem: 375 metres long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 15
Rationale: "26 trees have 25 gaps between them , required distance ( 375 / 25 ) = 15 e"
Answer: e
Problem: when toys are grouped into 12 and 18 , always 3 toys remain ungrouped . what is the minimum number of toys to be added so that when they are grouped into 7 , no toys will remain ungrouped ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: t = 12 a + 3 = 18 b + 3 2 a = 3 b - - > min ( a , b ) = ( 3,2 ) so minimum number of toys - - > 12 * 3 + 3 = 39 when toys are grouped into 7 , 4 will remain ungrouped so in order to make another group of 7 toys - - > 7 - 4 = 3 toys at least to be added . answer : d
Answer: d
Problem: in a particular state , 62 % of the counties received some rain on monday , and 54 % of the counties received some rain on tuesday . no rain fell either day in 28 % of the counties in the state . what percent of the counties received some rain on monday and tuesday ?
Options: a ) 25 % , b ) 44 % , c ) 56 % , d ) 62 % , e ) 70 %
Rationale: "62 + 54 + 28 = 144 % the number is 44 % above 100 % because 44 % of the counties were counted twice . the answer is b ."
Answer: b
Problem: the average temperature for monday , tuesday , wednesday and thursday was 48 degrees and for tuesday , wednesday , thursday and friday was 46 degrees . if the temperature on monday was 41 degrees . find the temperature on friday ?
Options: a ) 65 degrees , b ) 73 degrees , c ) 37 degrees , d ) 34 degrees , e ) 33 degrees
Rationale: "m + tu + w + th = 4 * 48 = 192 tu + w + th + f = 4 * 46 = 184 m = 41 tu + w + th = 192 - 41 = 151 f = 184 – 151 = 33 answer : e"
Answer: e
Problem: a courtyard is 18 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 20000 , d ) 27999 , e ) 14400
Rationale: "number of bricks = courtyard area / 1 brick area = ( 1800 × 1600 / 20 × 10 ) = 14400 answer : e"
Answer: e
Problem: a can finish a work in 21 days and b can do the same work in 15 days . b worked for 10 days and left the job . in how many days , a alone can finish the remaining work ?
Options: a ) 6 , b ) 5 , c ) 5.5 , d ) 7 , e ) 8
Rationale: "b ' s 10 day ' s work = ( 1 x 10 ) = 2 . 15 3 remaining work = ( 1 - 2 ) = 1 . 3 3 now , 1 work is done by a in 1 day . 21 therefore 1 work is done by a in ( 21 x 1 ) = 7 days . d"
Answer: d
Problem: a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of man is :
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 96 kg , e ) none of these
Rationale: "solution volume of water displaced = ( 3 × 2 × 0.01 ) m 3 = 0.06 m 3 . ∴ mass of man = volume of water displaced × density of water = ( 0.06 × 100 ) kg = 60 kg . answer b"
Answer: b
Problem: what profit percent is made by selling an article at a certain price , if by selling at 2 / 3 rd of that price , there would be a loss of 16 % ?
Options: a ) 26 % , b ) 28 % , c ) 27 % , d ) 40 % , e ) 70 %
Rationale: "sp 2 = 2 / 3 sp 1 cp = 100 sp 2 = 84 2 / 3 sp 1 = 84 sp 1 = 126 100 - - - 26 = > 26 % answer : a"
Answer: a
Problem: uba capital recently bought brand new vehicles for office use . uba capital only went for toyota and honda and bought less of toyota than honda at the ratio of 4 : 6 . if 40 % of the toyota bought and 60 % of the honda bought were suv ã ¢ â ‚ ¬ â „ ¢ s . how many suv ã ¢ â ‚ ¬ â „ ¢ s did uba capital buy in the aforementioned purchase ?
Options: a ) 66 % , b ) 64 % , c ) 68 % , d ) 52 % , e ) 72 %
Rationale: "let total no of vehicles bought be 100 , toyota 40 and honda 60 , so total number of suv ' s bought for toyota and honda respectively 40 * 40 / 100 = 16 and 60 * 60 / 100 = 36 so total 52 suv ' s were bought out of 100 vehicles bought . . so required % is 52 % answer : d"
Answer: d
Problem: an investor can sell her microtron stock for 36 $ per share and her dynaco stock for 56 $ per share , if she sells 300 shares altogether , some of each stock , at an average price per share of 40 $ , how many shares of dynaco stock has she sold ?
Options: a ) 52 , b ) 75 , c ) 60 , d ) 136 , e ) 184
Rationale: "w 1 / w 2 = ( a 2 - aavg ) / ( aavg - a 1 ) = ( 56 - 40 ) / ( 40 - 36 ) = 16 / 4 = 4 / 1 = number of microtron stocks / number of dynaco stocks so for every 4 microtron stock , she sold 1 dynaco stock . so out of 300 total stocks , ( 1 / 5 ) th i . e . 300 / 5 = 60 must be dynaco stock . answer ( c )"
Answer: c
Problem: if each edge of cube increased by 20 % , the percentage increase in
Options: a ) 42 , b ) 44 , c ) 48 , d ) 45 , e ) 47
Rationale: "100 × ( 120 ) / 100 × ( 120 ) / 100 = 144 = > 44 % answer is b ."
Answer: b
Problem: if 15 % of 40 is greater than 25 % of a number by 2 , then the number is ?
Options: a ) 12 , b ) 8 , c ) 15 , d ) 20 , e ) 16
Rationale: "let the number be x 50 % of 40 - 25 % of x = 2 25 / 100 x = ( 15 / 100 * 40 ) - 2 x / 4 = 4 x = 16 answer is e"
Answer: e
Problem: what is the angle between the hands of a clock when time is 8 : 20 ?
Options: a ) 65 deg , b ) 75 deg , c ) 50 deg , d ) 15 deg , e ) 30 deg
Rationale: "angle between two hands = 20 h - 11 / 2 m = 20 * 8 - 20 * 11 / 2 = 160 - 110 = 50 deg answer : c"
Answer: c
Problem: month average price per dozen april $ 1.2 may $ 1.20 june $ 3.00 the table above shows the average ( arithmetic mean ) price per dozen of the large grade a eggs sold in a certain store during 3 successive months . if 2 / 3 as many dozen were sold in april as in may , and twice as many were sold in june as in april , what was the average price per dozen of the eggs sold over the 3 - month period ?
Options: a ) 1.8 , b ) 2.2 , c ) 2 , d ) 1.9 , e ) 2.4
Rationale: say x dozen eggs were sold in may . then 2 x / 3 dozen eggs were sold in april and 2 * 2 x / 3 = 4 x / 3 dozen eggs were sold in may . total x + 2 x / 3 + 4 x / 3 = 3 x dozen eggs were sold in three months . total sales : 2 x / 3 * 1.2 + x * 1.2 + 4 x / 3 * 3.00 = $ 6.00 x . the average price per dozen 6.00 x / 3 x = $ 2.00 c
Answer: c
Problem: walking 7 / 6 of his usual rate , a boy reaches his school 7 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 28 , c ) 99 , d ) 49 , e ) 66
Rationale: "speed ratio = 1 : 7 / 6 = 6 : 7 time ratio = 7 : 6 1 - - - - - - - - 7 7 - - - - - - - - - ? 49 m answer : d"
Answer: d
Problem: a company received $ 2 million in royalties on the first $ 10 million in sales and then $ 8 million in royalties on the next $ 100 million in sales . by what percent did the ratio of royalties to sales decrease from the first $ 10 million in sales to the next $ 100 million in sales ?
Options: a ) 30 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 70 %
Rationale: first find out ( ratio of royalties to sales ) : 2 : 10 first 0.2 8 : 100 second 0.08 decrease = 0.2 - 0.08 = 0.12 percent = ( 0.12 / 0.20 ) = 60 % . answer : d
Answer: d
Problem: the cost price of a radio is rs . 1500 and it was sold for rs . 1200 , find the loss % ?
Options: a ) 18 , b ) 16 , c ) 26 , d ) 17 , e ) 20
Rationale: "explanation : 1500 - - - - 300 100 - - - - ? = > 20 % answer : e"
Answer: e
Problem: a trailer carries 3 , 4 and 6 crates on a trip . each crate weighs no less than 100 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 100 , b ) 625 , c ) 600 , d ) 7500 , e ) 375
Rationale: "max no . of crates = 6 . max weight = 100 kg max . weight carried = 6 * 100 = 100 kg = a ."
Answer: a
Problem: the toll for crossing a certain bridge is $ 0.70 each crossing . drivers who frequently use the bridge may instead purchase a sticker each month for $ 13.00 and then pay only $ 0.30 each crossing during that month . if a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day , what is the least value of x for which this driver can save money by using the sticker ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 28 , e ) 29
Rationale: "option # 1 : $ 0.75 / crossing . . . . cross twice a day = $ 1.5 / day option # 2 : $ 0.30 / crossing . . . . cross twice a day = $ 0.6 / day + $ 13 one time charge . if we go down the list of possible answers , you can quickly see that 14 days will not be worth purchasing the sticker . 1.5 x 14 ( 21 ) is cheaper than 0.6 x 14 + 13 ( 21.4 ) . . . it ' s pretty close so let ' s see if one more day will make it worth it . . . if we raise the number of days to 15 , the sticker option looks like a better deal . . . 1.5 x 15 ( 22.5 ) vs 0.6 x 15 + 13 ( 22 ) . answer : c"
Answer: c
Problem: zinc and copper are melted together in the ratio 9 : 11 . what is the weight of melted mixture , if 35.1 kg of zinc has been consumed in it ?
Options: a ) 78 kg , b ) 60 kg , c ) 64 kg , d ) 70 kg , e ) none
Rationale: "sol . for 9 kg zinc , mixture melted = ( 9 + 11 ) kg . for 35.1 kg zinc , mixture , melted = [ 20 / 9 x 35.1 ] kg = 78 kg . answer a"
Answer: a
Problem: p and q started a business investing rs . 54,000 and rs . 36,000 respectively . out of a total profit of rs . 18,000 , q ' s share is :
Options: a ) 5980 , b ) 5990 , c ) 6000 , d ) 6010 , e ) 6020
Rationale: "ratio of their shares = 54000 : 27000 = 6 : 3 . q ’ s share = rs . 18000 * 3 / 9 = rs . 6000 answer : c"
Answer: c
Problem: two numbers are respectively 71 % and 80 % more than a third number . the percentage that is first of the second is ?
Options: a ) 4 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "i ii iii 171 180 100 180 - - - - - - - - - - 171 100 - - - - - - - - - - - ? = > 5 % answer : b"
Answer: b
Problem: a machine , working at a constant rate , manufactures 20 candles in 40 minutes . how many candles does it make in 1 hr 20 min ?
Options: a ) 25 , b ) 30 , c ) 40 , d ) 45 , e ) 50
Rationale: "change 1 hr 20 min to 80 min . for this , we need to set up a simple proportion of staplers per time 20 / 40 = s / 80 the absolutely worst thing you could do at this point in the problem is to cross - multiply . that would be a supremely unstrategic move . instead , cancel before you multiply . for what we can and can ’ t cancel in a proportion , seethis post . we can cancel the factor of 10 in the 20 and 40 . 2 / 4 = s / 80 1 / 2 = s / 80 ; 1 / 2 * 2 = s / 80 * 2 1 / 1 = s / 40 now that the fraction is entirely simplified , we can cross - multiply . s = 1 * 40 = 40 the machine would be 40 candles in 1 hr 20 min . answer : c ."
Answer: c
Problem: a person can swim in still water at 4 km / h . if the speed of water 2 km / h , how many hours will the man take to swim back against the current for 8 km ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 9 , e ) 6
Rationale: "m = 4 s = 2 us = 4 - 2 = 2 d = 8 t = 8 / 2 = 4 answer : a"
Answer: a
Problem: if a and b are both odd prime numbers and a < b , then how many different positive integer factors does 2 ab have ?
Options: a ) 3 , b ) 4 , c ) 6 , d ) 8 , e ) 12
Rationale: a and b are both odd prime numbers - it means either a or b is not 2 and since prime numbers have only two factors - 1 and the number itself a and b each will have ( 1 + 1 ) = 2 factors hence 2 ab will have ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 8 factors d is the answer
Answer: d
Problem: rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 130 . how much was lent at 5 % ?
Options: a ) 2000 , b ) 2777 , c ) 2688 , d ) 1000 , e ) 2871
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 130 x = 2000 answer : a"
Answer: a
Problem: find the lowest common multiple of 15 , 25 and 35 .
Options: a ) 360 , b ) 420 , c ) 510 , d ) 525 , e ) 280
Rationale: "lcm = 3 * 5 * 5 * 7 = 525 . answer is d"
Answer: d
Problem: a person travels equal distances with speeds of 5 km / hr , 10 km / hr , 15 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 1500 mts , c ) 1600 mts , d ) 2 km , e ) 1250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 5 ) + ( x / 10 ) + ( x / 15 ) = 11 / 60 x = 0.5 total distance = 3 * 0.5 = 1.5 km = 1500 meters correct option is b"
Answer: b
Problem: a charitable woman gave one penny more than half pennies in her purse to a farmer . afterwards she came across a beggar whom she gave 2 pennies more than half of what she had in her purse . in the end she gave 3 pennies more than half of what she had in her purse and left with a penny with her to a boy . find what she had in the beginning ?
Options: a ) 41 , b ) 42 , c ) 43 , d ) 44 , e ) 45
Rationale: she gave 1 penny more than the half in the purse i . e ( x / 2 + 1 ) now she is left with : : ( x - ( x / 2 + 1 ) ) = ( x - 2 ) / 2 now to the beggar : : she gave 2 pennies more than the half in the purse i . e ( x - 2 ) / 4 + 2 and she is left with : : ( ( x - 2 ) / 2 ) - ( ( x - 2 ) / 4 + 2 ) = ( x - 10 ) / 4 now at last sh gave 3 pennies more then the half she was left with i . e ( ( x - 10 ) / 8 + 3 ) = a so she is left with ( x - 10 ) / 4 - a = ( x - 34 ) / 8 now acc . to quest ( x - 34 ) / 8 = 1 hence x = 42 answer : b
Answer: b
Problem: if x , y , and z are positive integers , and 2 x = 5 y = 6 z , then the least possible value of x + y + z is
Options: a ) 15 , b ) 26 , c ) 37 , d ) 42 , e ) 60
Rationale: "take lcm of 2,5 and 6 = 30 now 2 x = 30 = > x = 15 5 y = 30 = > y = 6 6 z = 30 = > z = 5 15 + 6 + 5 = 26 . option b ."
Answer: b
Problem: a rectangular circuit board is designed to have width w inches , perimeter p inches , and area x square inches . which of the following equations must be true ?
Options: a ) w ^ 2 + pw + x = 0
b ) w ^ 2 - pw + 2 x = 0
c ) 2 w ^ 2 + pw + 2 x = 0
d ) 2 w ^ 2 - pw - 2 x = 0
e ) 2 w ^ 2 - pw + 2 x = 0
Rationale: notice that we can discard options a , and c right away . the sum of 3 positive values can not be 0 . now , assume : width = w = 1 inchand length = 1 inch ; perimeter = p = 4 inches ; area = x = 1 square inches . plug the values of w , p , and x into the answer choices : only for e 2 w ^ 2 - pw + 2 x = 2 - 4 + 2 = 0 . answer : e .
Answer: e
Problem: one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 80000 as total savings , how much has he saved in public provident fund ?
Options: a ) 81000 , b ) 85000 , c ) 75000 , d ) 72000 , e ) 77000
Rationale: let savings in national savings certificate = x and savings in public provident fund = ( 180000 - x ) 1 / 3 x = 1 / 2 ( 180000 − x ) ⇒ 2 x = 3 ( 180000 − x ) ⇒ 2 x = 540000 − 3 x ⇒ 5 x = 540000 ⇒ x = 540000 / 5 = 108000 savings in public provident fund = ( 180000 - 108000 ) = 72000 answer is d .
Answer: d
Problem: the weight of every type a widget is the same , the weight of every type b widget is the same , and the weight of every type c widget is the same . if the weight of 7 type a widgets is equal to the weight of 2 type b widgets , and the weight of 3 type b widgets is equal to the weight of 7 type c widgets . what is the ratio of the total weight of 1 type a widget and 1 type b widget , to the total weight of 1 type b widget and 1 type c widget ?
Options: a ) 1 : 2 , b ) 3 : 4 , c ) 5 : 6 , d ) 7 : 8 , e ) 9 : 10
Rationale: 3 b = 7 c and so b = 7 c / 3 7 a = 2 b and so a = 2 b / 7 = 2 c / 3 a + b = 2 c / 3 + 7 c / 3 = 9 c / 3 b + c = 7 c / 3 + c = 10 c / 3 the ratio of a + b : b + c = 9 : 10 the answer is e .
Answer: e
Problem: what least number must be added to 1170 , so that the sum is completely divisible by 23 ?
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 11
Rationale: "51 * 23 = 1173 1173 - 1170 = 3 answer : a"
Answer: a
Problem: in a 500 member association consisting of men and women , exactly 20 % of men and exactly 50 % women are homeowners . what is the least number of members who are homeowners ?
Options: a ) 149 , b ) 147 , c ) 101 , d ) 143 , e ) 141
Rationale: "solution simple out of 500 20 % are male i . e 100 and 50 % are female i . e 250 , so total homeowner is 350 . now min number homeowner is 100 and max is 250 so question ask us to find least and 101 has least value among all option . so ans is 101 . ans : c"
Answer: c
Problem: two trains 140 m and 160 m long run at the speed of 60 kmph and 48 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10 sec , d ) 12.6 sec , e ) 15 sec
Rationale: "relative speed = 60 + 48 = 108 kmph * 5 / 18 = 30 m / s distance covered in crossing each other = 140 + 160 = 300 m required time = 300 * 1 / 30 = 10 sec answer is c"
Answer: c
Problem: there are 408 boys and 192 girls in a school which are to be divided into equal sections of either boys or girls alone . find the total number of sections thus formed .
Options: a ) 25 , b ) 32 , c ) 35 , d ) 30 , e ) 45
Rationale: "explanation : hcf ( 408 , 192 ) = 24 the number of boys or girls that can be placed in a section = 24 . thus the total number of sections is given by 408 / 24 + 192 / 24 = 17 + 8 = 25 answer : a"
Answer: a
Problem: joe needs to paint all the airplane hangars at the airport , so he buys 360 gallons of paint to do the job . during the first week , he uses 1 / 4 of all the paint . during the second week , he uses 1 / 7 of the remaining paint . how many gallons of paint has joe used ?
Options: a ) 18 , b ) 128 , c ) 175 , d ) 216 , e ) 250
Rationale: "total paint initially = 360 gallons paint used in the first week = ( 1 / 4 ) * 360 = 90 gallons . remaning paint = 270 gallons paint used in the second week = ( 1 / 7 ) * 270 = 38 gallons total paint used = 128 gallons . option b"
Answer: b
Problem: the sale price sarees listed for rs . 540 after successive discount is 5 % and 2 % is ?
Options: a ) 288 , b ) 500 , c ) 502 , d ) 540 , e ) 262
Rationale: "540 * ( 95 / 100 ) * ( 98 / 100 ) = 502 answer : c"
Answer: c
Problem: a bag contains 3 red , 2 blue and 3 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 21 , b ) 3 / 41 , c ) 3 / 28 , d ) 3 / 31 , e ) 5 / 32
Rationale: "p ( both are red ) , = 3 c 2 / 8 c 2 = 6 c 213 c 2 = 3 / 28 c"
Answer: c
Problem: company p had 15 percent more employees in december than it had in january . if company p had 480 employees in december , how many employees did it have in january ?
Options: a ) 391 , b ) 417 , c ) 410 , d ) 423 , e ) 445
Rationale: "d = number of employees in december j = number of employees in january j x 1.15 = d j x 1.15 = 480 j = 480 / 1.15 j = 48,000 / 115 = 417 thus b is the correct answer ."
Answer: b
Problem: at deluxe paint store , fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint . mauve paint is made by mixing 3 parts of red paint with 5 parts blue paint . how many liters of blue paint must be added to 40 liters of fuchsia to change it to mauve paint ?
Options: a ) 9 , b ) 12 , c ) 15 , d ) 16 , e ) 26.6
Rationale: "in 40 liters , red = 5 / 8 * 40 = 25 and blue = 15 so , 25 / ( 15 + x ) = 3 / 5 or , x = 26.6 ( answer e )"
Answer: e
Problem: how many 4 digits number contain the number 2 .
Options: a ) 3170 , b ) 3172 , c ) 3174 , d ) 3168 , e ) 3167
Rationale: "total no . of 4 digit nos are 9000 ( btwn 1000 and 9999 ) . consider the case where the nos contain no 2 in it . so units place can be filled in 9 ways ( 0 , 1,3 , 4,5 , 6,7 , 8,9 ) smlry , tenths place in 9 ways hunderedths place in 9 ways thousands place can be filled in 8 ways only ( because 0 can not come ) so total nos are ( 9000 - ( 8 * 9 * 9 * 9 ) ) = 3168 answer : d"
Answer: d
Problem: according to the directions on the can of frozen orange juice concentrate , 1 can of concentrate is to be mixed with 3 cans of water to make orange juice . how many 12 ounces cans of the concentrate are required to prepare 320 6 ounces servings of orange juice ?
Options: a ) a ) 25 , b ) b ) 34 , c ) c ) 50 , d ) d ) 40 , e ) e ) 100
Rationale: its d . total juice rquired = 320 * 6 = 1920 ounce 12 ounce concentate makes = 12 * 4 = 48 ounce juice total cans required = 1920 / 48 = 40 . answer d
Answer: d
Problem: the largest natural number which exactly divides the product of any 4 consecutive natural numbers is
Options: a ) 6 , b ) 12 , c ) 24 , d ) 120 , e ) none
Rationale: sol . required number = 1 × 2 × 3 × 4 = 24 . answer c
Answer: c
Problem: the area of a circle is increased by 1500 % . by what percent has the diameter of the circle increased ?
Options: a ) 100 % , b ) 500 % , c ) 300 % , d ) 600 % , e ) 800 %
Rationale: "the area of the circle is increased by 1500 % , thus the area is increased 16 times . the area of a circle it proportional to the square of the diameter ( area = π d ^ 2 / 4 ) , therefore the diameter must increase 4 times ( diameter increase 4 times = area increase 16 times ) , which is increase by 500 % . answer : b ."
Answer: b
Problem: 16 boys or 24 girls can construct the wall in 6 days . the number of days that 16 boys and 12 girls will take to construct ?
Options: a ) 7 days , b ) 4 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 16 boys + 12 girls = 16 ã — 6 / 4 + 12 = 24 + 12 = 36 girls 4 days to complete the work answer : option b"
Answer: b
Problem: 9873 + x = 13800 , then x is ?
Options: a ) 3327 , b ) 3237 , c ) 3927 , d ) 2337 , e ) none of these
Rationale: "answer x = 13800 - 9873 = 3927 option : c"
Answer: c
Problem: in a sports club with 40 members , 20 play badminton and 18 play tennis and 5 do not play either . how many members play both badminton and tennis ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 3
Rationale: "20 + 18 = 38 but where as total number is 40 - 5 = 35 therefore answer is 38 - 35 = 3 hence answer is e"
Answer: e
Problem: an article is bought for rs . 600 and sold for rs . 300 , find the loss percent ?
Options: a ) 12 % , b ) 16 % , c ) 19 % , d ) 50 % , e ) 60 %
Rationale: "600 - - - - 300 100 - - - - ? = > 50 % answer : d"
Answer: d
Problem: the ratio of 2 numbers is 1 : 2 and their h . c . f . is 10 . their l . c . m . is ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 50 , e ) 40
Rationale: "let the numbers be x and 2 x their h . c . f . = 10 so the numbers are 1 * 10 , 2 * 10 = 10,20 l . c . m . = 20 answer is b"
Answer: b
Problem: a 300 m long train crosses a platform in 33 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 286 m , b ) 250 m , c ) 277 m , d ) 278 m , e ) 267 m
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 33 = 50 / 3 = > x = 250 m . answer : b"
Answer: b
Problem: youseff lives x blocks from his office . it takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work . it is takes him exactly 14 minutes more to walk to work than to ride his bike to work , then x equals ?
Options: a ) 4 , b ) 7 , c ) 10 , d ) 15 , e ) 21
Rationale: please follow posting guidelines , link is in my signatures . as for your question , x / 60 = blocks / time / block = block ^ 2 / time . this is not what you want . you are given x blocks and 60 seconds per block . thus you need to put it as 60 * x to give you units of seconds as you are equating this to 840 ( which is time in seconds . ) . thus the correct equation is : 60 * x - 20 * x = 840 - - - - > 40 x = 840 - > x = 21 . option e
Answer: e
Problem: what sum of money will produce rs . 60 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 337 , b ) 429 , c ) 266 , d ) 288 , e ) 211
Rationale: "60 = ( p * 4 * 7 / 2 ) / 100 p = 429 answer : b"
Answer: b
Problem: a not - so - good clockmaker has four clocks on display in the window . clock # 1 loses 45 minutes every hour . clock # 2 gains 15 minutes every hour relative to clock # 1 ( i . e . , as clock # 1 moves from 12 : 00 to 1 : 00 , clock # 2 moves from 12 : 00 to 1 : 15 ) . clock # 3 loses 20 minutes every hour relative to clock # 2 . finally , clock # 4 gains 20 minutes every hour relative to clock # 3 . if the clockmaker resets all four clocks to the correct time at 12 noon , what time will clock # 4 display after 6 actual hours ( when it is actually 6 : 00 pm that same day ) ?
Options: a ) 5 : 00 , b ) 5 : 34 , c ) 5 : 42 , d ) 6 : 34 , e ) 6 : 24
Rationale: "c 1 loses 15 minutes every hour . so after 60 minutes have passed , c 1 displays that 60 - 15 = 45 minutes have passed . c 2 gains 15 minutes for every 60 minutes displayed on c 1 . thus , the time displayed on c 2 is 75 / 60 = 5 / 4 the time displayed on c 1 . so after 60 minutes have passed , c 2 displays the passing of ( 5 / 4 * 45 ) minutes . c 3 loses 20 minutes for every 60 minutes displayed on c 2 . thus , the time displayed on c 3 is 40 / 60 = 2 / 3 the time displayed on c 2 . so after 60 minutes have passed , c 3 displays the passing of ( 2 / 3 * 5 / 4 * 45 ) minutes . c 4 gains 20 minutes for every 60 minutes displayed on c 3 . thus , the time displayed on c 4 is 80 / 60 = 4 / 3 the time displayed on clock 3 . so after 60 minutes have passed , c 4 displays the passing of 4 / 3 * 2 / 3 * 5 / 4 * 45 = 50 minutes . c 4 loses 10 minutes every hour . in 6 hours , c 4 will lose 6 * 10 = 60 minutes = 1 hour . since the correct time after 6 hours will be 6 pm , c 4 will show a time of 6 - 1 = 6 : 34 pm . the correct answer is d ."
Answer: d
Problem: an woman sitting in a train which is travelling at 25 kmph observes that a goods train travelling in a opposite direction , takes 3 seconds to pass him . if the goods train is 140 m long , find its speed .
Options: a ) 141 , b ) 142 , c ) 143 , d ) 144 , e ) 145
Rationale: "relative speed = ( 140 / 3 ) m / s = ( 140 / 3 ) * ( 18 / 5 ) = 168 kmph speed of goods train = 168 - 25 = 143 kmph answer is c"
Answer: c
Problem: on a trip , a cyclist averaged 12 miles per hour for the first 18 miles and 10 miles per hour for the remaining 18 miles . if the cyclist returned immediately via the same route and took a total of 7.3 hours for the round trip , what was the average speed ( in miles per hour ) for the return trip ?
Options: a ) 8.4 , b ) 8.6 , c ) 8.8 , d ) 9 , e ) 9.2
Rationale: "the time to go 36 miles was 18 / 12 + 18 / 10 = 1.5 + 1.8 = 3.3 hours . the average speed for the return trip was 36 miles / 4 hours = 9 mph . the answer is d ."
Answer: d
Problem: there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the measure q in inches of the width of the foil covered prism ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = q = 10 ans e ."
Answer: e
Problem: in covering a distance of 30 km , arun takes 2 hours more than anil . if arun doubles his speed , then he would take 1 hour less than anil . what is arun ' s speed ?
Options: a ) 2 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let the speed of arun = x kmph and the speed of anil = y kmph distance = 30 km we know that distancespeed = timehence 30 x − 30 y = 2 . . . . . . . . . . . ( equation 1 ) 30 y − 302 x = 1 . . . . . . . . . . . ( equation 2 ) equation 1 + equation 2 ⇒ 30 x − 302 x = 3 ⇒ 302 x = 3 ⇒ 15 x = 3 ⇒ 5 x = 1 ⇒ x = 5 hence arun ' s speed = 5 kmph answer : b"
Answer: b
Problem: the racing magic takes 150 seconds to circle the racing track once . the charging bull makes 40 rounds of the track in an hour . if they left the starting point together , how many minutes will it take for them to meet at the starting point for the second time ?
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: "time taken by racing magic to make one circle = 150 seconds time taken bycharging bullto make one circle = 60 mins / 40 = 1.5 mins = 90 seconds lcm of 90 and 150 seconds = 450 seconds time taken for them to meet at the starting point for the second time = 2 * 450 = 900 seconds = 15 mins answer e"
Answer: e
Problem: the sector of a circle has radius of 21 cm and central angle 144 o . find its perimeter ?
Options: a ) 80 cm , b ) 82 cm , c ) 90 cm , d ) 94.8 cm , e ) 95 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 144 / 360 * 2 * 22 / 7 * 21 ) + 2 ( 21 ) = 52.8 + 42 = 94.8 cm answer : d"
Answer: d
Problem: a grocer is storing soap boxes in cartons that measure 25 inches by 42 inches by 60 inches . if the measurement of each soap box is 7 inches by 6 inches by 5 inches , then what is the maximum number of soap boxes that can be placed in each carton ?
Options: a ) 210 , b ) 252 , c ) 280 , d ) 300 , e ) 420
Rationale: maximum number of soap boxes that can be placed in each carton = volume of each carton / volume of each box = ( 25 * 42 * 60 ) / ( 7 * 6 * 5 ) = 300 answer : d
Answer: d
Problem: how many multiples of 10 are there between 100 and 10000 ( both are inclusive ) ?
Options: a ) 456 , b ) 789 , c ) 991 , d ) 1020 , e ) 1100
Rationale: "the answer is ( 10000 - 100 ) / 10 + 1 = 991 answer is c"
Answer: c
Problem: there are 20 poles with a constant distance between each pole . a car takes 25 second to reach the 12 th pole . how much will it take to reach the last pole .
Options: a ) 43.1543 , b ) 43.1818 , c ) 43.45128 , d ) 43.41288 , e ) 43.41222
Rationale: "assuming the car starts at the first pole . to reach the 12 th pole , the car need to travel 11 poles ( the first pole does n ' t count , as the car is already there ) . 11 poles 25 seconds 1 pole ( 25 / 11 ) seconds to reach the last ( 20 th ) pole , the car needs to travel 19 poles . 19 pole 19 x ( 25 / 11 ) seconds = 43.1818 seconds answer : b"
Answer: b
Problem: if x > 0 , x / 25 + x / 20 is what percent of x ?
Options: a ) 5 % , b ) 25 % , c ) 37 1 / 2 % , d ) 60 % , e ) 75 %
Rationale: "just plug and chug . since the question asks for percents , pick 100 . ( but any number will do . ) 100 / 25 + 100 / 20 = 4 + 5 = 9 9 is 9 % of 100 = a ."
Answer: a
Problem: two numbers are in the ratio of 5 : 7 . if 25 is subtracted from each number , they are in the ratio of 5 : 9 . what are the two numbers ?
Options: a ) 45 , 63 , b ) 50 , 70 , c ) 55 , 77 , d ) 60 , 84 , e ) 65 , 91
Rationale: "( 5 x - 25 ) : ( 7 x - 25 ) = 5 y : 9 y 5 x - 25 = 5 y 7 x - 25 = 9 y 175 - 125 = 45 y - 35 y 50 = 10 y y = 5 5 x - 25 = 25 x = 10 the two numbers are 5 x and 7 x which are 50 and 70 . the answer is b ."
Answer: b
Problem: two employees x and y are paid a total of rs . 572 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 260 , e ) s . 300
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 572 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 572 ⇒ y [ 12 / 10 + 1 ] = 572 ⇒ 22 y / 10 = 572 ⇒ 22 y = 5720 ⇒ y = 5720 / 22 = 520 / 2 = rs . 260 d"
Answer: d
Problem: a certain lab experiments with white and brown mice only . in one experiment , 3 / 7 of the mice are white . if therare 24 brown mice in the experiment , how many mice in total are in the experiment ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 12 , e ) 20
Rationale: "let total number of mice = m number of white mice = 3 / 7 m number of brown mice = 4 / 3 m = 18 = > m = 18 answer c"
Answer: c
Problem: how many of the positive factors of 42 , 104 and how many common factors are there in numbers ?
Options: a ) 4 , b ) 2 , c ) 3 , d ) 5 , e ) 1
Rationale: "factors of 42 - 1,2 , 3,6 , 7,14 , 21,42 factors of 104 - 1,2 , 4,8 , 13,26 , 52,104 comparing both , we have two common factors of 40 and 104 - 1,2 , answer ( b )"
Answer: b
Problem: a batsman scored 130 runs which included 3 boundaries and 8 sixes . what percent of his total score did he make by running between the wickets ?
Options: a ) 45 ( 4 / 11 ) % , b ) 45 % , c ) 53 ( 11 / 13 ) % , d ) 44 ( 5 / 11 ) % , e ) none of these
Rationale: "explanation : total runs scored = 130 total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60 total runs scored by running between the wickets = 130 - 60 = 70 required % = ( 70 / 130 ) × 100 = 700 / 13 = 53 ( 11 / 13 ) % answer : option c"
Answer: c
Problem: a sum of money at simple interest amounts to $ 815 in 3 years and to $ 854 in 4 years . the sum is :
Options: a ) $ 153 , b ) $ 698 , c ) $ 398 , d ) $ 549 , e ) $ 675
Rationale: "b $ 698 s . i . for 1 year = $ ( 854 - 815 ) = $ 39 . s . i . for 3 years = $ ( 39 x 3 ) = $ 117 . principal = $ ( 815 - 117 ) = $ 698 ."
Answer: b
Problem: along a yard 434 metres long , 32 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between two consecutive trees
Options: a ) 14 , b ) 16 , c ) 10 , d ) 11 , e ) 12
Rationale: "explanation : 32 trees have 31 gaps between them , required distance ( 434 / 31 ) = 14 option a"
Answer: a
Problem: a shopkeeper sells 20 % of his stock at 10 % profit ans sells the remaining at a loss of 5 % . he incurred an overall loss of rs . 300 . find the total worth of the stock ?
Options: a ) 20029 , b ) 20000 , c ) 20289 , d ) 20027 , e ) 15000
Rationale: "let the total worth of the stock be rs . x . the sp of 20 % of the stock = 1 / 5 * x * 1.1 = 11 x / 50 the sp of 80 % of the stock = 4 / 5 * x * 0.95 = 19 x / 25 = 38 x / 50 total sp = 11 x / 50 + 38 x / 50 = 49 x / 50 overall loss = x - 49 x / 50 = x / 50 x / 50 = 300 = > x = 15000 answer : e"
Answer: e
Problem: the product of a and b is equal to 11 more than twice the sum of a and b . if b = 7 , what is the value of b - a ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35
Rationale: "given : ab = 2 ( a + b ) + 11 and b = 7 hence 7 a = 2 a + 14 + 11 5 a = 25 , a = 5 ( a potential trap . do not get excited here . we need to find b - a , not a ) b - a = 7 - 5 = 2 correct option : a"
Answer: a
Problem: thirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 5 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?
Options: a ) 60 , b ) 80 , c ) 50 , d ) 120 , e ) 140
Rationale: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 5 = 42 members have not passed the test , thus 0.7 * total = 35 - - > total = 50 . answer : c ."
Answer: c
Problem: a is 2 times as fast as b . a alone can do the work in 20 days . if a and b work on alternative days , beginning with a , in how many days will the work be completed ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 24 , e ) 26
Rationale: "a can finish 1 work in 20 days b can finish 1 / 2 work in 20 days - since a is 2 faster than b this means b can finish 1 work in 20 * 2 days = 40 days now using the awesome gmat formula when two machines work together they can finish the job in = ab / ( a + b ) = 20 * 40 / ( 20 + 40 ) = 13 days since they alternate on days , it will take them double this time so total time = 13 * 2 = 26 days so answer is e"
Answer: e
Problem: how many different positive integers are factors of 125 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "125 = 5 * 25 answer : b"
Answer: b
Problem: what is the greatest integer m for which the number 30 ! / 10 ^ m is an integer ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "10 ^ m = 2 ^ m * 5 ^ m . let ' s figure out how many 5 ' s are in the prime factorization of 30 ! the multiples of 5 are : 5 , 10 , 15 , 20 , 5 * 5 , 30 . thus 5 ^ 7 will divide 30 ! but 5 ^ 8 will not . clearly 2 ^ 7 will divide 30 ! so m = 7 is the largest possible integer . the answer is a ."
Answer: a
Problem: the smallest 5 digit number exactly divisible by 41 is ?
Options: a ) 10003 , b ) 10004 , c ) 10007 , d ) 10009 , e ) 10010
Rationale: "the smallest 5 - digit number = 10000 . 41 ) 10000 ( 243 82 - - - 180 164 - - - - 160 123 - - - 37 - - - required number = 10000 + ( 41 - 37 ) = 10004 . option b"
Answer: b
Problem: 9 men are equal to as many women as are equal to 7 boys . all of them earn rs . 216 only . men ’ s wages are ?
Options: a ) 6 , b ) 5 , c ) 2 , d ) 8 , e ) 2
Rationale: "9 m = xw = 7 b 9 m + xw + 7 b - - - - - 216 rs . 9 m + 9 m + 9 m - - - - - 216 rs . 27 m - - - - - - 216 rs . = > 1 m = 8 rs . answer : d"
Answer: d
Problem: the speed at which a man can row a boat in still water is 20 kmph . if he rows downstream , where the speed of current is 4 kmph , what time will he take to cover 80 metres ?
Options: a ) 10.51 , b ) 11.51 , c ) 9.51 , d ) 13.51 , e ) 15.51
Rationale: speed of the boat downstream = 20 + 4 = 24 kmph = 24 * 5 / 18 = 6.66 m / s hence time taken to cover 70 m = 70 / 6.66 = 10.51 seconds . answer : a
Answer: a
Problem: the sides of a triangle are in the ratio 5 : 12 : 13 and its perimeter is 360 m , its area is ?
Options: a ) 180 , b ) 882 , c ) 277 , d ) 261 , e ) 281
Rationale: "5 x + 12 x + 13 x = 360 = > x = 12 a = 60 , b = 144 , c = 156 s = ( 60 + 144 + 156 ) / 2 = 180 answer : a"
Answer: a
Problem: the cost of 2 chairs and 3 tables is rs . 1800 . the cost of 3 chairs and 2 tables is rs . 1200 . the cost of each table is more than that of each chair by ?
Options: a ) 228 , b ) 287 , c ) 277 , d ) 188 , e ) 600
Rationale: "explanation : 2 c + 3 t = 1800 - - - ( 1 ) 3 c + 3 t = 1200 - - - ( 2 ) subtracting 2 nd from 1 st , we get - c + t = 600 = > t - c = 600 answer : e"
Answer: e
Problem: jim is able to sell a hand - carved statue for $ 670 which was a 35 % profit over his cost . how much did the statue originally cost him ?
Options: a ) $ 496.30 , b ) $ 512.40 , c ) $ 555.40 , d ) $ 574.90 , e ) $ 588.20
Rationale: "670 is the final price that is the selling price . now suppose , x is the cost price . therefore 670 = 1.35 * x now while doing x = 670 / 1.35 calculation . i saw that the answer choices begin with 5 . so i did 135 * 5 = 675 . as 670 is less than 675 . therefore the quotient will be less than 5 . which is only in the answer a ."
Answer: a
Problem: a baseball team played 10 games and won 5 . what is the ratio of the number of games played to the number of losses ?
Options: a ) 5 : 1 , b ) 1 : 1 , c ) 20 : 4 , d ) 10 : 3 , e ) 2 : 1
Rationale: the number of games played is 10 . the number of games won is 5 , so 10 - 5 = 5 = number of game losses . answer = ! 0 : 5 = 2 : 1 answer is e
Answer: e
Problem: 3 buffaloes eat as much as 4 cows or 2 oxen . at a farm , there are 15 buffaloes , 8 oxen , and 24 cows . the fodder for these cattle is available for 48 days . if 40 more cows and 15 more buffaloes are brought in , how many days will the fodder last ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: "2 oxen = 3 buffaloes = 4 cows also : 15 buffaloes + 8 oxen + 24 cows = 10 oxen + 8 oxen + 12 oxen = 30 oxen there is enough fodder for 1 oxen for 30 * 48 days . 40 cows + 15 buffaloes = 20 oxen + 10 oxen = 30 oxen the new total is equal to 60 oxen instead of 30 oxen . 30 * 48 / 60 oxen = 24 days the answer is b ."
Answer: b
Problem: cp of 2 buffaloes are $ 30,000 . by selling 1 at a loss of 15 % and other at a profit of 19 % , he foundthat sp of both buffaloes is the same . find the cp of each ?
Options: a ) $ 10,500 , b ) $ 10,500 , c ) $ 11,500 , d ) $ 12,000 , e ) $ 12,500
Rationale: "let the c . p of 1 st buffalo = x ∴ c . p of 2 nd buffalo = 30,000 - x s . p of 1 st buffalo = ( 100 - loss % ) - - - - - - - - - - - - - - - - - - - x c . p 100 s . p = 100 - 15 x - - - - - - - - - - - = 85 x / 100 100 s . p of 2 nd buffalo = ( 100 - profit % ) - - - - - - - - - - - - - - - - - - - - - x c . p 100 s . p = ( 100 + 19 ) ( 30,000 - x ) 119 ( 30,000 - x ) - - - - - - - - - - - - - - - - - - - - = - - - - - - - - - - - - - - - - 100 100 s . p of 1 st buffalo = s . p of 2 nd buffalo 85 x / 100 = 119 ( 30,000 - x ) / 100 ⇒ 85 x = 119 ( 30,000 - x ) ⇒ 85 x = 3 , 570,000 - 119 x ⇒ 85 x + 119 x = 3 , 570,000 ⇒ 204 x = 3 , 570,000 ⇒ x = 3 , 570,000 / 204 ⇒ x = $ 17,500 c . p of 1 st buffalo = $ 17,500 c . p of 2 nd buffalo = 30,000 - 17,500 = $ 12,500 e"
Answer: e
Problem: the purchase price of an article is $ 48 . in order to include 10 % of cost for overhead and to provide $ 12 of net profit , the markup should be
Options: a ) 15 % , b ) 25 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "cost price of article = 48 $ % of overhead cost = 10 net profit = 12 $ we need to calculate % markup net profit as % of cost price = ( 12 / 48 ) * 100 = 25 % total markup should be = 25 + 10 = 35 % answer c"
Answer: c
Problem: in a certain animal population , for each of the first 3 months of life , the probability that an animal will die during that month is 1 / 8 . for a group of 200 newborn members of the population , approximately how many would be expected to survive the first 3 months of life ?
Options: a ) 134 , b ) 146 , c ) 152 , d ) 162 , e ) 170
Rationale: "the probability of survival for each of the first 3 months of life is 1 - 1 / 8 = 7 / 8 , so of 200 newborn 200 * 7 / 8 * 7 / 8 * 7 / 8 = ~ 134 is expected to survive . answer : a ."
Answer: a
Problem: increasing the original price of a certain item by 15 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent ?
Options: a ) 31.25 , b ) 37.5 , c ) 50.0 , d ) 52.5 , e ) 43.75
Rationale: "we ' re told that the original price of an item is increased by 15 % and then that price is increased by 25 % . . . . if . . . . starting value = $ 100 + 15 % = 100 + . 15 ( 100 ) = 115 + 25 % = 115 + . 25 ( 115 ) = 115 + 28.75 = 143.75 the question asks how the final price relates to the original price . this is essentially about percentage change , which means we should use the percentage change formula : percentage change = ( new - old ) / old = difference / original doing either calculation will yield the same result : 43.75 / 100 = 43.75 % final answer : e"
Answer: e
Problem: find the least number must be subtracted from 378461 so that remaining no . is divisible by 13 ?
Options: a ) 4 , b ) 5 , c ) 7 , d ) 6 , e ) 8
Rationale: "on dividing 378461 by 13 we get the remainder 5 , so 5 should be subtracted b"
Answer: b
Problem: the profit earned by selling an article for $ 832 is equal to the loss incurred when the same article is sold for $ 448 . what should be the sale price for making 40 % profit ?
Options: a ) $ 480 , b ) $ 450 , c ) $ 896 , d ) $ 870 , e ) $ 660
Rationale: let c . p . = $ x . then , 832 - x = x - 448 2 x = 1280 = > x = 640 required s . p . = 140 % of $ 640 = $ 896 . c
Answer: c