Cheukting/mathqa huggingface dataset:
Question (probability): a box contains 4 red balls and 4 black balls . one by one , every ball is selected at random without replacement . what is the probability that the fourth ball selected is black ?
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 / 2 , d ) 5 / 8 , e ) 2
Rationale: "my complicated version of your simple approach let the 4 black balls be bbbband 4 red balls be rrrr they can be arranged in 8 slots _ _ _ _ _ _ _ _ in ( 8 ! ) / ( 4 ! x 4 ! ) if the fourth slot is black ball then the arrangement will be to fill _ _ _ b _ _ _ _ we have 7 slots and 3 black ( bbb ) and 4 red ( rrrr ) they can be arranged in ( 7 ! ) / ( 4 ! x 3 ! ) hence required probability = [ ( 8 ! ) / ( 4 ! x 4 ! ) ] / [ ( 7 ! ) / ( 4 ! x 3 ! ) ] = 2 e"
Answer: e
Question (general): if 50 % of ( x - y ) = 30 % of ( x + y ) , then what percent of x is y ?
Options: a ) 20 % , b ) 30 % , c ) 25 % , d ) 15 % , e ) 50 %
Rationale: "50 % of ( x - y ) = 30 % of ( x + y ) 50 / 100 ( x - y ) = 30 / 100 ( x + y ) x = 4 y required percentage = y / x * 100 = y / 4 y * 100 = 25 % answer is c"
Answer: c
Question (general): 30 ^ 10 / 180 ^ 5 = ?
Options: a ) 5 ^ 5 , b ) 5 ^ 6 , c ) 3 ^ 6 , d ) 6 ^ 3 , e ) 15 ^ 3
Rationale: "30 ^ 10 / 180 ^ 5 = ? a . 5 ^ 5 b . 5 ^ 6 c . 3 ^ 6 d . 6 ^ 3 e . 15 ^ 3 - > 30 ^ 10 / 180 ^ 5 = ( 30 ^ 10 ) / ( 6 ^ 5 ) ( 30 ^ 5 ) = ( 30 ^ 5 ) / ( 6 ^ 5 ) = ( 6 ^ 5 ) ( 5 ^ 5 ) / ( 6 ^ 5 ) = 5 ^ 5 . thus , a is the answer ."
Answer: a
Question (general): an army ’ s recruitment process included n rounds of selection tasks . for the first a rounds , the rejection percentage was 60 percent per round . for the next b rounds , the rejection percentage was 50 percent per round and for the remaining rounds , the selection percentage was 70 percent per round . if there were 100000 people who applied for the army and 245 were finally selected , what was the value of n ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: fastly i reduce 60 % till it gets closer to our required 2000 candidates step ( 1 ) 40000 accepted . step ( 2 ) another 40 % of 40000 = 16000 accepted . here it is quiet observable that if we further deduct candidate by 60 % it would change our probablity of easy going 2000 candidate . so i would get to second stage of recruitment where 50 % is accepted step ( 3 ) 50 % of 16000 = 8000 step ( 4 ) 50 % of 8000 = 4000 step ( 5 ) 50 % of 4000 = 2000 step ( 6 ) 50 % of 2000 = 1000 step ( 7 ) 50 % of 1000 = 500 step ( 8 ) 70 % of 500 = 350 step ( 9 ) 70 % of 350 = 245 ( our target ) total 9 steps required . ans e
Answer: e
Question (gain): when the price of an article was reduced by 30 % its sale increased by 80 % . what was the net effect on the sale ?
Options: a ) 26 % increase , b ) 44 % decrease , c ) 60 % increase , d ) 66 % increase , e ) 66 % decrease
Rationale: "if n items are sold for $ p each , revenue is $ np . if we reduce the price by 30 % , the new price is 0.7 p . if we increase the number sold by 80 % , the new number sold is 1.8 n . so the new revenue is ( 0.7 p ) ( 1.8 n ) = 1.26 np , which is 1.26 times the old revenue , so is 26 % greater . answer : a"
Answer: a
Question (gain): 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
Question (general): 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
Question (other): 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
Question (physics): 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
Question (physics): 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
Question (gain): 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
Question (gain): 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
Question (general): 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
Question (probability): 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
Question (geometry): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (physics): 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
Question (physics): 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
Question (gain): 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
Question (other): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (geometry): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (gain): 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
Question (general): 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
Question (general): 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
Question (general): 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
Question (gain): 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
Question (gain): 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
Question (physics): 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
Question (physics): 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
Question (other): 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
Question (gain): 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
Question (general): 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
Question (physics): 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
Question (general): 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
Question (general): 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
Question (geometry): 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
Question (general): 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