Cheukting/mathqa huggingface dataset:
Question (physics): a boat having a length 3 m and breadth 2 m is floating on a lake . the boat sinks by 1.5 cm when a man gets on it . the mass of man is
Options: a ) 12 kg , b ) 90 kg , c ) 72 kg , d ) 96 kg , e ) none
Rationale: "solution volume of water displaced = ( 3 x 2 x 0.015 ) m 3 = 0.09 m 3 . mass of man = volume of water displaced × density of water = ( 0.09 × 1000 ) kg = 90 kg . answer b"
Answer: b
Question (general): three numbers are in the ratio 1 : 3 : 6 and their average is 100 . the largest number is :
Options: a ) 180 , b ) 98 , c ) 27 , d ) 21 , e ) 22
Rationale: "explanation : let the numbers be x , 3 x and 6 x , then , ( x + 3 x + 6 x ) / 3 = 100 = > 10 x = 100 * 3 = > x = 30 largest number 6 x = 6 * 30 = 180 answer : a"
Answer: a
Question (general): how many 3 digit positive integers r exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."
Answer: e
Question (general): a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 20 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 7 / 8 , e ) 8 / 7
Rationale: "let there be g geese , of which 0.3 g are male and 0.7 g are female lets say m geese migrated , 0.2 m are male and 0.8 m are female migration rate male = 0.2 m / 0.3 g = ( 2 / 3 ) * ( m / g ) migration rate female = 0.8 m / 0.7 g = ( 8 / 7 ) * ( m / g ) ratio of migration rates = ( 2 / 3 ) / ( 8 / 7 ) = 7 / 12 answer is ( b )"
Answer: b
Question (general): the average weight of a group of persons increased from 48 kg to 51 kg , when two persons weighing 88 kg and 93 kg join the group . find the initial number of members in the group ?
Options: a ) 23 , b ) 24 , c ) 25 , d ) 26 , e ) 27
Rationale: "let the initial number of members in the group be n . initial total weight of all the members in the group = n ( 48 ) from the data , 48 n + 88 + 93 = 51 ( n + 2 ) = > 51 n - 48 n = 79 = > n = 26 therefore there were 26 members in the group initially . answer : d"
Answer: d
Question (gain): what percent of 60 is 25 ?
Options: a ) 60 % , b ) 50 % , c ) 42 % , d ) 25 % , e ) 10 %
Rationale: "the phrasing of the question is difficult for some students . ` ` what percent of 60 is 25 ? ' ' is the same question as ` ` 25 is what percent of 60 ? ' ' many students find this later way of phrasing the question easier to work with . if x is y percent of z , then x / z = y / 100 ; for example , 10 is 50 % of 20 ; x = 10 , y = 50 , and z = 20 similarly , if you wanted to know what percent of 100 is 50 , you would intuitively know that it is 50 % since it is 50 / 100 or 50 per cent ( literally , per 100 ) . applying this logic to the problem at hand : 25 / 60 = . 42 = 42 % thus , 25 is 42 % of 60 if this way of solving the problem is difficult to conceptualize , consider another approach . it should be clear that 30 is 50 % ( or 1 / 2 ) or 60 . since 25 is less than 30 , 25 must be less than 50 % of 60 . this means that any answer that is not less than 50 % is wrong . since 25 % is 1 / 4 and 1 / 4 of 60 is 15 ( since 15 * 4 = 60 ) , 25 % is too small . by process of elimination , the answer is 42 % answer c"
Answer: c
Question (physics): two trains 121 meters and 153 meters in length respectively are running in opposite directions , one at the rate of 80 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 6.8 , c ) 7.2 , d ) 7.15 , e ) 7.11
Rationale: "t = ( 121 + 153 ) / ( 80 + 65 ) * 18 / 5 t = 6.8 answer : b"
Answer: b
Question (general): find the average of first 4 multiples of 15 ?
Options: a ) 10 , b ) 12.6 , c ) 22.5 , d ) 31.3 , e ) 37.5
Rationale: "average = ( 15 + 30 + 45 + 60 ) / 4 = 37.5 answer is e"
Answer: e
Question (general): the price of 3 chudi and 6 tops is rs . 1500 . with the same money one can buy 1 chudi and 12 tops . if one wants to buy 5 tops , how much shall she have to pay ?
Options: a ) 500 , b ) 1000 , c ) 1200 , d ) 1300 , e ) 1500
Rationale: let the price of a chudi and a top be rs . x and rs . y respectively . then , 3 x + 6 y = 1500 . . . . ( i ) and x + 12 y = 1500 . . . . ( ii ) divide equation ( i ) by 3 , we get the below equation . = x + 2 y = 500 . - - - ( iii ) now subtract ( iii ) from ( ii ) x + 12 y = 1500 ( - ) x + 2 y = 500 - - - - - - - - - - - - - - - - 10 y = 1000 - - - - - - - - - - - - - - - - cost of 5 tops = 5 * 100 = 500 answer : a
Answer: a
Question (general): the output of a factory is increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output is increased by 10 % . by approximately what percent would the output of the factory now have to be decreased in order to restore the original output ?
Options: a ) 17 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: "take it as original output = 100 . to meet demand increase by 10 % , then output = 110 . to meet holiday demand , new output increase by 10 % then output equals 121 to restore new holidy demand output to original 100 . final - initial / final * 100 = 21 / 121 * 100 = 8 / 33 * 100 = 17 % approxiamately . option a is correct ."
Answer: a
Question (other): a bag contains 3 red , 4 blue and 4 green balls . if 2 ballsare picked at random , what is the probability that both are red ?
Options: a ) 2 / 15 , b ) 2 / 21 , c ) 3 / 55 , d ) 3 / 29 , e ) 4 / 27
Rationale: "p ( both are red ) , = 3 c 211 c 2 = 3 c 211 c 2 = 3 / 55 c"
Answer: c
Question (general): tom reads at an average rate of 30 pages per hour , while jan reads at an average rate of 39 pages per hour . if tom starts reading a novel at 4 : 30 , and jan begins reading an identical copy of the same book at 5 : 06 , at what time will they be reading the same page ?
Options: a ) 6 : 06 , b ) 6 : 36 , c ) 7 : 06 , d ) 7 : 36 , e ) 8 : 06
Rationale: "since tom reads an average of 1 page every 2 minutes , tom will read 18 pages in the first 36 minutes . jan can catch tom at a rate of 9 pages per hour , so it will take 2 hours to catch tom . the answer is c ."
Answer: c
Question (general): let f ( x , y ) be defined as the remainder when ( x – y ) ! is divided by x . if x = 24 , what is the maximum value of y for which f ( x , y ) = 0 ?
Options: a ) 12 , b ) 15 , c ) 18 , d ) 20 , e ) 21
Rationale: "the question is finding y such that ( 24 - y ) ! is a multiple of 24 . that means we need to have 2 ^ 3 * 3 in ( 24 - y ) ! 4 ! is the smallest factorial number with 2 ^ 3 * 3 as a factor . 24 - y = 4 y = 20 the answer is d ."
Answer: d
Question (general): for every x , the action [ x ] is defined : [ x ] is the greatest integer less than or equal to x . what is the value of [ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.5 ?
Options: a ) 12.6 . , b ) 14.4 . , c ) 15.8 . , d ) 15.7 . , e ) 16.4 .
Rationale: "[ 6.5 ] x [ 2 / 3 ] + [ 2 ] x 7.2 + [ 8.4 ] - 6.5 = 6 * 0 + 2 * 7.2 + 8 - 6.5 = 0 + 14.4 + 1.5 15.7 answer d"
Answer: d
Question (physics): 15 girls can complete a rangoli in 12 days , and 10 boys can complete the same work in 15 days . to complete the work earlier 10 boys and 15 girls are employed , in how many days will this work get completed ?
Options: a ) 6 , b ) 7 , c ) 6.5 , d ) 6 2 / 3 , e ) 6 1 / 4
Rationale: work done by 15 girls per day = 1 / 12 work done by 10 boys per day = 1 / 15 work done by 15 girls and 10 boys per day = 1 / 12 + 1 / 15 = 3 / 20 = 6 2 / 3 10 boys and 15 girls will complete the work in = 6 2 / 3 days d
Answer: d
Question (general): when a certain number x is divided by 63 , the remainder is 27 . what is the remainder when x is divided by 8 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "when a certain number x is divided by 63 , the remainder is 27 . what is the remainder when x is divided by 8 ? putting a value say x = 27 we get remainder as 27 when divided by 63 . when 27 divided by 8 we get 3 as remainder . b is the answer ."
Answer: b
Question (general): on dividing 100 by a number , the quotient is 9 and the remainder is 1 . find the divisor ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "d = ( d - r ) / q = ( 100 - 1 ) / 9 = 99 / 9 = 11 b )"
Answer: b
Question (physics): a can do a work in 15 days and b in 20 days . if they work on it together for 5 days , then the fraction of the work that is left is :
Options: a ) 1 / 3 , b ) 7 / 12 , c ) 5 / 12 , d ) 2 / 3 , e ) 1 / 2
Rationale: "ans is : c a ' s 1 day ' s work = 1 / 15 b ' s 1 day ' s work = 1 / 20 ( a + b ) ' s 1 day ' s work = ( 1 / 15 + 1 / 20 ) = 7 / 60 ( a + b ) ' s 5 day ' s work = ( 7 / 60 * 5 ) = 7 / 12 therefore , remaining work = ( 1 - 7 / 12 ) = 5 / 12 . answer : c"
Answer: c
Question (physics): a monkey ascends a greased pole 6 meters high . he ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute . if this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
Options: a ) 9 th minute , b ) 21 st minute , c ) 11 th minute , d ) 22 nd minute , e ) 13 th minute
Rationale: "the money is climbing 1 meter in 2 min . this pattern will go on till he reaches 4 meters . i mean this will continue for first 4 * 2 = 8 mins . he would have reached 4 meters . after that he will climb 2 meters and he will reach the pole . so total time taken = 8 + 1 = 9 mins . so , asnwer will be a"
Answer: a
Question (general): what will be the reminder when ( 67 ^ 67 + 67 ) is divided by 68 ?
Options: a ) 1 , b ) 63 , c ) 66 , d ) 67 , e ) none of these
Rationale: "( x ^ n + 1 ) will be divisible by ( x + 1 ) only when n is odd ; ( 67 ^ 67 + 1 ) will be divisible by ( 67 + 1 ) ; ( 67 ^ 67 + 1 ) + 66 when divided by 68 will give 66 as remainder . correct option : c"
Answer: c
Question (gain): if leo gains 10 pounds , he will weigh 50 % more than his sister kendra . currently their combined weight is 140 pounds . what is leo ' s current weight ?
Options: a ) 80 , b ) 90 , c ) 100 , d ) 110 , e ) 120
Rationale: "l + k = 140 and so k = 140 - l l + 10 = 1.5 k = 1.5 ( 140 - l ) 2.5 l = 200 l = 80 the answer is a ."
Answer: a
Question (general): aunt marge is giving candy to each of her nephews and nieces . she has 20 pieces of candy and she gives all the candy to the children according to her wish . if robert gets 2 more pieces than kate , bill gets 6 less than mary , mary gets 2 more pieces than robert , and kate gets 2 more pieces than bill , how many pieces of candy does kate get ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: use the initial letter of each name as a variable : r = k + 2 b = m − 6 m = r + 2 k = 2 + bk = = r − 2 b = k − 2 = ( r − 2 ) − 2 = r − 4 m = r + 2 r + b + m + k = 20 r + r − 4 + r + 2 + r − 2 = 20 r = 6 k = r − 2 = 6 − 2 = 4 answer : b
Answer: b
Question (general): in the list 3 , 3 , 4 , 4 , 5 , 5 , 5 , 5 , 7 , 11 , 21 , what fraction of the data is less than the mode ?
Options: a ) 2 / 9 , b ) 1 / 3 , c ) 4 / 11 , d ) 2 / 3 , e ) 7 / 9
Rationale: mode : the mode of any set is the term which has the highest frequency ( occurrence ) highest frequent term in the set is 5 ( with frequency 4 ) hence mode = 5 two terms ( 3 , 3 , 4 , 4 ) out of a total of 11 terms are less than mode of the set . fraction of set that are less than mode of set = 4 / 11 answer : option c
Answer: c
Question (general): how many multiples of 4 are less than 3200 , and also multiples of 16 ?
Options: a ) 104 , b ) 200 , c ) 625 , d ) 832 , e ) 833
Rationale: the lcm of 4 and 16 is 16 . divide 3200 / 16 = 200 . xxx . so b is your answer .
Answer: b
Question (physics): a man can row a boat at 10 kmph in still water and the speed of the stream is 8 kmph . what is then time taken to row a distance of 90 km down the stream ?
Options: a ) 8 hrs , b ) 5 hrs , c ) 15 hrs , d ) 15 hrs , e ) 20 hrs
Rationale: speed in down stream = 10 + 8 = 18 time taken to cover 90 km down stream = 90 / 18 = 5 hrs . answer : b
Answer: b
Question (physics): the sum of two consecutive number is 109 . which is the larger number ?
Options: a ) 42 , b ) 43 , c ) 44 , d ) 45 , e ) 55
Rationale: "let consecutive number be x , x + 1 therefore sum of the consecutive number is x + x + 1 = 109 2 x + 1 = 109 2 x = 108 x = 54 therefore larger number is x + 1 = 55 answer : e"
Answer: e
Question (general): what is the least number to be added to 1480 to make it a perfect square ?
Options: a ) 105 , b ) 160 , c ) 200 , d ) 71 , e ) 120
Rationale: "the numbers greater than 1480 and are square of number is 1600 . the least number that should be added 1480 to make it perfect square = 1600 - 1480 = 120 . answer : e"
Answer: e
Question (general): a hat company ships its hats , individually wrapped , in 8 - inch by 10 - inch by 12 - inch boxes . each hat is valued at $ 7.00 . if the company ’ s latest order required a truck with at least 288,000 cubic inches of storage space in which to ship the hats in their boxes , what was the minimum value of the order ?
Options: a ) $ 960 , b ) $ 1,350 , c ) $ 1,725 , d ) $ 2,100 , e ) $ 2,250
Rationale: "total volume is 288000 given lbh = 8 * 10 * 12 . the number of hats inside it = 288000 / 10 * 8 * 12 = 300 . price of each hat is 7.5 $ then total value is 300 * 7.0 = 2100 . imo option d is correct answer . ."
Answer: d
Question (gain): in order to obtain an income of rs . 15000 from 80 % stock at rs . 200 , one must make an investment of
Options: a ) rs . 30000 , b ) rs . 37000 , c ) rs . 37500 , d ) rs . 40000 , e ) rs . 40500
Rationale: "explanation : market value = rs . 200 . required income = rs . 15000 . here face value is not given . take face value as rs . 100 if it is not given in the question to obtain rs . 80 ( ie , 80 % of the face value 100 ) , investment = rs . 200 to obtain rs . 15000 , investment = 200 / 80 ã — 15000 = rs . 37500 answer : option c"
Answer: c
Question (geometry): the area of sector of a circle whose radius is 12 metro and whose angle at the center is 40 ° is ?
Options: a ) 53 m 2 , b ) 51 m 2 , c ) 50.2 m 2 , d ) 45 m 2 , e ) 40 m 2
Rationale: "40 / 360 * 22 / 7 * 12 * 12 = 50.2 m 2 answer : c"
Answer: c
Question (general): the average runs scored by a batsman in 22 matches is 28 . in the next 13 matches the batsman scored an average of 15 runs . find his average in all the 35 matches ?
Options: a ) 31.23 , b ) 25.12 , c ) 36.25 , d ) 23.17 , e ) 27.66
Rationale: total score of the batsman in 22 matches = 616 . total score of the batsman in the next 13 matches = 195 . total score of the batsman in the 35 matches = 811 . average score of the batsman = 811 / 35 = 23.17 . answer : d
Answer: d
Question (general): the sum of the numbers is 330 . if the first number be twice the second and third number be one - third of the first , then the second number is :
Options: a ) 48 , b ) 54 , c ) 72 , d ) 84 , e ) 90
Rationale: "let the second number be x . then , first number = 2 x and third number = 2 x / 3 . 2 x + x + 2 x / 3 = 330 11 x / 3 = 330 x = 90 answer : e"
Answer: e
Question (general): a trailer carries 3 , 4 and 5 crates on a trip . each crate weighs no less than 150 kg . what is the maximum weight of the crates on a single trip ?
Options: a ) 1250 , b ) 625 , c ) 600 , d ) 750 , e ) 375
Rationale: "max no . of crates = 5 . max weight = 150 kg max . weight carried = 5 * 150 = 750 kg = d"
Answer: d
Question (gain): the weight of a glass of jar is 20 % of the weight of the jar filled with coffee beans . after some of the beans have been removed , the weight of the jar and the remaining beans is 60 % of the original total weight . what fraction part of the beans remain in the jar ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 2 / 5 , d ) 1 / 2 , e ) 2 / 3
Rationale: "let weight of jar filled with beans = 100 g weight of jar = 20 g weight of coffee beans = 80 g weight of jar and remaining beans = 60 g weight of remaining beans = 40 g fraction remaining = 40 / 80 = 1 / 2 answer is d ."
Answer: d
Question (geometry): the diagonals of a rhombus are 16 cm and 20 cm . find its area ?
Options: a ) 160 , b ) 288 , c ) 150 , d ) 238 , e ) 31
Rationale: "1 / 2 * 16 * 20 = 160 answer : a"
Answer: a
Question (geometry): the points a ( 0 , 0 ) , b ( 0 , 4 a - 5 ) and c ( 2 a + 1 , 2 a + 4 ) form a triangle . if angle abc = 90 , what is the area of triangle abc ?
Options: a ) 80 , b ) 75 , c ) 70 , d ) 60 , e ) 65
Rationale: "1 / 2 bh = 1 / 2 ( 2 a + 1 ) ( 2 a + 4 ) now 4 a - 5 = 2 a + 4 2 a = 9 therefore , a ( 0,0 ) ; b ( 0,13 ) ; c ( 10,13 ) 1 / 2 * 10 * 13 = 65 answer : e"
Answer: e
Question (geometry): carmen made a sculpture from small pieces of wood . the sculpture is 2 feet 10 inches tall . carmen places her sculpture on a base that is 6 inches tall . how tall are the sculpture andbase together ?
Options: a ) 3.1 feet , b ) 3.2 feet , c ) 3.3 feet , d ) 3.4 feet , e ) 3.5 feet
Rationale: "we know 1 feet = 12 inch then 2 feet = 24 inch 24 + 10 = 34 then 34 + 6 = 40 40 / 12 = 3.3 feet answer : c"
Answer: c
Question (general): xy = 2 then what is ( 2 ^ ( x + y ) ^ 2 ) / ( 2 ^ ( x - y ) ^ 2 )
Options: a ) 2 , b ) 4 , c ) 8 , d ) 16 , e ) 256
Rationale: ( x + y ) ^ 2 - ( x - y ) ^ 2 ( x + y + x - y ) ( x + y - x + y ) ( 2 x ) ( 2 y ) 4 xy 8 2 ^ 8 = 256 answer e
Answer: e
Question (geometry): in a rectangular coordinate system , what is the area of a rhombus whose vertices have the coordinates ( 0 , 5.5 ) , ( 8 , 0 ) , ( 0 , - 5.5 ) , ( - 8 , 0 ) ?
Options: a ) 56
b ) 88
c ) 112
d ) 116
e ) 120
Rationale: ares of rhombus = 1 / 2 * d 1 * d 2 length of 1 st diagonal = 8 + 8 = 16 length of 2 nd diagonal = 5.5 + 5.5 = 11 area = 1 / 2 * 16 * 11 = 88 b is the answer
Answer: b
Question (gain): a sum of money becomes 7 / 6 of itself in 5 years at a certain rate of simple interest . the rate per annum is ?
Options: a ) 20 / 7 , b ) 20 / 3 , c ) 23 / 6 , d ) 10 / 3 , e ) 10 / 7
Rationale: "let sum = x . then , amount = 7 x / 6 s . i . = 7 x / 6 - x = x / 6 ; time = 5 years . rate = ( 100 * x ) / ( x * 6 * 5 ) = 10 / 3 % . answer : d"
Answer: d
Question (general): a is two years older than b who is twice as old as c . if the total of the ages of a , b and c be 22 , then how old is b ?
Options: a ) 17 years , b ) 19 years , c ) 29 years , d ) 8 years , e ) 12 years
Rationale: "let c ' s age be x years . then , b ' s age = 2 x years . a ' s age = ( 2 x + 2 ) years . ( 2 x + 2 ) + 2 x + x = 22 5 x = 20 = > x = 4 hence , b ' s age = 2 x = 8 years . answer : d"
Answer: d
Question (general): all the students of class are told to sit in circle shape . here the boy at the 6 th position is exactly opposite to 16 th boy . total number of boys in the class ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: as half the circle shape consist of 16 - 6 = 10 boys , so total number of boys in full circle = 2 * 10 = 20 answer : c
Answer: c
Question (geometry): the area of a square is 4624 sq cm . find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square .
Options: a ) 5 : 28 , b ) 5 : 19 , c ) 5 : 12 , d ) 5 : 13 , e ) 11 : 34
Rationale: "let the length and the breadth of the rectangle be l cm and b cm respectively . let the side of the square be a cm . a 2 = 4624 a 68 l = 2 a and b = a - 24 b : l = a - 24 : 2 a = 44 : 136 = 11 : 34 answer : e"
Answer: e
Question (physics): in what time will a train 100 meters long cross an electric pole , if its speed is 162 km / hr
Options: a ) 8.5 seconds , b ) 2.22 seconds , c ) 3.5 seconds , d ) 2.5 seconds , e ) 2.6 seconds
Rationale: "first convert speed into m / sec speed = 162 * ( 5 / 18 ) = 45 m / sec time = distance / speed = 100 / 45 = 2.22 seconds answer : b"
Answer: b
Question (general): a certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint . if 2 gallons of the mixture is needed and the individual colors can be purchased only in one gallon or half gallon cans , what is the least amount of paint t , in gallons , that must be purchased in order to measure out the portions needed for the mixture ?
Options: a ) 2 , b ) 2 1 / 2 , c ) 3 , d ) 3 1 / 2 , e ) 4
Rationale: "given w : b = 3 : 5 that means say 3 gallons of white paint + 5 gallons of black paint = 8 gallons of paint mixture . but we want least amount of whiteblack paints for minimum of 2 gallons of mixture , so lets reduce keeping same ratio , 1.5 : 2.5 gives 1.5 + 2.5 = 4 gallons of mixture , but we want only 2 gallons , lets further reduce 0.75 : 1.25 gives 1 + 1.5 = 2.5 gallons of mixture . this looks ok , but lets reduce further just to be sure 0.375 : 0.625 gives 0.5 + 1 = 1.5 gallons of mixture , thats less than 2 gallons of mixture , so not acceptable . so correct ans is 2.5 gallons . b"
Answer: b
Question (general): find the principle on a certain sum of money at 5 % per annum for 2 2 / 5 years if the amount being rs . 2120 ?
Options: a ) rs . 1000.15 , b ) rs . 1100.95 , c ) rs . 1892.85 , d ) rs . 1050.85 , e ) rs . 1200.25
Rationale: "2120 = p [ 1 + ( 5 * 12 / 5 ) / 100 ] p = 1892.85 answer : c"
Answer: c
Question (general): the average age of an adult class is 40 years . 8 new students with an avg age of 32 years join the class . therefore decreasing the average by 4 year . find what was theoriginal strength of class ?
Options: a ) 8 , b ) 12 , c ) 15 , d ) 17 , e ) 18
Rationale: "let original strength = y then , 40 y + 8 x 32 = ( y + 8 ) x 36 â ‡ ’ 40 y + 256 = 36 y + 288 â ‡ ’ 4 y = 32 â ˆ ´ y = 8 a"
Answer: a
Question (other): what is the ratio of two no . 5 xy and 8 xy .
Options: a ) 2 : 5 , b ) 3 : 4 , c ) 5 : 8 , d ) 2 : 3 , e ) 1 : 2
Rationale: "5 xy / 8 xy = 5 : 8 answer c"
Answer: c
Question (general): how many positive integers less than 17 can be expressed as the sum of a positive multiple of 2 and a positive multiple of 3 ?
Options: a ) 14 , b ) 13 , c ) 12 , d ) 11 , e ) 10
Rationale: "the number = 2 a + 3 b < 17 when a = 1 , b = 1 , 2 , 3 , 4 , 5 - > 2 a = 2 ; 3 b = 3 , 6 , 9 , 12 , 15 - > the number = 5 , 8 , 11 , 14 - - > 4 numbers when a = 2 , b = 1,2 , 3,4 - > . . . . - - > 4 numbers when a = 3 , b = 1 , 2,3 - - > . . . . - - > 3 numbers total number is already 11 . look at the answer there is no number greater than 11 - - > we dont need to try any more answer must be d"
Answer: d
Question (general): what least number should be added to 1056 , so that the sum is completely divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "that is 1056 / 23 = 45 remainder = 21 = > 21 + 2 = 23 hence 2 should be added to 1056 so that the sum will be divisible by 23 answer is option b"
Answer: b