Cheukting/mathqa huggingface dataset:
Question (general): in a recent election , james received 1.5 percent of the 2,000 votes cast . to win the election , a candidate needed to receive more than 50 percent of the vote . how many additional votes would james have needed to win the election ?
Options: a ) 901 , b ) 989 , c ) 990 , d ) 971 , e ) 1,001
Rationale: "james = ( 1.5 / 100 ) * 2000 = 30 votes to win = ( 50 / 100 ) * total votes + 1 = ( 50 / 100 ) * 2000 + 1 = 1001 remaining voted needed to win election = 1001 - 30 = 971 answer : option d"
Answer: d
Question (gain): jolene entered an 18 - month investment contract that guarantees to pay 2 percent interest at the end of 6 months , another 3 percent interest at the end of 10 months , and 4 percent interest at the end of the 18 month contract . if each interest payment is reinvested in the contract , and jolene invested $ 10,000 initially , what will be the total amount of interest paid during the 18 - month contract ?
Options: a ) $ 506.00 , b ) $ 726.24 , c ) $ 900.00 , d ) $ 920.24 , e ) $ 926.24
Rationale: if interest were not compounded in every six months ( so if interest were not earned on interest ) then we would have ( 2 + 3 + 4 ) = 9 % simple interest earned on $ 10,000 , which is $ 900 . so , you can rule out a , b and c right away . interest earned after the first time interval : $ 10,000 * 2 % = $ 200 ; interest earned after the second time interval : ( $ 10,000 + $ 200 ) * 3 % = $ 300 + $ 6 = $ 306 ; interest earned after the third time interval : ( $ 10,000 + $ 200 + $ 306 ) * 4 % = $ 400 + $ 8 + ( ~ $ 12 ) = ~ $ 420 ; total : 200 + 306 + ( ~ 420 ) = ~ $ 726.24 . answer : b .
Answer: b
Question (gain): walking 4 / 3 of his usual rate , a boy reaches his school 4 min early . find his usual time to reach the school ?
Options: a ) 22 , b ) 16 , c ) 27 , d ) 28 , e ) 20
Rationale: "speed ratio = 1 : 4 / 3 = 3 : 4 time ratio = 4 : 3 1 - - - - - - - - 4 4 - - - - - - - - - ? 16 m . answer : b"
Answer: b
Question (general): which is the least number that must be subtracted from 1256 so that the remainder when divided by 7 , 12 , 16 is 4 ?
Options: a ) 242 , b ) 232 , c ) 236 , d ) 240 , e ) 244
Rationale: "first we need to figure out what numbers are exactly divisible by 7 , 12,16 . this will be the set { lcm , lcmx 2 , lcmx 3 , . . . } lcm ( 7 , 12,16 ) = 48 * 7 = 336 the numbers which will leave remainder 4 will be { 336 + 4 , 336 x 2 + 4 , 336 x 3 + 4 , . . . } the largest such number less than or equal to 1256 is 336 x 3 + 4 or 1012 to obtain this you need to subtract 244 . e"
Answer: e
Question (geometry): if n is the smallest integer such that 108 times n is the square of an integer , what is the value of n ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 12 , e ) 24
Rationale: "108 can written as = 2 * 2 * 3 * 3 * 3 - - > 2 ^ 2 * 3 ^ 3 - - - ( 1 ) so for 108 * n to be a square of an integer , the integer should have even powers to the prime numbers it composed of . here 2 already has even power - > so n has to be 2 to make the power of 2 in ( 1 ) even option a is correct"
Answer: a
Question (gain): of the 500 employees in a certain company , 25 percent will be relocated to city x and the remaining 75 percent will be relocated to city y . however , 40 percent of the employees prefer city y and 60 percent prefer city x . what is the highest possible number of employees who will be relocated to the city they prefer ?
Options: a ) 65 , b ) 100 , c ) 115 , d ) 130 , e ) 325
Rationale: "300 prefer x ( group 1 ) ; 200 prefer y ( group 2 ) . city y needs 375 people : letall 200 who prefer y ( entire group 2 ) be relocated there , the rest 175 will be those who prefer x from group 1 ; city x needs 125 people : 300 - 175 = 125 from group 1 will be relocated to x , which they prefer . so , the highest possible number of employees who will be relocated to the city they prefer is 200 + 125 = 325 . answer : e ."
Answer: e
Question (general): the average of 1 st 3 of 4 numbers is 6 and of the last 3 are 5 . if the sum of the first and the last number is 11 . what is the last numbers ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "a + b + c = 18 b + c + d = 15 a + d = 11 a – d = 3 a + d = 11 2 d = 8 d = 4 answer : a"
Answer: a
Question (gain): if the cost price of 50 articles is equal to the selling price of 35 articles , then the gain or loss percent is ?
Options: a ) 16 , b ) 127 , c ) 12 , d ) 18 , e ) 43
Rationale: "percentage of profit = 15 / 35 * 100 = 43 % answer : e"
Answer: e
Question (general): a batch of cookies was divided amomg 3 tins : 3 / 4 of all the cookies were placed in either the blue or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction of the cookies that were placed in the other tins were placed in the green tin
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 3 / 5 , e ) 9 / 7
Rationale: "this will help reduce the number of variables you have to deal with : g + b = 3 / 4 r = 1 / 3 b = 1 / 4 we can solve for g which is 1 / 2 what fraction ( let it equal x ) of the cookies that were placed in the other tins were placed in the green tin ? so . . x * ( g + r ) = g x * ( 1 / 2 + 1 / 3 ) = 1 / 2 x = 3 / 5 answer : d"
Answer: d
Question (other): 10 different biology books and 8 different chemistry books lie on a shelf . in how many ways can a student pick 2 books of each type ?
Options: a ) 80 , b ) 160 , c ) 720 , d ) 1100 , e ) 1260
Rationale: "no . of ways of picking 2 biology books ( from 10 books ) = 10 c 2 = ( 10 * 9 ) / 2 = 45 no . of ways of picking 2 chemistry books ( from 8 books ) = 8 c 2 = ( 8 * 7 ) / 2 = 28 total ways of picking 2 books of each type = 45 * 28 = 1260 ( option e )"
Answer: e
Question (general): a grocer has a sale of rs . 6400 , rs . 7000 , rs . 6800 , rs . 7200 and rs . 6500 for 5 consecutive months . how much sale must he have in the sixth month so that he gets an average sale of rs . 6500 ?
Options: a ) rs . 4500 , b ) rs . 4700 , c ) rs . 4800 , d ) rs . 5000 , e ) rs . 5100
Rationale: "total sale for 5 months = rs . ( 6400 + 7000 + 6800 + 7200 + 6500 ) = rs . 33900 required sale = rs . [ ( 6500 x 6 ) - 34009 ] = rs . ( 39000 - 33900 ) = rs . 5100 answer : e"
Answer: e
Question (general): given that a is the average ( arithmetic mean ) of the first 5 positive multiples of 6 and b is the median of the first 12 positive multiples of 6 , what is the ratio of a to b ?
Options: a ) 3 : 4 , b ) 6 : 13 , c ) 5 : 6 , d ) 13 : 10 , e ) 4 : 3
Rationale: the first nine positive multiples of six are { 6 , 12 , 18 , 24,30 } the first twelve positive multiples of six are { 6 , 12 , 18 , 24 , 30 , 36,42 , 48 , 54 , 60 , 66 , 72 } both sets are evenly spaced , thus their median = mean : a = 18 and b = ( 36 + 42 ) / 2 = 39 - - > a / b = 18 / 39 = 6 / 13 . answer : b .
Answer: b
Question (gain): find the compound interest on rs . 7500 at 4 % per annum for 2 years , compounded annually .
Options: a ) rs . 610 , b ) rs . 612 , c ) rs . 614 , d ) rs . 616 , e ) none of these
Rationale: "explanation : amount = [ 7500 × ( 1 + 4100 ) 2 ] = ( 7500 × 2625 × 2625 ) = 8112 so compound interest = ( 8112 - 7500 ) = 612 answer : b"
Answer: b
Question (geometry): how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 13 inches than that of a rectangular sheet of paper measuring 6.5 inches by 11 inches ?
Options: a ) 50 %
b ) 87 %
c ) 100 %
d ) 187 %
e ) 200 %
Rationale: let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 13 is twice 6.5 then the area will be double which means 100 % greater . the answer is c .
Answer: c
Question (geometry): in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,9 ) . if a point ( a , b ) is selected at random from the triangular region , what is the probability that a - b > 0 ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 9 , e ) 4 / 5
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 9 = 18 . only the points ( a , b ) below the line y = x satisfy a - b > 0 . the part of the triangle which is below the line y = x has an area of ( 1 / 2 ) ( 4 ) ( 4 ) = 8 . p ( a - b > 0 ) = 8 / 18 = 2 / 9 the answer is d ."
Answer: d
Question (gain): if a sum of money doubles itself in 5 years at simple interest , the ratepercent per annum is
Options: a ) 12 , b ) 12.5 , c ) 20 , d ) 13.5 , e ) 14
Rationale: "explanation : let sum = x then simple interest = x rate = ( 100 * x ) / ( x * 5 ) = 20 option c"
Answer: c
Question (general): elvin ' s monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for internet service . elvin ' s total telephone bill for january was $ 52 and elvin ' s total telephone bill for february was 76 $ . if elvin ' s charge for the calls he made in february was twice the charge for the calls he made in january , what is elvin ' s fixed monthly charge for internet service ?
Options: a ) $ 5 , b ) $ 10 , c ) $ 14 , d ) $ 28 , e ) $ 29
Rationale: "bill = fixed charge + charge of calls made in jan , bill = fixed charge ( let , y ) + charge of calls made in jan ( let , x ) = $ 52 in feb , bill = fixed charge ( let , y ) + charge of calls made in feb ( then , 2 x ) = $ 76 i . e . x + y = 52 and 2 x + y = 76 take the difference if two equations i . e . ( 2 x + y ) - ( x + y ) = 76 - 52 i . e . x = 24 i . e . fixed monthly charge , y = 28 answer : option d"
Answer: d
Question (gain): a started a business with an investment of rs . 70000 and after 9 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 76000 , then the share of b is ?
Options: a ) 33008 , b ) 24000 , c ) 28000 , d ) 48000 , e ) 81122
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 3 ) = 7 : 12 total profit = rs . 76000 share of b = 12 / 19 ( 76000 ) = rs . 48000 answer : d"
Answer: d
Question (general): how many 7 in between 1 to 110 ?
Options: a ) 18 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "7 , 17,27 , 37,47 , 57,67 , 70,71 , 72,73 , 74,75 , 76,77 ( two 7 ' s ) , 78 , 79,87 , 97,107 21 7 ' s between 1 to 110 answer : b"
Answer: b
Question (physics): a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3000 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1800 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3000 / 25 = 120 so , a ’ s amount = 120 × 15 = rs . 1800 . answer : option c"
Answer: c
Question (gain): a started a business with an investment of rs . 70000 and after 6 months b joined him investing rs . 120000 . if the profit at the end of a year is rs . 78000 , then the share of b is ?
Options: a ) a ) 34500 , b ) b ) 36099 , c ) c ) 36000 , d ) d ) 38007 , e ) e ) 42000
Rationale: "ratio of investments of a and b is ( 70000 * 12 ) : ( 120000 * 6 ) = 7 : 6 total profit = rs . 78000 share of b = 6 / 13 ( 78000 ) = rs . 36000 answer : c"
Answer: c
Question (physics): if an object travels 90 feet in 3 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 17.36 , b ) 20.45 , c ) 23.87 , d ) 26.92 , e ) 29.56
Rationale: "90 feet / 3 seconds = 30 feet / second ( 30 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 20.45 miles / hour ( approximately ) the answer is b ."
Answer: b
Question (general): if 2 x + y = 7 and x + 2 y = 5 , then xy / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 5 , d ) 18 / 5 , e ) 4
Rationale: "2 * ( x + 2 y = 5 ) equals 2 x + 4 y = 10 2 x + 4 y = 10 - 2 x + y = 7 = 3 y = 3 therefore y = 1 plug and solve . . . 2 x + 1 = 7 2 x = 6 x = 3 xy / 3 = 3 * 1 / 3 = 1 a"
Answer: a
Question (probability): there are 21 students in a class . in how many different ways can a committee of 3 students be formed ?
Options: a ) 1180 , b ) 1330 , c ) 1540 , d ) 1760 , e ) 1920
Rationale: "21 c 3 = 21 * 20 * 19 / 6 = 1330 the answer is b ."
Answer: b
Question (general): the average age of boys in a class is 16 years and that of the girls is 15 years . the average age for the whole class is
Options: a ) 15 years , b ) 15.5 years , c ) 16 years , d ) 17 years , e ) can not be computed
Rationale: "clearly , to find the average , we ought to know the numbers of boys , girls or students in the class , neither of which has been given . so the data provided is inadequate . answer : e"
Answer: e
Question (gain): of 800 surveyed students , 20 % of those who read book a also read book b and 25 % of those who read book b also read book a . if each student read at least one of the books , what is the difference between the number of students who read only book a and the number of students who read only book b ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 55 , e ) 100
Rationale: "say the number of students who read book a is a and the number of students who read book b is b . given that 20 % of those who read book a also read book b and 25 % of those who read book b also read book a , so the number of students who read both books is 0.2 a = 0.25 b - - > a = 1.25 b . since each student read at least one of the books then { total } = { a } + { b } - { both } - - > 800 = 1.25 b + b - 0.25 b - - > b = 400 , a = 1.25 b = 500 and { both } = 0.25 b = 100 . the number of students who read only book a is { a } - { both } = 500 - 100 = 400 ; the number of students who read only book b is { b } - { both } = 400 - 100 = 300 ; the difference is 400 - 300 = 100 . answer : e ."
Answer: e
Question (gain): what annual payment will discharge a debt of rs . 1090 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 586.21 , c ) 534.33 , d ) 543.33 , e ) 646.33
Rationale: explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1090 820 x + 1090 * 441 x = 586.21 so , value of each installment = rs . 586.21 answer : option b
Answer: b
Question (gain): a man sells a car to his friend at 15 % loss . if the friend sells it for rs . 54000 and gains 20 % , the original c . p . of the car was :
Options: a ) rs . 22941.18 , b ) rs . 32941.18 , c ) rs . 52941.18 , d ) rs . 62941.18 , e ) none of these
Rationale: "explanation : s . p = rs . 54,000 . gain earned = 20 % c . p = rs . [ 100 / 120 ã — 54000 ] = rs . 45000 this is the price the first person sold to the second at at loss of 15 % . now s . p = rs . 45000 and loss = 15 % c . p . rs . [ 100 / 85 ã — 45000 ] = rs . 52941.18 correct option : c"
Answer: c
Question (physics): the area of a square field 3136 sq m , if the length of cost of drawing barbed wire 3 m around the field at the rate of rs . 1 per meter . two gates of 1 m width each are to be left for entrance . what is the total cost ?
Options: a ) 399 , b ) 272 , c ) 666 , d ) 277 , e ) 311
Rationale: "answer : option c explanation : a 2 = 3136 = > a = 56 56 * 4 * 3 = 672 â € “ 6 = 666 * 1 = 666 answer : c"
Answer: c
Question (general): how many 0 ' s are there in the binary form of 6 * 1024 + 4 * 64 + 2
Options: a ) 6 , b ) 7 , c ) 8 , d ) 10 , e ) 9
Rationale: 6 * 1024 + 4 * 64 + 2 = 6144 + 256 + 2 = 6402 in binary code 6402 base 10 = 11001 000000 10 in base 2 . so 9 zeros are there . answer : e
Answer: e
Question (general): what is 7 1 / 4 - 4 2 / 3 divided by 7 / 8 - 3 / 4 ?
Options: a ) 87 / 36 , b ) 36 / 17 , c ) 7 / 6 , d ) 62 / 3 , e ) 5 / 4
Rationale: "7 1 / 4 - 4 2 / 3 = 29 / 4 - 14 / 3 = ( 87 - 56 ) / 12 = 31 / 12 7 / 8 - 3 / 4 = ( 7 - 6 ) / 8 = 1 / 8 so 31 / 12 / 1 / 8 = 31 / 12 * 8 = 62 / 3 answer - d"
Answer: d
Question (gain): the mean daily profit made by a shopkeeper in a month of 30 days was rs . 350 . if the mean profit for the first fifteen days was rs . 225 , then the mean profit for the last 15 days would be
Options: a ) rs . 200 , b ) rs . 350 , c ) rs . 475 , d ) rs . 425 , e ) none of these
Rationale: "average would be : 350 = ( 225 + x ) / 2 on solving , x = 475 . answer : c"
Answer: c
Question (general): find out the c . i on rs . 8000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 489.66 , b ) 406.07 , c ) 406.04 , d ) 306.03 , e ) 306.01
Rationale: "a = 8000 ( 51 / 50 ) 3 = 8489.66 8000 - - - - - - - - - - - 489.66 answer : a"
Answer: a
Question (physics): jayes can eat 25 marshmallows is 20 minutes . dylan can eat 25 in one hour . in how much time will the two eat 150 marshmallows ?
Options: a ) 40 minutes . , b ) 1 hour and 30 minutes . , c ) 1 hour . , d ) 1 hour and 40 minutes . , e ) 2 hours and 15 minutes .
Rationale: rate = output / time jayes rate = 25 / 20 = 5 / 4 dylan rate = 25 / 60 = 5 / 12 combined rate = 5 / 4 + 5 / 12 = 20 / 12 combinedrate * combinedtime = combinedoutput 20 / 12 * t = 150 t = 90 mins = > 1 hr 30 min
Answer: c
Question (general): how many even number in the range between 10 to 120 inclusive are not divisible by 3
Options: a ) 15 , b ) 30 , c ) 31 , d ) 37 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 10 , 12,14 . . . 120 using ap formula , we can say 120 = 10 + ( n - 1 ) * 2 or n = 56 . for 6 , 12,18 , . . . 120 using ap formula , we can say 120 = 12 + ( n - 1 ) * 6 or n = 19 . hence , only divisible by 2 but not 3 = 56 - 19 = 37 . hence , answer d"
Answer: d
Question (general): in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 74000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 50
Rationale: 0.037 * 10 ^ 5 can be written as 3700 74000 * 10 ^ ( - 3 ) can be written as 74 required = 3700 / 74 = 50 answer : e
Answer: e
Question (general): the largest 4 digit number exactly divisible by 44 is ?
Options: a ) 9988 , b ) 9939 , c ) 9944 , d ) 9954 , e ) 9960
Rationale: "largest 4 - digit number = 9999 44 ) 9999 ( 227 9988 largest number : 9988 answer : a"
Answer: a
Question (general): if a certain number is divided by 2 , the quotient , dividend , and divisor , added together , will amount to 62 . what is the number ?
Options: a ) 18 , b ) 28 , c ) 40 , d ) 38 , e ) 59
Rationale: "let x = the number sought . then x / 2 + x + 2 = 62 . x = 40 . c"
Answer: c
Question (physics): a and b can do a work in 10 days and 15 days respectively . a starts the work and b joins him after 5 days . in how many days can they complete the remaining work ?
Options: a ) 6 days , b ) 2 days , c ) 8 days , d ) 4 days , e ) 3 days
Rationale: "work done by a in 5 days = 5 / 10 = 1 / 2 remaining work = 1 / 2 work done by both a and b in one day = 1 / 10 + 1 / 15 = 5 / 30 = 1 / 6 remaining work = 1 / 2 * 6 / 1 = 3 days . answer : e"
Answer: e
Question (general): for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 4 ” 2 ?
Options: a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: "4 ” 2 = 4 - 4 = 0 answer : e"
Answer: e
Question (gain): in an office in singapore there are 60 % female employees . 50 % of all the male employees are computer literate . if there are total 62 % employees computer literate out of total 1100 employees , then the no . of female employees who are computer literate ?
Options: a ) 462 , b ) 674 , c ) 672 , d ) 960 , e ) none
Rationale: "solution : total employees , = 1100 female employees , 60 % of 1100 . = ( 60 * 1100 ) / 100 = 660 . then male employees , = 440 50 % of male are computer literate , = 220 male computer literate . 62 % of total employees are computer literate , = ( 62 * 1100 ) / 100 = 682 computer literate . thus , female computer literate = 682 - 220 = 462 . answer : option a"
Answer: a
Question (general): total 48 matches are conducted in knockout match type . how many players will be participated in that tournament ?
Options: a ) 48 , b ) 47 , c ) 40 , d ) 42 , e ) 47
Rationale: "47 players answer : e"
Answer: e
Question (physics): in 130 m race , a covers the distance in 36 seconds and b in 45 seconds . in this race a beats b by :
Options: a ) 20 m , b ) 25 m , c ) 22.5 m , d ) 26 m , e ) 12 m
Rationale: "distance covered by b in 9 sec . = 130 / 45 x 9 m = 26 m . a beats b by 26 metres . answer : option d"
Answer: d
Question (gain): at a certain university , 69 % of the professors are women , and 70 % of the professors are tenured . if 90 % of the professors are women , tenured , or both , then what percent of the men are tenured ?
Options: a ) 25 , b ) 37.5 , c ) 50 , d ) 52.5 , e ) 75
Rationale: "answer is 75 % total women = 69 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 21 % but question wants to know the percent of men that are tenured 21 % / 40 % = 52.5 % d"
Answer: d
Question (physics): in a dairy farm , 26 cows eat 26 bags of husk in 26 days . in how many days one cow will eat one bag of husk ?
Options: a ) 1 , b ) 40 , c ) 20 , d ) 26 , e ) 30
Rationale: "explanation : one bag of husk = 26 cows per day ⇒ 26 × 1 × 26 = 1 × 26 × x for one cow = 26 days answer : d"
Answer: d
Question (general): the average age of a group of n people is 14 years old . one more person aged 34 joins the group and the new average is 16 years old . what is the value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "14 n + 34 = 16 ( n + 1 ) 2 n = 18 n = 9 the answer is c ."
Answer: c
Question (general): the number 0.650 is how much greater than 1 / 8 ?
Options: a ) ½ , b ) 21 / 40 , c ) 1 / 50 , d ) 1 / 500 , e ) 2 / 500
Rationale: "let x be the difference then . 65 - 1 / 8 = x 65 / 100 - 1 / 8 = x x = 21 / 40 ans b"
Answer: b
Question (other): if $ 1092 are divided between worker a and worker b in the ratio 5 : 8 , what is the share that worker b will get ?
Options: a ) 60.32 % , b ) 61.54 % , c ) 62.21 % , d ) 62.76 % , e ) 63.87 %
Rationale: "worker b will get 8 / 13 = 61.54 % the answer is b ."
Answer: b
Question (probability): a card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart ?
Options: a ) 8 / 58 , b ) 9 / 25 , c ) 1 / 26 , d ) 6 / 25 , e ) 8 / 45
Rationale: "here n ( s ) = 52 let e be the event of getting queen of the club or king of kings n ( e ) = 2 p ( e ) = n ( e ) / n ( s ) = 2 / 52 = 1 / 26 answer ( c )"
Answer: c
Question (physics): 1000 men have provisions for 17 days . if 500 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.5 , c ) 11.3 , d ) 12.2 , e ) 12.1
Rationale: "1000 * 17 = 1500 * x x = 11.3 answer : c"
Answer: c
Question (physics): a person travels equal distances with speeds of 3 km / hr , 4 km / hr and 5 km / hr and takes a total time of 47 minutes . the total distance is ?
Options: a ) 1 km , b ) 2 km , c ) 3 km , d ) 4 km , e ) 5 km
Rationale: "c 3 km let the total distance be 3 x km . then , x / 3 + x / 4 + x / 5 = 47 / 60 47 x / 60 = 47 / 60 = > x = 1 . total distance = 3 * 1 = 3 km ."
Answer: c
Question (general): if x is an integer such that 0 < x < 7 , 0 < x < 15 , 5 > x > – 1 , 3 > x > 0 , and x + 2 < 4 , then x is
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "0 < x < 7 , 0 < x < 15 , 5 > x > – 1 3 > x > 0 x < 2 from above : 0 < x < 2 - - > x = 1 . answer : a ."
Answer: a
Question (gain): an error 5 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is :
Options: a ) 10.01 , b ) 9.25 , c ) 10.25 , d ) 8.25 , e ) 6.25
Rationale: "explanation : 100 cm is read as 105 cm . a 1 = ( 100 × 100 ) cm 2 = 10000 and a 2 = ( 105 × 105 ) cm 2 = 10816 ( a 2 - a 1 ) = 11025 - 10000 = 1025 = > 1025 / 10000 * 100 = 10.25 answer : c"
Answer: c
Question (general): 1 + 1
Options: a ) 9 , b ) 8 , c ) 3 , d ) 0 , e ) 2
Rationale: e
Answer: e
Question (physics): rahul can do a work in 3 days while rajesh can do the same work in 2 days . both of them finish the work together and get $ 150 . what is the share of rahul ?
Options: a ) $ 50 , b ) $ 40 , c ) $ 60 , d ) $ 100 , e ) $ 90
Rationale: "rahul ' s wages : rajesh ' s wages = 1 / 3 : 1 / 2 = 2 : 3 rahul ' s share = 150 * 2 / 5 = $ 60 answer is c"
Answer: c