Cheukting/mathqa huggingface dataset:
Question (general): find the product of the localvalue and absolutevalue of 5 in 20568 ?
Options: a ) 1000 , b ) 2500 , c ) 1200 , d ) 5000 , e ) 1600
Rationale: "local value of 5 = 5 x 100 = 500 place value of 5 = 5 there fore = 5 x 500 = 2500 b"
Answer: b
Question (gain): a man cheats while buying as well as while selling . while buying he takes 10 % more than what he pays for and while selling he gives 20 % less than what he claims to . find the profit percent , if he sells at 9.09 % below the cost price of the claimed weight .
Options: a ) 19.81 % , b ) 20 % , c ) 37.5 % , d ) 25 % , e ) 37.5 %
Rationale: "( 1 + m 1 % ) ( 1 + m 2 % ) ( 1 - d % ) = ( 1 + p % ) 11 / 10 * 5 / 4 * 10 / 11 = ( 1 + p % ) profit % = 25 % answer : d"
Answer: d
Question (geometry): a 1.5 by 2 rectangle is inscribed in circle . what is the circumference of the circle ?
Options: a ) 2.5 π
b ) 3 π
c ) 3.5 π
d ) 4 π
e ) 5.5 π
Rationale: the diagonal of the rectangle will be the diameter of the circle . and perimeter = 2 * pi * r ans : a
Answer: a
Question (gain): a sum of rs . 2665 is lent into two parts so that the interest on the first part for 5 years at 3 % per annum may be equal to the interest on the second part for 3 years at 5 % per annum . find the second sum ?
Options: a ) rs . 1178.55 , b ) rs . 1978.25 , c ) rs . 1332.5 , d ) rs . 1678 , e ) rs . 1675.55
Rationale: "( x * 5 * 3 ) / 100 = ( ( 2665 - x ) * 3 * 5 ) / 100 15 x / 100 = 39975 / 100 - 15 x / 100 30 x = 39975 = > x = 1332.5 second sum = 2665 – 1025 = 1332.5 answer : c"
Answer: c
Question (general): 2 , 3 , 6 , 15 , _ , 123 ?
Options: a ) 42 , b ) 38 , c ) 28 , d ) 29 , e ) 11
Rationale: answer : a
Answer: a
Question (other): nitin ranks 15 th in a class of 47 students . what is rank from the last ?
Options: a ) 33 , b ) 38 , c ) 32 , d ) 28 , e ) 19
Rationale: "explanation : number students behind the nitin in rank = ( 47 - 15 ) = 32 nitin is 33 rd from the last answer : a ) 33"
Answer: a
Question (physics): cole drove from home to work at an average speed of 70 kmh . he then returned home at an average speed of 105 kmh . if the round trip took a total of 2 hours , how many minutes did it take cole to drive to work ?
Options: a ) 66 , b ) 70 , c ) 72 , d ) 75 , e ) 78
Rationale: "let the distance one way be x time from home to work = x / 70 time from work to home = x / 105 total time = 2 hrs ( x / 70 ) + ( x / 105 ) = 2 solving for x , we get x = 84 time from home to work in minutes = ( 84 ) * 60 / 70 = 72 minutes ans = c"
Answer: c
Question (general): what is the least common multiple of 152 and 190 ?
Options: a ) 304 , b ) 14440 , c ) 760 , d ) 28880 , e ) 1520
Rationale: "yes there is a shorter way 152 = 2 * 2 * 2 * 19 190 = 2 * 5 * 19 i think everyone knows how to do this . then choose 2 * 2 * 2 and choose 5 and choose 19 2 * 2 * 2 * 5 * 19 = 760 answer is c"
Answer: c
Question (general): in how many ways can an answer key for a quiz be written if the quiz contains 5 true - false questions followed by 3 multiple - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 1220 , b ) 1650 , c ) 1920 , d ) 2440 , e ) 2860
Rationale: "there are 2 ^ 5 = 32 possibilities for the true - false answers . however we need to remove two cases for ttttt and fffff . there are 4 * 4 * 4 = 64 possibilities for the multiple choice questions . the total number of possibilities is 30 * 64 = 1920 . the answer is c ."
Answer: c
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 15 cm .
Options: a ) 289 cm 2
b ) 285 cm 2
c ) 287 cm 2
d ) 267 cm 2
e ) 207 cm 2
Rationale: area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 15 ) = 285 cm 2 answer : b
Answer: b
Question (general): canister c is 1 / 2 full of water and canister d , which has twice the capacity of canister c , is 1 / 3 full of water . if the water in canister d is poured in canister c until canister c is completely full of water , canister d will still contain what fraction of its capacity of water ?
Options: a ) 0 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 6 , e ) 1 / 4
Rationale: say canister c has a capacity of 6 liters . it ' s half full , thus there can be poured 3 liters of water . canister b is 12 liters and there are 4 liters of water . we can pour 3 liters from d to c and 1 liter will still be left in d , which is 1 / 12 of its total capacity . answer : c .
Answer: c
Question (other): three numbers are in the ratio 3 : 4 : 5 and their l . c . m . is 6000 . their h . c . f is ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 100
Rationale: "let the numbers be 3 x , 4 x and 5 x their l . c . m . = 60 x 60 x = 6000 x = 100 the numbers are 3 * 100 , 4 * 100 , 5 * 100 hence required h . c . f . = 100 answer is e"
Answer: e
Question (physics): jose is uploading a file to the internet for a college project . the file weighs 160 megabytes . if jose ' s internet speed for uploading tops 8 megabytes per minute , how long will it take until the upload is completed ?
Options: a ) 1 hour , b ) 45 minutes , c ) 20 minutes , d ) 5 minutes , e ) 1 hour and 10 minutes
Rationale: answer is ( c ) . jose calculates that if the files weighs 160 megabytes , and his internet uploads at 8 megabytes per minute , it would take 20 minutes to upload as 160 divided by 8 megabytes per minute equals 20 .
Answer: c
Question (general): the average monthly salary of 20 employees in an organisation is rs . 1600 . if the manager ' s salary is added , then the average salary increases by rs . 100 . what is the manager ' s monthly salary ?
Options: a ) 3700 , b ) 3890 , c ) 88798 , d ) 2789 , e ) 2891
Rationale: "explanation : manager ' s monthly salary rs . ( 1700 * 21 - 1600 * 20 ) = rs . 3700 . answer : a ) 3700"
Answer: a
Question (general): a man spend 1 / 5 of his salary on food , 1 / 10 of his salary on house rent and 3 / 5 salary on clothes . he still has $ 19000 left with him . find salary . .
Options: a ) $ 10900 , b ) $ 19000 , c ) $ 190000 , d ) $ 1900 , e ) none
Rationale: "[ 1 / ( x 1 / y 1 + x 2 / y 2 + x 3 / y 3 ) ] * total amount = balance amount [ 1 - ( 1 / 5 + 1 / 10 + 3 / 5 ) } * total salary = $ 19000 , = [ 1 - 9 / 10 ] * total salary = $ 19000 , total salary = $ 19000 * 10 = $ 190000 , correct answer ( c )"
Answer: c
Question (general): in an examination , there were 2,000 candidates , out of which 900 candidates were girls and rest were boys . if 30 % of the boys and 32 % of the girls passed , then the total percentage of failed candidates is ?
Options: a ) 35.67 % , b ) 64.75 % , c ) 68.57 % , d ) 69.10 % , e ) none of these
Rationale: "girls = 900 , boys = 1100 passed = ( 30 % of 1100 ) + ( 32 % of 900 ) = 330 + 288 = 618 failed = 2000 - 618 = 1382 failed % = [ ( 1382 / 2000 ) x 100 ] % = 69.1 % . answer : d"
Answer: d
Question (general): if 2 x + y = 7 and x + 2 y = 10 , then ( x + y ) / 3 =
Options: a ) 1 , b ) 4 / 3 , c ) 17 / 9 , d ) 18 / 5 , e ) 4
Rationale: "we have two equations : 2 x + y = 7 x + 2 y = 10 notice that something nice happens when we add them . we get : 3 x + 3 y = 17 divide both sides by 3 to get : x + y = 17 / 3 so , ( x + y ) / 3 = 17 / 9 answer : c"
Answer: c
Question (physics): two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 40 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 110 , c ) 120 , d ) 16 , e ) 180
Rationale: "c 120 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 40 mph = 120 miles"
Answer: c
Question (other): puzzle ! ! ! 🙂 if 111 = 09 444 = 12 777 = 15 then 888 = ? ? ?
Options: a ) 13 , b ) 17 , c ) 18 , d ) 11 , e ) 15
Rationale: e 15 one + one + one ( 3 + 3 + 3 ) = 09 four + four + four ( 4 + 4 + 4 ) = 12 seven + seven + seven ( 5 + 5 + 5 ) = 15 therefore eight + eight + eight ( 5 + 5 + 5 ) = 15
Answer: e
Question (physics): town m town n town o town p town q town r ; town a town b town c town d town e town f in the table above , what is the least number of table entries that are needed to show the mileage between each town and each of the other 5 towns ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: easy way to go about this problem is we have 6 * 6 = 36 enteries in table the least number of enteries would be ( 36 - 6 ) / 2 since 6 enteries represent the distances between same points . alternatively this can be solved as combination problem . correct answer e
Answer: e
Question (physics): what is the greatest of 3 consecutive integers whose sum is 33 ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 14
Rationale: "33 / 3 = 11 the three numbers are 10 , 11 , and 12 . the answer is c ."
Answer: c
Question (geometry): a diagonal of a polygon is an segment between two non - adjacent vertices of the polygon . how many diagonals does a regular 45 - sided polygon have ?
Options: a ) 875 , b ) 945 , c ) 1425 , d ) 2025 , e ) 2500
Rationale: "there ' s a direct formula for this . number of diagonals in a regular polygon = [ n * ( n - 3 ) ] / 2 , n = number of sides of the regular polygon . here , n = 45 . plugging it in , we get 945 diagonals ! answer ( b ) ."
Answer: b
Question (general): divide rs . 1600 among a , b and c so that a receives 1 / 3 as much as b and c together and b receives 2 / 3 as a and c together . a ' s share is ?
Options: a ) rs . 800 , b ) rs . 400 , c ) rs . 600 , d ) rs . 500 , e ) rs . 900
Rationale: "a + b + c = 1600 a = 1 / 3 ( b + c ) ; b = 2 / 3 ( a + c ) a / ( b + c ) = 1 / 3 a = 1 / 4 * 1600 = > 400 answer : b"
Answer: b
Question (general): 112 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 66 , b ) 26 , c ) 49 , d ) 27 , e ) 11
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 112 = 49 answer : c"
Answer: c
Question (gain): a , b and c started a shop by investing rs . 5,000 , rs . 15,000 and rs . 30,000 respectively . at the end of the year , the profits were distributed among them . if c â € ™ s share of profit be rs . 3000 , then the total profit was :
Options: a ) 30,000 , b ) 5,000 , c ) 80,000 , d ) 120,000 , e ) none
Rationale: sol . a : b : c = 5000 : 15000 : 30000 = 1 : 3 : 6 . so , c â € ™ s share : total profit = 6 : 10 let the total profit be rs . x . then , 6 / 10 = 3000 / x or x = 3000 * 10 / 6 = 5000 . answer b
Answer: b
Question (general): christine selects an item at a 25 % off ticket price sale . the item is ticket priced at $ 25 . how much should christine expect to pay at the register ?
Options: a ) 22.5 , b ) 20.0 , c ) 18.75 , d ) 12.5 , e ) 10.0
Rationale: r . p . = $ 25.00 sale % = 25 s . p . = r . p . * ( 1 - ( sale % / 100 ) ) = 25 * ( 1 - ( 25 / 100 ) ) = 18.75 answer : c
Answer: c
Question (general): two employees x and y are paid a total of rs . 500 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 . 227 , b ) s . 287 , c ) s . 297 , d ) s . 300 , e ) s . 380
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 500 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 500 ⇒ y [ 12 / 10 + 1 ] = 500 ⇒ 22 y / 10 = 500 ⇒ 22 y = 5000 ⇒ y = 5000 / 22 = rs . 227.77 a )"
Answer: a
Question (geometry): if the perimeter of square region e and the perimeter of rectangular region r are equal and the sides of r are in the ratio 2 : 3 then the ratio of the area of r to the area of e
Options: a ) 25 : 16
b ) 24 : 25
c ) 5 : 6
d ) 4 : 5
e ) 4 : 9
Rationale: we know perimeter of a square ( pe ) = 4 * side perimeter of a rectangle ( pr ) = 2 ( length + breath ) let us assume 40 to be the perimeter of the square ( since we know each side of a square is equal and the perimeter is divisible by 4 , also take in to account the length and breadth of the rectangle is in the ration 2 k : 3 k = 5 k ; we can assume such a number ) therefore , pe = pr = 40 area of the square = 100 sq . units we know 2 ( length + breadth ) = 40 i . e . length + breadth = 20 ( or 5 k = 20 given that l : b ( or b : l ) = 2 : 3 ) therefore length = 8 , breath = 12 area of the rectangle = 8 * 12 = 96 sq . units question asked = area of the rectangle : area of the square = 96 : 100 = = > 24 : 25 = b
Answer: b
Question (physics): p can do a work in the same time in which q and r together can do it . if p and q work together , the work can be completed in 10 days . r alone needs 30 days to complete the same work . then q alone can do it in
Options: a ) 10 , b ) 22 , c ) 25 , d ) 27 , e ) 30
Rationale: work done by p and q in 1 day = 1 / 10 work done by r in 1 day = 1 / 30 work done by p , q and r in 1 day = 1 / 10 + 1 / 30 = 4 / 30 but work done by p in 1 day = work done by q and r in 1 day . hence the above equation can be written as work done by p in 1 day ã — 2 = 4 / 30 = > work done by p in 1 day = 4 / 60 = > work done by q and r in 1 day = 4 / 60 hence work done by q in 1 day = 4 / 60 â € “ 1 / 30 = 2 / 60 = 1 / 30 so q alone can do the work in 30 days answer is e .
Answer: e
Question (general): calculate the average of all the numbers between 11 and 27 which are divisible by 2 .
Options: a ) 11 , b ) 10 , c ) 18 , d ) 19 , e ) 21
Rationale: "explanation : numbers divisible by 2 are 12,14 , 16,18 , 20,22 , 24,26 , average = ( 12 + 14 + 16 + 18 + 20 + 22 + 24 + 26 , ) / 8 = 152 / 8 = 19 answer : d"
Answer: d
Question (gain): we had $ 3500 left after spending 30 % of the money that we took for shopping . how much money did we start with ?
Options: a ) $ 4600 , b ) $ 4800 , c ) $ 5000 , d ) $ 5200 , e ) $ 5400
Rationale: "let x be the amount of money we started with . 0.7 x = 3500 x = 5000 the answer is c ."
Answer: c
Question (gain): at the end of the month , a certain ocean desalination plant ’ s reservoir contained 40 million gallons of water . this amount is one fifth of the normal level . if this amount represents 80 % of the reservoir ’ s total capacity , how many million gallons short of total capacity is the normal level ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "the q talks of total capacity , normal level , present level , shortage etc . . so it is all about not going wrong in these terms 40 mg = 80 % of total . . total = 40 / . 8 = 50 mg . . normal level = 1 / 5 of 50 = 10 mg . . shortage of normal level = 50 - 10 = 40 mg . . c"
Answer: c
Question (other): on a certain farm the ratio of horses to cows is 3 : 1 . if the farm were to sell 15 horses and buy 15 cows , the ratio of horses to cows would then be 5 : 3 . after the transaction , how many more horses than cows would the farm own ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 50 , e ) 60
Rationale: "originally , there were 3 k horses and k cows . 3 ( 3 k - 15 ) = 5 ( k + 15 ) 9 k - 5 k = 75 + 45 4 k = 120 k = 30 the difference between horses and cows is ( 3 k - 15 ) - ( k + 15 ) = 2 k - 30 = 30 the answer is b ."
Answer: b
Question (general): what is the total number of integers between 2 and 38 that are divisible by 4 ?
Options: a ) 8 , b ) 9 , c ) 7 , d ) 6 , e ) 11
Rationale: "4 , 6 , 8 , . . . , 32,36 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 36 - 4 ) / ( 4 ) + 1 = 32 / 4 + 1 = 8 + 1 = 9 answer is b"
Answer: b
Question (general): a gardener wants to plant trees in his garden in such a way that the number of trees in each row should be the same . if there are 7 rows or 6 rows or 4 rows , then no tree will be left . find the least number of trees required
Options: a ) 22 , b ) 84 , c ) 28 , d ) 76 , e ) 21
Rationale: "explanation : the least number of trees that are required = lcm ( 7 , 6,4 ) = 84 . answer : b"
Answer: b
Question (general): the number n is 5 , h 64 , where h represents the 100 ' s digit . if n is divisible by 4 , what is the value of h ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) all the above value
Rationale: if the number is divisible by 4 , the last two digits must be divisible by 4 . all the values yields such a number . answer : e
Answer: e
Question (general): if { x } is the product of all even integers from 1 to x inclusive , what is the greatest prime factor of { 22 } + { 20 } ?
Options: a ) 23 , b ) 20 , c ) 11 , d ) 5 , e ) 2
Rationale: "soln : { 22 } + { 20 } = 22 * { 20 } + { 20 } = 23 * { 20 } answer : a"
Answer: a
Question (geometry): what is the maximum number t of 27 cubic centimetre cubes that can fit in a rectangular box measuring 8 centimetre x 9 centimetre x 12 centimetre ?
Options: a ) 36
b ) 32
c ) 24
d ) 21
e ) 15
Rationale: 27 cubic centimetre cubes gives side = 3 cm so if : l * w * h is 9 * 12 * 8 , then max . cube we can have are 3 * 4 * 2 = 24 l * w * h is 9 * 8 * 12 , then max . cube we can have are 3 * 2 * 4 = 24 l * w * h is 12 * 8 * 9 , then max . cube we can have are 4 * 2 * 3 = 24 l * w * h is 12 * 9 * 8 , then max . cube we can have are 4 * 3 * 2 = 24 l * w * h is 8 * 12 * 9 , then max . cube we can have are 2 * 4 * 3 = 24 l * w * h is 8 * 9 * 12 , then max . cube we can have are 2 * 3 * 4 = 24 in all cases we get t = 24 cubes . ans . c
Answer: c
Question (general): if x gets 25 % more than y and y gets 20 % more than z , the share of z out of rs . 1480 will be :
Options: a ) rs . 300 , b ) rs . 200 , c ) rs . 240 , d ) rs . 400 , e ) none of these
Rationale: "z share = z , y = 1.2 z x = 1.25 ã — 1.2 z , x + y + z = 1480 ( 1.25 ã — 1.2 + 1.2 + 1 ) z = 1480 3.7 z = 1480 , z = 400 answer : . d"
Answer: d
Question (general): the sum of the present ages of two persons a and b is 60 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 70 , b ) 25 , c ) 60 , d ) 80 , e ) 55
Rationale: "a + b = 60 , a = 2 b 2 b + b = 60 = > b = 20 then a = 40 . 5 years , their ages will be 45 and 25 . sum of their ages = 45 + 25 = 70 . answer a"
Answer: a
Question (other): if the ratio of apples to bananas is 5 to 2 and the ratio of bananas to cucumbers is 1 to 3 , what is the ratio of apples to cucumbers ?
Options: a ) 2 : 3 , b ) 5 : 3 , c ) 5 : 6 , d ) 1 : 4 , e ) 3 : 4
Rationale: "the ratio of bananas to cucumbers is 1 to 3 which equals 2 to 6 . the ratio of apples to bananas to cucumbers is 5 to 2 to 6 . the ratio of apples to cucumbers is 5 to 6 . the answer is c ."
Answer: c
Question (geometry): in the xy - plane , a triangle has vertices ( 0,0 ) , ( 4,0 ) and ( 4,6 ) . 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 / 3 , e ) 4 / 5
Rationale: "the area of the right triangle is ( 1 / 2 ) * 4 * 6 = 12 . 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 / 12 = 2 / 3 the answer is d ."
Answer: d
Question (geometry): the edge of a cube is 4 a cm . find its surface ?
Options: a ) 24 a 8 , b ) 24 a 4 , c ) 96 a 2 , d ) 24 a 2 , e ) 24 a 7
Rationale: "6 a 2 = 6 * 4 a * 4 a = 96 a 2 answer : c"
Answer: c
Question (other): the ratio of the present age of two brothers is 1 : 2 and 5 years back , the ratio was 1 : 3 . what will be the ratio of their ages after 5 years ?
Options: a ) 3 : 9 , b ) 3 : 0 , c ) 3 : 5 , d ) 3 : 2 , e ) 3 : 1
Rationale: let the present ages of the two brothers be x and 2 x years respectively . then , ( x - 5 ) / ( 2 x - 5 ) = 1 / 3 3 ( x - 5 ) = ( 2 x - 5 ) = > x = 10 required ratio = ( x + 5 ) : ( 2 x + 5 ) = 15 : 25 = 3 : 5 answer : c
Answer: c
Question (general): find the least number must be subtracted from 724946 so that remaining no . is divisible by 10 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "on dividing 724946 by 10 we get the remainder 6 , so 6 should be subtracted d"
Answer: d
Question (general): if x is 20 percent more than y and y is 30 percent less than z , then x is what percent of z ?
Options: a ) 500 % , b ) 250 % , c ) 500 / 3 % , d ) 84 % , e ) 60 %
Rationale: "z = 100 ; y = 70 so x = 84 x as % of z = 84 / 100 * 100 = > 84 % answer will be ( d )"
Answer: d
Question (physics): a truck covers a distance of 240 km at a certain speed in 8 hours . how much time would a car take at an average speed which is 18 kmph more than that of the speed of the truck to cover a distance which is 0 km more than that travelled by the truck ?
Options: a ) 6 hours , b ) 5 hours , c ) 7 hours , d ) 8 hours , e ) none
Rationale: "explanation : speed of the truck = distance / time = 240 / 8 = 30 kmph now , speed of car = ( speed of truck + 18 ) kmph = ( 30 + 18 ) = 48 kmph distance travelled by car = 240 + 0 = 240 km time taken by car = distance / speed = 240 / 48 = 5 hours . answer – b"
Answer: b
Question (general): evaluate : 57 - 12 * 3 * 2 = ?
Options: a ) 42 , b ) 49 , c ) 62 , d ) 72 , e ) 82
Rationale: "according to order of operations , 12 ? 3 ? 2 ( division and multiplication ) is done first from left to right 12 * * 2 = 4 * 2 = 8 hence 57 - 12 * 3 * 2 = 57 - 8 = 49 correct answer b"
Answer: b
Question (general): a mixture of 180 liters of wine and water contains 20 % water . how much more water should be added so that water becomes 25 % of the new mixture ?
Options: a ) 4 liters , b ) 8 liters , c ) 10 liters , d ) 12 liters , e ) 12.5 liters
Rationale: "number of liters of water in 180 liters of the mixture = 20 % of 120 = 20 / 100 * 180 = 36 liters . p liters of water added to the mixture to make water 25 % of the new mixture . total amount of water becomes ( 36 + p ) and total volume of mixture is ( 180 + p ) . ( 36 + p ) = 25 / 100 * ( 180 + p ) 96 + 4 p = 180 + p p = 12 liters . answer : d"
Answer: d
Question (general): the sum of all the integers k such that – 23 < k < 24 is
Options: a ) 0 , b ) - 43 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: "- 22 - - - - - - - - - - - - - - - - - - 0 - - - - - - - - - - - - - - - - - 23 values upto + 23 cancels outwe are left with only - 22 - 21 sum of which is - 43 . hence option d . b"
Answer: b
Question (general): there are 3 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ?
Options: a ) 10 , b ) 12 , c ) 24 , d ) 60 , e ) 100
Rationale: "there are 3 red chips and 2 blue ones . when arranged in a row , they form a certain color pattern , for example rbrrb . how many color patterns ? 10 12 24 60 100 soln : total number of patterns is 5 ! since 3 red chips are identical and 2 blue ones are identical thus we have = 5 ! / ( 2 ! * 3 ! ) = 10 such different patterns a"
Answer: a
Question (physics): john traveled 80 % of the way from yellow - town to green - fields by train at an average speed of 80 miles per hour . the rest of the way john traveled by car at an average speed of v miles per hour . if the average speed for the entire trip was 45 miles per hour , what is v in miles per hour ?
Options: a ) 30 , b ) 40 , c ) 50 , d ) 55 , e ) 70
Rationale: "hibunuel the question seems incorrect . it should not be 80 % at the speed of 80 . however if it ' s 20 % at the speed of 80 , answer comes out 55 . the question is correct . here ' s the explanation : let distance be d . we can find the total timeequate it , which comes as : 0.8 d / 80 + 0.2 d / v = d / 40 = > v = 40 ( option b ) ."
Answer: b
Question (general): what is the sum between the place values of three 7 ' s in the numeral 87953.0727
Options: a ) 21 , b ) 7000.0707 , c ) 7777 , d ) 7014 , e ) 7000.0077
Rationale: "required sum = 7000 + 0.0700 + 0.0007 = 7000.0707 answer is b"
Answer: b
Question (general): the average salary of all the workers in a workshop is rs . 8000 . the average salary of 6 technicians is rs . 12000 and the average salary of the rest is rs . 6000 . the total number of workers in the workshop is ?
Options: a ) a ) 23 , b ) b ) 21 , c ) c ) 18 , d ) d ) 56 , e ) e ) 12
Rationale: "let the total number of workers be x . then , 8000 x = ( 12000 * 6 ) + 6000 ( x - 6 ) = > 2000 x = 36000 = x = 18 . answer : c"
Answer: c