Cheukting/mathqa huggingface dataset:
Question (general): if 60 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50 % , b ) 44.4 % , c ) 22.2 % , d ) 33.3 % , e ) 25 %
Rationale: "60 % of ( x - y ) = 20 % of ( x + y ) 60 / 100 ( x - y ) = 20 / 100 ( x + y ) 4 x = 8 y required percentage = y / x * 100 = 4 y / 8 y * 100 = 50 % answer is a"
Answer: a
Question (physics): a and b undertake to do a piece of work for rs . 600 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . ! find the share of each .
Options: a ) 25 , b ) 50 , c ) 75 , d ) 80 , e ) none of them
Rationale: c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 600 * 4 / 8 ) = rs . 300 , b ' s share = rs . ( 600 * 3 / 8 ) = rs . 225 . c ' s share = rs . [ 600 - ( 300 + 225 » ) = rs . 75 . answer is c
Answer: c
Question (general): how many even integers n , such that 20 < = n < = 220 are of the form 3 k + 4 , where k is any natural number ?
Options: a ) 28 , b ) 31 , c ) 34 , d ) 37 , e ) 40
Rationale: "the first number is 22 = 16 + 6 ( 1 ) . we can continue adding 6 to make a list : 22 , 28 , 34 , . . . the last number is 220 = 16 + 6 ( 34 ) there are 34 numbers in the list . the answer is c ."
Answer: c
Question (physics): the edges of three metal cubes are 1 cm , 3 cm , and 4 cm respectively . a new cube is made by melting these three cubes together . what is the edge of the new cube ( in centimeters ) ?
Options: a ) 3.9 , b ) 4.2 , c ) 4.5 , d ) 4.8 , e ) 5.1
Rationale: the total volume is 1 ^ 3 + 3 ^ 3 + 4 ^ 3 = 92 the edge of the new cube is the cube root of 92 which is about 4.5 cm . the answer is c .
Answer: c
Question (gain): an inspector rejects 10 % of the meters as defective . how many will he examine to reject 12 ?
Options: a ) a ) 100 , b ) b ) 120 , c ) c ) 250 , d ) d ) 200 , e ) e ) 160
Rationale: "then , 10 % of x = 12 ( 10 / 100 ) x = 12 x = ( 12 * 100 * ) / 10 = 120 answer is b"
Answer: b
Question (gain): a survey was sent to 60 customers , 7 of whom responded . then the survey was redesigned and sent to another 72 customers , 9 of whom responded . by approximately what percent did the response rate increase from the original survey to the redesigned survey ?
Options: a ) 2 % , b ) 7 % , c ) 14 % , d ) 28 % , e ) 63 %
Rationale: "rate of first survey = 7 / 60 rate of second survey = 9 / 72 % response rate increase ( 9 / 72 - 7 / 60 ) / ( 7 / 60 ) = 7 % answer is b = 7 %"
Answer: b
Question (geometry): if the sides of a square are multiplied by 5 , the area of the original square is how many times as large as the area of the resultant square ?
Options: a ) 4 % , b ) 25 % , c ) 50 % , d ) 200 % , e ) 400 %
Rationale: "let x be the original length of one side . then the original area is x ^ 2 . the new square has sides of length 5 x , so the area is 25 x ^ 2 . the area of the original square is 1 / 25 = 4 % times the area of the new square . the answer is a ."
Answer: a
Question (physics): car a runs at the speed of 50 km / hr & reaches its destination in 6 hr . car b runs at the speed of 100 km / h & reaches its destination in 1 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 5 , b ) 3 : 1 , c ) 13 : 7 , d ) 15 : 7 , e ) 16 : 9
Rationale: "sol . distance travelled by car a = 50 × 6 = 300 km distance travelled by car b = 100 × 1 = 100 km ratio = 300 / 100 = 3 : 1 answer : b"
Answer: b
Question (geometry): a cubical block of metal weighs 8 pounds . how much will another cube of the same metal weigh if its sides are twice as long ?
Options: a ) 48 , b ) 32 , c ) 24 , d ) 18 , e ) 64
Rationale: "for example our cube have a side 1 meter , so we have 1 cubical meter in this cube and this cubical meter weigth 6 pounds if we take cube with side 2 meters we will have 8 cubical meters in this cube 8 meters * 8 pounds = 64 pounds so answer is e and similar but more theoretical approach : if we have sides a and b than they have equal ration with their areas : a / b = a ^ 2 / b ^ 2 and they have equal ration with their volumes : a / b = a ^ 3 / b ^ 3 we have two sides 1 / 2 so their volume will be in ratio 1 / 8 weight of one cube * volume of another cube 8 * 8 = 64 so answer is e"
Answer: e
Question (general): of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 20 grades are d ' s . what is the number of students in the course ?
Options: a ) 80 , b ) 110 , c ) 160 , d ) 200 , e ) 400
Rationale: "we start by creating a variable for the total number of students in the math course . we can say : t = total number of students in the math course next , we can use variable t in an equation that we translate from the given information . we are given that , of the final grades received by the students in a certain math course , 1 / 5 are a ' s , 1 / 4 are b ' s , 1 / 2 are c ' s , and the remaining 20 grades are d ' s . since this represents all the grades in the class , it represents all the students in the class . thus we know : # a ’ s + # b ’ s + # c ’ s + # d ’ s = total number of students in the class 1 / 5 ( t ) + ¼ ( t ) + ½ ( t ) + 20 = t we can multiply the entire equation by 20 to cancel out the denominators of the fractions and we have : 4 t + 5 t + 10 t + 400 = 20 t 19 t + 400 = 20 t 400 = t there are a total of 400 students in the math class . answer is e ."
Answer: e
Question (physics): how many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long
Options: a ) 30 , b ) 40 , c ) 50 , d ) 60 , e ) 70
Rationale: explanation : we need so simple divide 42.5 / 0.85 , = ( 4250 / 85 ) = 50 option c
Answer: c
Question (other): ratio between rahul and deepak is 5 : 2 , after 6 years rahul age will be 26 years . what is deepak present age .
Options: a ) 14 , b ) 15 , c ) 8 , d ) 22 , e ) 24
Rationale: "explanation : present age is 5 x and 2 x , = > 5 x + 6 = 26 = > x = 4 so deepak age is = 2 ( 4 ) = 8 option c"
Answer: c
Question (physics): in what time will a train 400 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.5 sec , b ) 12.9 sec , c ) 11.3 sec , d ) 21.9 sec , e ) 10.0 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 400 / 40 = 10.0 sec . answer : e"
Answer: e
Question (general): set a consists of all the prime numbers between 62 and 85 . what is the range of set a ?
Options: a ) 12 , b ) 13 , c ) 16.6 , d ) 16 , e ) 23
Rationale: the range of a set of data is the difference between the highest and lowest values in the set in this set , highest number = 83 lowest number = 67 range = highest - lowest = 83 - 67 = 16 option d
Answer: d
Question (gain): a fruit seller had some apples . he sells 60 % apples and still has 300 apples . originally , he had :
Options: a ) 656 apples , b ) 700 apples , c ) 750 apples , d ) 780 apples , e ) 800 apples
Rationale: "a fruit seller had some apples . he sells 60 % apples and still has 300 apples . originally , he had : a . 656 apples b . 700 apples c . 750 apples d . 780 apples 800 apples answer : option d explanation : suppose originally he had x apples . then , ( 100 - 60 ) % of x = 300 . 40 / 100 x x = 300 100 x = ( 300 x 1000 ) / 40 = 750 . answer : c"
Answer: c
Question (general): s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits w are in s ( 99 ) ?
Options: a ) w = 350 , b ) w = 353 , c ) w = 354 , d ) 356 , e ) 357
Rationale: "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 . b"
Answer: b
Question (gain): a candidate got 35 % of the votes and lost to the rival by 1650 votes . how many votes were cast ?
Options: a ) 5000 , b ) 5500 , c ) 6000 , d ) 6500 , e ) 7000
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % = 1650 10 % = 550 100 % of the votes = 5500 answer : b"
Answer: b
Question (general): a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 8 miles per gallon , and from town b to town c , the car averaged 18 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 13 , b ) 15.5 , c ) 14 , d ) 14.5 , e ) 15
Rationale: "ans is b given d _ ab = 2 * d _ bc let d _ ab = d and d _ bc = x so d = 2 x for average miles per gallon = ( d + x ) / ( ( d / 8 ) + ( x / 18 ) ) = 15.5 ( formula avg speed = total distance / total time )"
Answer: b
Question (general): the total age of a and b is 10 years more than the total age of b and c . c is how many years younger than a . ?
Options: a ) 16 , b ) 12 , c ) 10 , d ) 20 , e ) 10
Rationale: "( a + b ) - ( b - c ) = 10 a - c = 10 answer is c"
Answer: c
Question (geometry): if the area of a circle is 25 pi square feet , find its circumference .
Options: a ) 10 pi feet , b ) 28 pi feet , c ) 38 pi feet , d ) 48 pi feet , e ) 58 pi feet
Rationale: "the area is given by pi * r * r . hence pi * r * r = 25 pi r * r = 25 ; hence r = 25 feet the circumference is given by 2 * pi * r = 2 * pi * 5 = 10 pi feet correct answer a"
Answer: a
Question (physics): excluding stoppages , the speed of a train is 67 kmph and including stoppages it is 51 kmph . of how many minutes does the train stop per hour ?
Options: a ) 82 , b ) 17 , c ) 14 , d ) 82 , e ) 18
Rationale: "explanation : t = 16 / 67 * 60 = 14 answer : option c"
Answer: c
Question (geometry): the sides of a square region , measured to the nearest centimeter , are 9 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 60.25 sq cm , b ) 66.25 sq cm , c ) 56.25 sq cm , d ) 72.25 sq cm , e ) 58.25 sq cm
Rationale: "though there might be some technicalities concerning the termnearest ( as 7.5 is equidistant from both 7 and 8 ) the answer still should be : 7.5 ^ 2 = 56.25 . answer : c"
Answer: c
Question (general): the average runs of a cricket player of 8 innings was 24 . how many runs must he make in his next innings so as to increase his average of runs by 8 ?
Options: a ) 12 , b ) 42 , c ) 64 , d ) 96 , e ) 84
Rationale: "explanation : average after 9 innings = 32 required number of runs = ( 32 * 9 ) – ( 24 * 8 ) = 288 – 192 = 96 answer d"
Answer: d
Question (physics): if jack walked 4 miles in 1 hour and 15 minutes , what was his rate of walking in miles per hour ?
Options: a ) 3.2 , b ) 4.5 , c ) 6 , d ) 6.25 , e ) 15
Rationale: distance walked in 1 hour and 15 mins = 4 miles speed per hour = distance / time = 4 / ( 5 / 4 ) = 3.2 miles per hour answer a
Answer: a
Question (physics): yesterday it took robert 6 hours to drive from city a to city b . today it took robert 4.5 hours to drive back from city в to city a along the same route . if he had saved 30 minutes in both trips , the speed for the round trip would be 90 miles per hour . what is the distance between city a and city b ?
Options: a ) 90 , b ) 120 , c ) 150 , d ) 440 , e ) 430
Rationale: 2 d / 90 = 9.5 ( because time = 6 + 4.5 - 1 hrs ) = > d = 430 answer - e
Answer: e
Question (general): a number consists of 3 digits whose sum is 10 . the middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed . the number is :
Options: a ) 251 , b ) 253 , c ) 255 , d ) 257 , e ) 260
Rationale: "let the middle digit be x . then , 2 x = 10 or x = 5 . so , the number is either 253 or 352 . since the number increases on reversing the digits , so the hundred ' s digits is smaller than the unit ' s digit . hence , required number = 253 . option b"
Answer: b
Question (physics): how many seconds will a train 110 meters long take to cross a railway platform 165 meters long if the speed of the train is 132 kmph ?
Options: a ) 6 sec , b ) 7.5 sec , c ) 8 sec , d ) 3 sec , e ) 10 sec
Rationale: "d = 110 + 165 = 275 s = 132 * 5 / 18 = 110 / 3 mps t = 275 * 3 / 110 = 7.5 sec b ) 7.5 sec"
Answer: b
Question (physics): 2 trains starting at the same time from 2 stations 200 km apart and going in opposite direction cross each other at a distance of 110 km from one of the stations . what is the ratio of their speeds
Options: a ) 11 : 9 , b ) 13 : 9 , c ) 17 : 9 , d ) 21 : 9 , e ) none of these
Rationale: "explanation : we know total distance is 200 km if both trains crossed each other at a distance of 110 km then one train covered 110 km and other 90 km [ 110 + 90 = 200 km ] so ratio of their speed = 110 : 90 = 11 : 9 option a"
Answer: a
Question (gain): 50 percent of andrea ' s living room floor is covered by a carpet that is 4 feet by 9 feet . what is the area of her living room floor ?
Options: a ) 14.4 , b ) 180 / 7 , c ) 50.4 , d ) 64.8 , e ) 90
Rationale: "50 % of area of the floor = 4 * 9 square feet = 36 square feet i . e . 100 % area of floor = ( 36 / 50 ) * 100 = 64.8 square feet answer : option d"
Answer: d
Question (physics): a work can be finished in 13 days by ten women . the same work can be finished in fifteen days by ten men . the ratio between the capacity of a man and a woman is
Options: a ) 14 : 13 , b ) 13 : 15 , c ) 12 : 13 , d ) 13 : 12 , e ) 14 : 15
Rationale: work done by 10 women in 1 day = 1 / 13 work done by 1 woman in 1 day = 1 / ( 13 ã — 10 ) work done by 16 men in 1 day = 1 / 15 work done by 1 man in 1 day = 1 / ( 15 ã — 10 ) ratio of the capacity of a man and woman = 1 / ( 15 ã — 10 ) : 1 / ( 13 ã — 10 ) = 1 / 15 : 1 / 13 = 1 / 15 : 1 / 13 = 13 : 15 answer is b .
Answer: b
Question (general): if 213 × 16 = 3408 , then 1.6 × 213.0 is equal to :
Options: a ) 0.3408 , b ) 3.408 , c ) 34.08 , d ) 340.8 , e ) none of these
Rationale: solution 1.6 × 21.3 = ( 16 / 10 x 213 ) = ( 16 x 213 / 10 ) = 3408 / 10 = 340.8 . answer d
Answer: d
Question (physics): a train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds . its length is
Options: a ) 100 , b ) 120 , c ) 130 , d ) 150 , e ) 140
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 25 = x / 15 x = 150 m . answer : option d"
Answer: d
Question (physics): the population of a bacteria colony doubles every day . if it was started 3 days ago with 3 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 1024 , c ) 768 , d ) 2048 , e ) 4096
Rationale: "9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 answer : b"
Answer: b
Question (physics): the h . c . f of two numbers is 15 and their l . c . m is 3300 . if one of the numbers is 225 , then the other is ?
Options: a ) 200 , b ) 210 , c ) 220 , d ) 230 , e ) 240
Rationale: "other number = ( 15 * 3300 ) / 225 = 220 . answer : c"
Answer: c
Question (gain): a bag marked at $ 80 is sold for $ 68 . the rate of discount is ?
Options: a ) 10 % , b ) 15 % , c ) 20 % , d ) 25 % , e ) 30 %
Rationale: "rate of discount = 12 / 80 * 100 = 15 % answer is b"
Answer: b
Question (general): { 5 , 6 , 3 , 8 , 4 } if we want to get the median value of the set to be 10 which value should be inserted in the set of 5 values ?
Options: a ) 5 , b ) 7 , c ) 15 , d ) 12 , e ) 13
Rationale: median is the middle number of a sorted distribution . in case of even number of items , median will be the average of middle two values . the question asks fora new number that will cause the median of new set at 10 . mentionable that given set is already sorted and number of items of new set will be 5 + 1 = 6 . to get median 10 , the sum of 3 th 4 th term should be 20 i . e . 3 + 7 . so to keep the median 10 , the new item should be > = 7 answer is b
Answer: b
Question (geometry): the area of a rhombus is equal to the area of a square whose side length is 8 cm . if one of the diagonals is 16 cm what is the length of other diagonal ?
Options: a ) 4
b ) 8
c ) 12
d ) 16
e ) 20
Rationale: area of the square = 8 x 8 = 64 let ' l ' be the unknown diagonal 0.5 x 16 x ' l ' = 64 which gives ' l ' = 8 cm answer : b
Answer: b
Question (gain): the cost price of 7 articles is equal to the selling price of 5 articles . what is the profit percent ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: "5 * sp = 7 * cp sp = 1.4 * cp the profit percent is 40 % . the answer is d ."
Answer: d
Question (physics): in a kilometer race , a beats b by 20 meters or 10 seconds . what time does a take to complete the race ?
Options: a ) 290 sec , b ) 190 sec , c ) 199 sec , d ) 192 sec , e ) 490 sec
Rationale: "time taken by b run 1000 meters = ( 1000 * 10 ) / 20 = 500 sec . time taken by a = 500 - 10 = 490 sec . answer : e"
Answer: e
Question (general): a positive number when decreased by 4 is equal to 21 times the reciprocal of the number . the number is
Options: a ) 3 , b ) 5 , c ) 7 , d ) 9 , e ) 12
Rationale: "sol . let the numbers be x . then , x - 4 = 21 / x ⇔ x 2 - 4 x - 21 = 0 ⇔ ( x - 7 ) ( x + 3 ) = 0 ⇔ x = 7 . answer c"
Answer: c
Question (gain): at what price must an book costing $ 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 25 % on the cost price ?
Options: a ) 72.5 , b ) 55.5 , c ) 62.5 , d ) 82.5 , e ) 60.5
Rationale: "c $ 62.50 cp = 47.50 sp = 47.50 * ( 125 / 100 ) = 59.375 mp * ( 95 / 100 ) = 59.375 mp = 62.5"
Answer: c
Question (physics): a car consumes 210 liters of petrol weekly . for how many days will 1470 liters of petrol be sufficient ?
Options: a ) 38 , b ) 20 , c ) 28 , d ) 49 , e ) 10
Rationale: explanation : no explanation is available for this question ! answer : d
Answer: d
Question (gain): one type of liquid contains 20 % of water and the second type of liquid contains 35 % of water . a glass is filled with 10 parts of 1 st liquid and 4 parts of 2 nd liquid . the percentage of water in the new mixture in the glass is ?
Options: a ) 22.15 % , b ) 23.5 % , c ) 24.3 % , d ) 25 % , e ) 29.6 %
Rationale: required percentage = ( 20 % of 10 + 35 % of 4 ) / 10 + 4 * 100 = 3.4 / 14 * 100 = 24.3 % answer is c
Answer: c
Question (physics): the sum of two consecutive integers is 61 . find the numbers .
Options: a ) 17 , 18 , b ) 30,31 , c ) 5 , 6 , d ) 1 , 2 , e ) 8 , 9
Rationale: "n + ( n + 1 ) = 61 2 n + 1 = 61 2 n = 60 n = 30 answer : b"
Answer: b
Question (geometry): cuboid volume and base area are 144 m ^ 3 and 18 m ^ 3 respectively . find the height of a cuboid ?
Options: a ) 5 m
b ) 12 m
c ) 6 m
d ) 8 m
e ) 10 m
Rationale: height of the cuboid = volume * base area = 144 / 18 = 8 metre answer is option d
Answer: d
Question (general): how many positive even integers less than 100 contain digits 7 or 9 ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 10
Rationale: "two digit numbers : 7 at tens place : 70 , 72,74 , 76,78 9 at tens place : 90 , 92,94 , 96,98 if 7 and 9 is at units place , the number cant be even total : 5 + 5 = 10 answer e"
Answer: e
Question (other): in a group of 650 readers who read science fiction or literacy works or both , 250 read science fiction and 550 read literacy works . how many read both science fiction and literacy works ?
Options: a ) 650 , b ) 250 , c ) 150 , d ) 100 , e ) 400
Rationale: "consider total number of reader n ( s u l ) = 650 people who read science fiction n ( s ) = 250 people who read literacy works n ( l ) = 550 both science fiction and literacy n ( s â ˆ © l ) = ? n ( s u l ) = n ( s ) + n ( l ) - n ( s â ˆ © l ) 650 = 250 + 550 - n ( s â ˆ © l ) n ( s â ˆ © l ) = 800 - 650 n ( s â ˆ © l ) = 150 so people read both science fiction and literacy works are 150 answer : c"
Answer: c
Question (geometry): if anangletis defined as 1 percent of 1 degree , then how many anglets are there in one half circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 360 , d ) 18,000 , e ) 36,000
Rationale: "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 180 degrees = 18,000 anglets answer - d"
Answer: d
Question (physics): the speed of a car is 80 km in the first hour and 40 km in the second hour . what is the average speed of the car ?
Options: a ) 72 kmph , b ) 60 kmph , c ) 30 kmph , d ) 80 kmph , e ) 82 kmph
Rationale: "s = ( 80 + 40 ) / 2 = 60 kmph answer : b"
Answer: b
Question (physics): two trains 200 m and 250 m long run at the speed of 72 kmph and 18 kmph in opposite directions in parallel tracks . the time which they take to cross each other is ?
Options: a ) 5.6 sec , b ) 8.9 sec , c ) 10.8 sec , d ) 12.6 sec , e ) 18 sec
Rationale: "relative speed = 72 + 18 = 90 kmph * 5 / 18 = 25 m / s distance covered in crossing each other = 200 + 250 = 450 m required time = 450 * 1 / 25 = 18 sec answer is e"
Answer: e
Question (general): the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 3000 ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 11 = 2048 < 3000 , then the greatest possible length of integer z is 11 . the answer is c ."
Answer: c
Question (physics): a cistern is filled by a tap in 4 1 / 2 hours . due to leak in the bottom of the cistern , it takes half an hour longer to fill the cistern . if the cistern is full how many hours will it take the leak to empty it ?
Options: a ) 30 , b ) 36 , c ) 42 , d ) 45 , e ) 48
Rationale: "filling rate - leak rate = net rate 1 / 4.5 - leak rate = 1 / 5 leak rate = 2 / 9 - 1 / 5 = 1 / 45 the answer is d ."
Answer: d
Question (general): what is ( 19 ^ 7 + 19 ) / 19 ?
Options: a ) 45225766 , b ) 46855821 , c ) 47045882 , d ) 48925947 , e ) 49325989
Rationale: "( 19 ^ 7 + 19 ) / 19 = 19 * ( 19 ^ 6 + 1 ) / 19 = 19 ^ 6 + 1 clearly this is a number which ends with a 2 in the units place . the answer is c ."
Answer: c
Question (general): a certain galaxy is known to comprise approximately 6 x 10 ^ 11 stars . of every 50 million of these stars , one is larger in mass than our sun . approximately how many stars in this galaxy are larger than the sun ?
Options: a ) 800 , b ) 1,250 , c ) 8,000 , d ) 12,000 , e ) 80,000
Rationale: "6 * 10 ^ 11 50 mln = 5 * 10 ^ 7 we divide 10 ^ 11 by 10 ^ 7 and we get ( 10 ^ 4 ) * 6 = 60,000 and divide by 5 . the result is 12,000 d"
Answer: d
Question (general): what is the remainder when 4 ^ 381 is divided by 5 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: i also agree that the remainder is ' 4 ' ( using the last digit of the powers of 7 ) . could we have the official answer please ? e
Answer: e
Question (gain): the present population of a town is 1000 . population increase rate is 25 % p . a . find the population of town before 1 years ?
Options: a ) 800 , b ) 1500 , c ) 1000 , d ) 750 , e ) 500
Rationale: "p = 1000 r = 25 % required population of town = p / ( 1 + r / 100 ) ^ t = 1000 / ( 1 + 25 / 100 ) = 1000 / ( 5 / 4 ) = 800 answer is a"
Answer: a
Question (other): a garrison of 400 men had a provision for 31 days . after 28 days 300 persons re - enforcement leave the garrison . find the number of days for which the remaining ration will be sufficient ?
Options: a ) 65 days , b ) 45 days , c ) 10 days , d ) 16 days , e ) 12 days
Rationale: "400 - - - 31 400 - - - 3 100 - - - ? 400 * 3 = 100 * x = > x = 12 days . answer : e"
Answer: e