Cheukting/mathqa huggingface dataset:
Question (gain): if 20 % of a is the same as 25 % of b , then a : b is :
Options: a ) 3 : 4 , b ) 4 : 3 , c ) 5 : 4 , d ) 6 : 7 , e ) 5 : 7
Rationale: "expl : 20 % of a i = 25 % of b = 20 a / 100 = 25 b / 100 = 5 / 4 = 5 : 4 answer : c"
Answer: c
Question (general): 4 , 7 , 16 , 43 , 124 , ( . . . )
Options: a ) 22 , b ) 367 , c ) 27 , d ) 32 , e ) 25
Rationale: "explanation : 4 4 × 3 - 5 = 7 7 × 3 - 5 = 16 16 × 3 - 5 = 43 43 × 3 - 5 = 124 124 × 3 - 5 = 367 answer : option b"
Answer: b
Question (gain): a man buys an article for $ 100 . and sells it for $ 120 . find the gain percent ?
Options: a ) 10 % , b ) 15 % , c ) 25 % , d ) 20 % , e ) 30 %
Rationale: "c . p . = $ 100 s . p . = $ 120 gain = $ 20 gain % = 20 / 100 * 100 = 20 % answer is d"
Answer: d
Question (general): the average weight of a class of 24 students is 35 kg . if the weight of the teacher be included , the average rises by 400 g . the weight of the teacher is
Options: a ) 45 kg , b ) 50 kg , c ) 53 kg , d ) 55 kg , e ) none of these
Rationale: "solution weight of the teacher = ( 35.4 × 25 - 35 × 24 ) kg = 45 kg . answer a"
Answer: a
Question (gain): what percent of 200 is 55 ?
Options: a ) 0.25 % , b ) 4 % , c ) 25 % , d ) 27.5 % , e ) 250 %
Rationale: "200 * x / 100 = 55 x = 27.5 ans : d"
Answer: d
Question (gain): a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 25 % ?
Options: a ) 600 , b ) 887 , c ) 625 , d ) 654 , e ) 712
Rationale: "cost price = rs . 500 profit = 25 % of 500 = rs . 125 selling price = cost price + profit = 500 + 125 = 625 answer : c"
Answer: c
Question (general): if 28 a + 30 b + 31 c = 545 . then a + b + c = ? . a , b , c are natural numbers
Options: a ) 12 , b ) 14 , c ) 8 , d ) 25 , e ) 18
Rationale: have a look on your calender since , we all knw a year consist of 365 days february is d only month which has 28 days 4 months in a year has 30 days and , rest 7 months has 31 days . . so , following d given eq . we can write 28 * 1 + 30 * 10 + 31 * 7 . . hence values of a , b and c are 1 , 10 and 7 respectively . . a + b + c = 18 answer : e
Answer: e
Question (probability): how many different ways can 2 students be seated in a row of 3 desks , so that there is always at least one empty desk between the students ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 12
Rationale: "1 ways to seat the students : with two empty seats between 1 empty w / one student on the left most 1 empty . . . . right most two students can be interchanged 1 x 2 = 2 a"
Answer: a
Question (gain): p and q started a business investing rs 75000 and rs 15000 resp . in what ratio the profit earned after 2 years be divided between p and q respectively .
Options: a ) 5 : 1 , b ) 17 : 3 , c ) 5 : 6 , d ) 17 : 7 , e ) 3 : 8
Rationale: "explanation : in this type of question as time frame for both investors is equal then just get the ratio of their investments . p : q = 75000 : 15000 = 75 : 15 = 5 : 1 option a"
Answer: a
Question (general): evaluate : 55 - 12 * 3 * 2 = ?
Options: a ) 47 , b ) 52 , c ) 32 , d ) 12 , e ) 22
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 55 - 12 * 3 * 2 = 55 - 8 = 47 correct answer a"
Answer: a
Question (geometry): the area of sector of a circle whose radius is 12 metro and whose angle at the center is 42 ° is ?
Options: a ) 56.8 m 2 , b ) 82.9 m 2 , c ) 52.8 m 2 , d ) 17.9 m 2 , e ) 72.9 m 2
Rationale: "42 / 360 * 22 / 7 * 12 * 12 = 52.8 m 2 answer : c"
Answer: c
Question (general): if 2 x = 4 y = z , what is x - y , in terms of z ?
Options: a ) z / 4 , b ) z / 2 , c ) z , d ) 2 z , e ) 4 z
Rationale: "2 x = 4 y = z i . e . x = z / 2 and y = z / 4 x - y = z / 2 - z / 4 = z / 4 answer : option a"
Answer: a
Question (general): the average weight of a group of boys is 35 kg . after a boy of weight 40 kg joins the group , the average weight of the group goes up by 1 kg . find the number of boys in the group originally ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: let the number off boys in the group originally be x . total weight of the boys = 35 x after the boy weighing 40 kg joins the group , total weight of boys = 35 x + 40 so 35 x + 40 = 36 ( x + 1 ) = > x = 5 . answer : b
Answer: b
Question (general): how many 13 - digits number are palindromic numbers ? a palindromic number reads the same forward and backward , example 1234567654321 .
Options: a ) 100 , b ) 610 , c ) 729 , d ) 900 , e ) 9000000
Rationale: "take the task of building palindromes and break it intostages . stage 1 : select the 13 th digit we can choose 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 1 in 9 ways stage 2 : select the 12 th 11 th 10 th , 9 th , 8 th , 7 th , we can choose 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , or 9 so , we can complete stage 2 in 10 ways important : at this point , the remaining digits are alreadylocked in . stage 3 : select the 6 th , 5 th , 4 th , 3 rd , 2 nd , 1 st digit so , we can complete this stage in 1 way . by thefundamental counting principle ( fcp ) , we can complete all 5 stages ( and thus build a 13 - digit palindrome ) in ( 9 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 10 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ( 1 ) ways ( = 9000000 ways ) answer : e"
Answer: e
Question (general): 5216 × 51 = ?
Options: a ) 266015 , b ) 266014 , c ) 266016 , d ) 266116 , e ) 266226
Rationale: "normal way of multiplication may take time . here is one alternative . 5216 × 51 = ( 5216 × 50 ) + 5216 = ( 5216 × 1002 ) + 5216 = 5216002 + 5216 = 260800 + 5216 = 266016 answer is c ."
Answer: c
Question (physics): points x , y , and z lie , in that order , on a straight railroad track . the distance from point x to point y is twice the distance from point y to point z . a train traveled from point x to point z without stopping . the train ' s average speed when traveling from point x to point y was 100 miles per hour and the train ' s average speed when traveling from point y to point z was 75 miles per hour . what was the train ' s average speed , in miles per hour , when traveling from point x to point z ?
Options: a ) 90 , b ) 85 , c ) 85.5 , d ) 70 , e ) 90
Rationale: "average speed = distance / time because we are looking for average speed we can pick a distance for the variable d . speed x - y = 100 speed y - z = 75 average speed = total distance / total rate rate = distance / time x = = = = = = = = = = = = = = = = = = = = y = = = = = = = = = = z if x - y is twice the length of y - z then let x - y = 2 d and let y - z = d average speed = 3 d / ( 2 d / 100 ) + ( d / 75 ) 3 d / ( 6 d / 300 ) + ( 4 d / 300 ) 3 d / ( 10 d / 300 ) 900 d / 10 d average speed = 90 answer : a"
Answer: a
Question (general): if there are 200 questions in a 3 hr examination . among these questions are 20 type a problems , which requires twice as much as time be spent than the rest of the type b problems . how many minutes should be spent on type a problems ?
Options: a ) 72 min , b ) 62 min , c ) 70 min , d ) 32.72727 min , e ) 76 min
Rationale: "x = time for type b prolems 2 x = time for type a problem total time = 3 hrs = 180 min 180 x + 20 * 2 x = 180 x = 180 / 220 x = 0.818182 time taken for type a problem = 20 * 2 * 0.818182 = 32.72727 min answer : d"
Answer: d
Question (general): an integer n between 1 and 100 , inclusive , is to be chosen at random . what is the probability that n ( n + 2 ) will be divisible by 2 ?
Options: a ) 1 / 9 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: "n ( n + 2 ) to be divisible by 2 either n or n + 2 must be a multiples of 2 . in each following group of numbers : { 1 , 2 , 3 , 4 } , { 5 , 6 , 7 , 8 } , . . . , { 97 , 98 , 99 , 100 } there are exactly 2 numbers out of 4 satisfying the above condition . for example in { 1 , 2 , 3 , 4 } n can be : 2 , or 4 . thus , the overall probability is 2 / 4 = 1 / 2 . answer : c ."
Answer: c
Question (general): a certain characteristic in a large population has a distribution that is symmetric about the mean m . if 36 percent of the distribution lies within one standard deviation d of the mean , what percent of the distribution is less than m + d ?
Options: a ) 16 % , b ) 32 % , c ) 68 % , d ) 84 % , e ) 92 %
Rationale: "this is easiest to solve with a bell - curve histogram . m here is equal to µ in the gaussian normal distribution and thus m = 50 % of the total population . so , if 36 % is one st . dev , then on either side of m we have 36 / 2 = 18 % . so , 18 % are to the right and left of m ( = 50 % ) . in other words , our value m + d = 50 + 18 = 68 % goingfrom the mean m , to the right of the distributionin the bell shaped histogram . . this means that 68 % of the values are below m + d . like i said , doing it on a bell - curve histogram is much easier to fullygethow this works , or you could apply gmat percentile jargon / theory to it c"
Answer: c
Question (general): every student in a room is either a junior or a senior . there is at least one junior and at least one senior in the room . if 4 / 5 of the juniors is equal to 1 / 2 of the seniors , what fraction of the students in the room are juniors ?
Options: a ) 13 / 20 , b ) 11 / 3 , c ) 5 / 13 , d ) 12 / 17 , e ) 17 / 20
Rationale: "let total number of juniors = j total number of seniors = s ( 4 / 5 ) j = ( 1 / 2 ) s = > s = 8 / 5 j total number of students = j + s = ( 13 / 5 ) j fraction of the students in the room are juniors = j / ( j + s ) = j / [ ( 13 / 5 ) j ] = 5 / 13 answer c"
Answer: c
Question (other): a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 4 : 1 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 3 , c ) 3 : 2 , d ) 2 : 3 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 12 : 8 . the ratio of economy cars to sport utility vehicles is 4 : 1 - - > e : s = 4 : 1 = 12 : 3 . thus , l : s = 8 : 3 . answer : b ."
Answer: b
Question (gain): if the simple interest on a sum of money for 2 years at 5 % per annum is rs . 40 , what is the compound interest on the same sum at the rate and for the same time ?
Options: a ) s . 41.00 , b ) s . 51.22 , c ) s . 51.219 , d ) s . 41.18 , e ) s . 51.11
Rationale: "explanation : sum = ( 40 * 100 ) / ( 2 * 5 ) = rs . 400 amount = [ 400 * ( 1 + 5 / 100 ) 2 ] = rs . 441 c . i . = ( 441 - 400 ) = rs . 41 answer : a"
Answer: a
Question (other): income and expenditure of a person are in the ratio 5 : 4 . if the income of the person is rs . 18000 , then find his savings ?
Options: a ) rs . 3600 , b ) rs . 3629 , c ) rs . 3279 , d ) rs . 3629 , e ) rs . 3283
Rationale: "let the income and the expenditure of the person be rs . 5 x and rs . 4 x respectively . income , 5 x = 18000 = > x = 3600 savings = income - expenditure = 5 x - 4 x = x so , savings = rs . 3600 . answer : a"
Answer: a
Question (general): in a certain diving competition , 5 judges score each dive on a scale from 1 to 10 . the point value of the dive is obtained by dropping the highest score and the lowest score and multiplying the sum of the remaining scores by the degree of difficulty . if a dive with a degree of difficulty of 3.2 received scores of 7.5 , 8.8 , 9.0 , 6.0 , and 8.5 , what was the point value of the dive ?
Options: a ) 68.8 , b ) 73.6 , c ) 75.2 , d ) 76.8 , e ) 79.36
Rationale: "degree of difficulty of dive = 3.2 scores are 6.0 , 7.5 , 8.8 , 8.5 and 9.0 we can drop 6.0 and 9.0 sum of the remaining scores = ( 7.5 + 8.8 + 8.5 ) = 24.8 point of value of the dive = 24 * 3.2 = 79.36 answer e"
Answer: e
Question (other): at the faculty of aerospace engineering , 310 students study random - processing methods , 232 students study scramjet rocket engines and 112 students study them both . if every student in the faculty has to study one of the two subjects , how many students are there in the faculty of aerospace engineering ?
Options: a ) 430 , b ) 432 , c ) 440 , d ) 442 , e ) 446
Rationale: "310 + 232 - 112 ( since 112 is counted twice ) = 430 a is the answer"
Answer: a
Question (general): gold is 19 times as heavy as water and copper is 9 times as heavy as water . in what ratio should these be mixed to get an alloy 12 times as heavy as water ?
Options: a ) 1 : 2 , b ) 3 : 7 , c ) 4 : 1 , d ) 5 : 2 , e ) 6 : 5
Rationale: "g = 19 w c = 9 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 19 w + 9 wx = x + 1 * 12 w 19 + 9 x = 12 ( x + 1 ) x = 7 / 3 ratio of gold with copper = 1 : 7 / 3 = 3 : 7 answer is b"
Answer: b
Question (gain): in 2008 , the profits of company n were 10 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 14 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 80 % , b ) 112 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "x = profits r = revenue x / r = 0,1 x = 10 r = 100 2009 : r = 80 x / 80 = 0,14 = 14 / 100 x = 80 * 14 / 100 x = 11.2 11.2 / 10 = 1,12 = 112 % , answer b"
Answer: b
Question (general): what is the 100 th digit of ( 3 ! * 5 ! + 4 ! * 3 ! ) / 2 ?
Options: a ) 4 , b ) 3 , c ) 2 , d ) 7 , e ) 6
Rationale: ( 3 ! * 5 ! + 4 ! * 3 ! ) / 2 = 3 ! ( 5 ! + 4 ! ) / 2 = 6 ( 120 + 24 ) / 2 = 432 100 th digit of the above product will be equal to 4 answer a
Answer: a
Question (physics): the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 9408 sq . m , the cost of fencing the field @ 25 paise per metre is
Options: a ) rs . 55.50
b ) rs . 67.50
c ) rs . 86.50
d ) rs . 98.00
e ) none of these
Rationale: solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 9408 ⇔ 12 x 2 = 9408 ⇔ x 2 = 784 ⇔ x = 28 . so , length = 84 m and breadth = 112 m . perimeter = [ 2 ( 84 + 112 ) ] m = 392 m . ∴ cost of fencing = rs . ( 0.25 × 392 ) = rs . 98.00 . answer d
Answer: d
Question (gain): an error 2 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?
Options: a ) 4.04 , b ) 4.02 , c ) 4.01 , d ) 4.05 , e ) 4.06
Rationale: "formula for calculation of percentage error is : = ( x − y − ( xy ) / 100 ) % = ( 2 + 2 + ( 2 × 2 ) / 100 ) % = 4.04 % answer is a ."
Answer: a
Question (gain): at a certain university , 70 % 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 ) 62.5 , e ) 75
Rationale: "answer is 75 % total women = 70 % total men = 40 % total tenured = 70 % ( both men and women ) therefore , women tenured + women professors + men tenured = 90 % men tenured = 20 % but question wants to know the percent of men that are tenured 20 % / 40 % = 50 % c"
Answer: c
Question (general): if p and t are positive integers such that p > t > 1 , what is the remainder when 92 p × 5 p + t + 11 t × 6 pt is divided by 10 ?
Options: a ) a . 0 , b ) b . 1 , c ) c . 3 , d ) d . 4 , e ) e . 5
Rationale: 92 p × 5 p + t + 11 t × 6 pt - - 1 = b
Answer: b
Question (physics): mary passed a certain gas station on a highway while traveling west at a constant speed of 40 miles per hour . then , 15 minutes later , paul passed the same gas station while traveling west at a constant speed of 50 miles per hour . if both drivers maintained their speeds and both remained on the highway for at least 2 hours , how long after he passed the gas station did paul catch up with mary ?
Options: a ) 1 / 2 , b ) 1 , c ) 3 / 4 , d ) 2 , e ) 3
Rationale: "d = rt m : r = 40 mph , t = t + 1 / 4 hr d = 40 ( t + 1 / 4 ) p : r = 50 , t = t d = 50 t since they went the same distance : 40 t + 40 / 4 = 50 t 10 t = 10 t = 1 hr , b"
Answer: b
Question (gain): a person buys an article at rs . 350 . at what price should he sell the article so as to make a profit of 30 % ?
Options: a ) 455 , b ) 277 , c ) 269 , d ) 261 , e ) 281
Rationale: "cost price = rs . 350 profit = 30 % of 350 = rs . 105 selling price = cost price + profit = 350 + 105 = 455 answer : a"
Answer: a
Question (physics): two trains 140 m and 200 m long run at the speed of 60 km / hr and 40 km / hr respectively in opposite directions on parallel tracks . the time which they take to cross each other is ?
Options: a ) 10.9 sec , b ) 10.1 sec , c ) 10.6 sec , d ) 10.8 sec , e ) 12.24 sec
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 140 + 200 = 340 m . required time = 340 * 9 / 250 = 12.24 sec . answer : e"
Answer: e
Question (physics): how many cubes of 5 cm edge can be put in a cubical box of 1 m edge .
Options: a ) 1770 cm , b ) 8000 cm , c ) 7860 cm , d ) 6170 cm , e ) 1870 cm
Rationale: "number of cubes = 100 â ˆ — 100 â ˆ — 100 / 5 * 5 * 5 = 8000 note : 1 m = 100 cm answer : b"
Answer: b
Question (general): the average of first seven multiples of 4 is :
Options: a ) 9 , b ) 16 , c ) 15 , d ) 8 , e ) 10
Rationale: "explanation : ( 4 ( 1 + 2 + 3 + 4 + 5 + 6 + 7 ) / 7 = 4 x 28 / 7 = 16 answer : b"
Answer: b
Question (general): there are 5 chess amateurs playing in villa ' s chess club tournament . if each chess amateur plays with exactly 4 other amateurs , what is the total number of chess games possible to be played in the tournament ?
Options: a ) 10 , b ) 20 , c ) 40 , d ) 60 , e ) 120
Rationale: "method 1 : take the first amateur . he plays a game with each of the other four i . e . 4 games . now take the second one . he has already played a game with the first one . he plays 3 games with the rest of the 3 amateurs i . e . 3 more games are played . now take the third amateur . he has already played a game each with the first and the second amateur . now he plays 2 games with the remaining 2 amateurs so 2 more games are played . now go on to the fourth amateur . he has already played 3 games with the first 3 amateurs . he just needs to play a game with the last one i . e . 1 more game is played . the last amateur has already played 4 games . total no of games = 4 + 3 + 2 + 1 = 10 method 2 : each person is one participant of 4 games . so there are in all 4 * 5 = 20 instances of one participant games . but each game has 2 participants so total number of games = 20 / 2 = 10 answer : a ."
Answer: a
Question (general): in a urban village of india named ` ` owlna ' ' , 75 % people have refrigerator , 90 % people have television , 85 % people got computers and 75 % got air - conditionor . how many people ( minimum ) got all these luxury .
Options: a ) 23 % , b ) 17 % , c ) 11 % , d ) 10 % , e ) 25 %
Rationale: "e 10 % 100 - [ ( 100 - 75 ) + ( 100 - 90 ) + ( 100 - 85 ) + ( 100 - 75 ) ] = 100 - ( 25 + 10 + 15 + 25 ) = 100 - 75"
Answer: e
Question (general): a bowl of nuts is prepared for a party . brand p mixed nuts are 20 % almonds and brand q ' s deluxe nuts are 25 % almonds . if a bowl contains a total of 67 ounces of nuts , representing a mixture of both brands , and 15 ounces of the mixture are almonds , how many ounces of brand q ' s deluxe mixed nuts are used ?
Options: a ) 16 , b ) 20 , c ) 32 , d ) 44 , e ) 48
Rationale: "lets say x ounces of p is mixed with q . = > 67 - x ounces of q is present in the mixture ( as the total = 67 ounces ) given total almond weight = 15 ounces ( 20 x / 100 ) + ( 25 / 100 ) ( 67 - x ) = 15 = > x = 35 = > 67 - 35 = 32 ounces of q is present in the mixture . answer is c ."
Answer: c
Question (gain): if $ 5,000 is invested in an account that earns 8 % interest compounded semi - annually , then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8 % simple yearly interest ?
Options: a ) $ 4 , b ) $ 8 , c ) $ 12 , d ) $ 16 , e ) $ 432
Rationale: "solution amount ( ci ) = p + ( 1 + r / n ) ^ nt = 5000 + ( 1 + 0.08 / 2 ) ^ 2 = 5408 amount ( si ) = p + ptr / 100 = 5000 + ( 5000 * 1 * 8 / 100 ) = 5400 difference = 5408 - 5400 = 8 $ answer : b"
Answer: b
Question (geometry): the length of a rectangular garden is three times its width . if the area of the rectangular garden is 675 square meters , then what is the width of the rectangular garden ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 17 , e ) 18
Rationale: "let x be the width of the garden . 3 x ^ 2 = 675 x ^ 2 = 225 x = 15 the answer is b ."
Answer: b
Question (general): how many odd 3 - digit integers smaller than 500 are there such that all their digits are different ?
Options: a ) 72 , b ) 88 , c ) 112 , d ) 122 , e ) 144
Rationale: case 1 : numbers starting with 1 1 _ _ the unit digit can take 4 numbers ( 3,5 , 7,9 ) to be odd so 4 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 4 = 32 case 2 : numbers starting with 2 2 _ _ the unit digit can take 5 numbers ( 1 , 3,5 , 7,9 ) to be odd so 5 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 5 = 40 case 3 : numbers starting with 3 3 _ _ the unit digit can take 4 numbers ( 1,5 , 7,9 ) to be odd so 4 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 4 = 32 case 4 : numbers starting with 4 4 _ _ the unit digit can take 5 numbers ( 1 , 3,5 , 7,9 ) to be odd so 5 ways . the tens digit can take remaining 8 numbers left after using 2 numbers so 8 ways . total = 8 * 5 = 40 hence 32 + 40 + 32 + 40 = 144 , correct answer is e
Answer: e
Question (physics): a van takes 5 hours to cover a distance of 435 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 50 , b ) 52 , c ) 54 , d ) 56 , e ) 58
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 435 / 7.5 = 58 kph the answer is e ."
Answer: e
Question (general): if the price of a tv is first decreased by 20 % and then increased by 50 % , then the net change in the price will be :
Options: a ) 20 % increase , b ) 10 % increase , c ) 10 % decrease , d ) 6 % increase , e ) none of these
Rationale: "explanation : solution : let the original price be rs . 100 . new final price = 150 % of ( 80 % of 100 ) = rs . 150 / 100 * 80 / 100 * 100 = rs . 120 . . ' . increase = 20 % answer : a"
Answer: a
Question (general): 18 % of 680 - ? = 68.7
Options: a ) 44.1 , b ) 32.4 , c ) 66.5 , d ) 75.2 , e ) 53.7
Rationale: "e 53.7 ( 18 * 680 ) / 100 - ? = 68.7 ? = 122.4 - 68.7 ? = 53.7"
Answer: e
Question (general): a sum of money is put out at compound interest for 2 years at 20 % . it would fetch rs . 241 more if the interest were payable half - yearly , then it were pay able yearly . find the sum .
Options: a ) 12200 , b ) 11897 , c ) 18799 , d ) 10000 , e ) 12782
Rationale: "p ( 11 / 10 ) ^ 4 - p ( 6 / 5 ) ^ 2 = 241 p = 10000 answer : d"
Answer: d
Question (physics): a , b and c can do a piece of work in 24 , 30 and 40 days respectively . they start the work together but c leaves 4 days before the completion of the work . in how many days is the work done ?
Options: a ) 11 , b ) 5 , c ) 70 , d ) 11 , e ) 13
Rationale: x / 24 + x / 30 + x / 40 = 1 x = 11 days answer : d
Answer: d
Question (gain): of the 120 passengers on flight 750 , 45 % are female . 10 % of the passengers sit in first class , and the rest of the passengers sit in coach class . if 1 / 3 of the passengers in first class are male , how many females are there in coach class ?
Options: a ) 44 , b ) 48 , c ) 46 , d ) 52 , e ) 56
Rationale: "number of passengers on flight = 120 number of female passengers = . 45 * 120 = 54 number of passengers in first class = ( 10 / 100 ) * 120 = 12 number of passengers in coach class = ( 90 / 100 ) * 120 = 108 number of male passengers in first class = 1 / 3 * 12 = 4 number of female passengers in first class = 12 - 4 = 8 number of female passengers in coach class = 54 - 8 = 46 answer c"
Answer: c
Question (geometry): what is the smallest positive integer x , such that 6000 x is a perfect cube ?
Options: a ) 4 , b ) 6 , c ) 36 , d ) 12 , e ) 18
Rationale: "take out the factors of 6000 that will come 2 * 3 * 10 ^ 3 . for perfect cube you need every no . raise to the power 3 . for 6000 x to be a perfect cube , need two 2 and 2 3 that means 36 or 6 ^ 2 c is the answer ."
Answer: c