Cheukting/mathqa huggingface dataset:
Question (general): a line that passes through ( – 1 , – 4 ) and ( 3 , k ) has a slope = k . what is the value of k ?
Options: a ) 3 / 4 , b ) 1 , c ) 4 / 3 , d ) 2 , e ) 7 / 2
Rationale: "this is a considerably more difficult one , which will involve some algebra . let ’ s say that the “ first ” point is ( – 1 , – 4 ) and the “ second , ” ( 3 , k ) . the rise = k + 4 , which involves a variable . the run = 3 – ( – 1 ) = 4 . there the slope is ( k + 4 ) / 4 , and we can set this equal to k and solve for k . { { k + 4 } / 4 } = k k + 4 = 4 k 4 = 3 k k = 4 / 3 answer = c"
Answer: c
Question (other): in a class of 94 students 41 are taking french , 22 are taking german . of the students taking french or german , 9 are taking both courses . how many students are not enrolled in either course ?
Options: a ) 6 , b ) 15 , c ) 24 , d ) 33 , e ) 40
Rationale: "formula for calculating two overlapping sets : a + b - both + not ( a or b ) = total so in our task we have equation : 41 ( french ) + 22 ( german ) - 9 ( both ) + not = 94 54 + not = 94 not = 94 - 54 = 40 so answer is e"
Answer: e
Question (general): the faces of storage box are to be painted by 6 different colors . in how many ways can be this be done ?
Options: a ) a . 720 , b ) b . 256 , c ) c . 1 , d ) d . 12 , e ) e . 36
Rationale: if i have to paint 6 sides with 6 different colour . . . first face can have 6 c 1 options , 2 nd would have 5 c 1 , and subsequent ones would have 4 c 1 , 3 c 1 , 2 c 1 and 1 options respectively . total options = 6 c 1 x 5 c 1 x 4 c 1 x 3 c 1 x 2 c 1 x 1 = 720 distinct ways correct answer - a
Answer: a
Question (gain): john had a stock of 1000 books in his bookshop . he sold 20 on monday , 120 on tuesday , 200 on wednesday , 250 on thursday and 300 on friday . what percentage of the books were not sold ?
Options: a ) 68 % , b ) 74 % , c ) 76 % , d ) 62 % , e ) 89 %
Rationale: "let n be the total number of books sold . hence n = 20 + 120 + 200 + 250 + 300 = 890 let m be the books not sold m = 1000 - n = 1200 - 890 = 798 percentage books not sold / total number of books = 890 / 1000 = 0.89 = 89 % correct answer e"
Answer: e
Question (gain): if a lends rs . 1000 to b at 10 % per annum and b lends the same sum to c at 11.5 % per annum then the gain of b in a period of 3 years is ?
Options: a ) 112.5 , b ) 122.5 , c ) 132.5 , d ) 114.5 , e ) 45
Rationale: "( 1000 * 1.5 * 3 ) / 100 = > 45 answer : e"
Answer: e
Question (general): in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors r ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have r = 2 * 3 * 5 * 7 = 840 thus , answer b
Answer: b
Question (physics): a can finish a work in 24 days , b in 9 days and c in 2 days , b and c start the work but are forced to leave after 3 days . the remaining work was done by a in ?
Options: a ) 10 days , b ) 12 days , c ) 6 days , d ) 7 days , e ) 8 days
Rationale: "b + c 1 day work = 1 / 9 + 1 / 12 = 7 / 36 work done by b and c in 3 days = 7 / 36 * 3 = 7 / 12 remaining work = 1 - 7 / 12 = 5 / 12 1 / 24 work is done by a in 1 day 5 / 12 work is done by a in 24 * 5 / 12 = 10 days answer is a"
Answer: a
Question (gain): a reduction of 50 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 800 , what is the reduced price for kg ?
Options: a ) s . 42 , b ) s . 46 , c ) s . 40 , d ) s . 80 , e ) s . 34
Rationale: "800 * ( 50 / 100 ) = 400 - - - - 5 ? - - - - 1 = > rs . 80 answer : d"
Answer: d
Question (general): if x / 4 + 24 / x = 5 , what are the values of 3 x - 4 ?
Options: a ) 8 and 9 , b ) 20 and 32 , c ) 17 and 19 , d ) 12 and 29 , e ) 17 and 29
Rationale: i got the same thing b is the answer 20 or 32
Answer: b
Question (gain): a candidate who gets 30 % of the marks fails by 50 marks . but another candidate who gets 45 % marks gets 25 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 150 , b ) 200 , c ) 250 , d ) 275 , e ) 285
Rationale: 30 % - - - - - - - - - - - - 50 45 % - - - - - - - - - - - - 25 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 75 30 % - - - - - - - - - - - - - - ? 150 + 50 = 200 marks answer : b
Answer: b
Question (general): if two integers x , y ( x > y ) are selected from - 6 to 6 ( inclusive ) , how many cases are there ?
Options: a ) 70 , b ) 74 , c ) 78 , d ) 82 , e ) 86
Rationale: "there are 13 integers from - 6 to 6 inclusive . 13 c 2 = 78 . the answer is c ."
Answer: c
Question (gain): the ratio of investments of two partners p and q is 7 : 5 and the ratio of their profits is 7 : 10 . if p invested the money for 2 months , find for how much time did q invest the money ?
Options: a ) 8 , b ) 10 , c ) 18 , d ) 4 , e ) 12
Rationale: "7 * 5 : 2 * x = 7 : 10 x = 4 answer : 4 answer is d"
Answer: d
Question (physics): working alone at their respective constant rates , a can complete a task in ‘ a ’ days and b in ‘ b ’ days . they take turns in doing the task with each working 2 days at a time . if a starts they finish the task in exactly 14 days . if b starts , they take a day more . how long does it take to complete the task if they both work together ?
Options: a ) 12 , b ) 14 , c ) 10 , d ) 11 , e ) 13
Rationale: "work done by ab in a day = xy respectively . when a starts : no . of days when a works = 8 no . of days when b works = 6 → 8 x + 6 y = 1 when b starts : no . of days when a works = 7 no . of days when a works = 7 → 7 x + 7 y = 1 solving the above two equations for xy x = 1 / 14 y = 1 / 14 → total work done by ab in a day = 1 / 14 + 1 / 14 = 2 / 28 = 1 / 14 → no . of days to complete the work when both work together = 14 answer : b"
Answer: b
Question (general): if money is invested at r percent interest , compounded annually , the amount of the investment will double in approximately 50 / r years . if luke ' s parents invested $ 15500 in a long term bond that pays 12 percent interest compounded annually , what will be the approximate total amount of the investment 12 years later , when luke is ready for college ?
Options: a ) 62,000 , b ) 85,500 , c ) 95,500 , d ) 100,500 , e ) 120,000
Rationale: answer equals e in 48 years . i thought by 50 th year it would reach 120,000 . options should have been separated more widely for clarity .
Answer: e
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 35 kg . what is the weight of the new person ?
Options: a ) 75 , b ) 65 , c ) 55 , d ) 95 , e ) 80
Rationale: "total increase in weight = 8 × 2.5 = 20 if x is the weight of the new person , total increase in weight = x − 35 = > 20 = x - 35 = > x = 20 + 35 = 55 answer is c ."
Answer: c
Question (general): a third of arun â € ™ s marks in mathematics exceed a half of his marks in english by 15 . if he got 170 marks in two subjects together how many marks did he got in english ?
Options: a ) 120,50 , b ) 180,60 , c ) 180,90 , d ) 120,40 , e ) none of them
Rationale: let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 3 ) x - ( 1 / 2 ) y = 15 2 x - 3 y = 90 â € ¦ â € ¦ > ( 1 ) x + y = 170 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 120 and y = 50 answer is a .
Answer: a
Question (gain): in the manufacture of a certain product , 4 percent of the units produced are defective and 4 percent of the defective units are shipped for sale . what percent of the units produced are defective units that are shipped for sale ?
Options: a ) 0.125 % , b ) 0.2 % , c ) 0.16 % , d ) 1.25 % , e ) 2.0 %
Rationale: "percent of defective produced = 4 % percent of the defective units that are shipped for sale = 4 % percent of units produced are defective units that are shipped for sale = ( 4 / 100 ) * ( 4 / 100 ) * 100 % = ( 16 / 10000 ) * 100 % = ( 16 / 100 ) % = . 16 % answer c"
Answer: c
Question (general): if you roll a fair - sided die twice , what is the probability of getting a ( 4.4 ) double ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 12 , d ) 1 / 3 ! , e ) 1 / 24
Rationale: total no . in two dice ( 1,1 ) , ( 2,2 ) . . . . . ( 6 , ) total number of events = 6 * 6 total events of getting same pair ( 4 , 4 ) = 6 probability = 6 / 6 * 6 = 1 / 6 = 1 / 3 ! d
Answer: d
Question (physics): how many seconds will a 770 m long train take to cross a man walking with a speed of 2.5 km / hr in the direction of the moving train if the speed of the train is 46.5 km / hr ?
Options: a ) 63 , b ) 88 , c ) 66 , d ) 44 , e ) 35
Rationale: "speed of train relative to man = 46.5 - 2.5 = 44 km / hr . = 44 * 5 / 18 = 110 / 9 m / sec . time taken to pass the man = 770 * 9 / 110 = 63 sec . answer : a"
Answer: a
Question (physics): buses a and b start from a common bus stop x . bus a begins to travel in a straight line away from bus b at a constant rate of 30 miles per hour . one hour later , bus b begins to travel in a straight line in the exact opposite direction at a constant rate of 70 miles per hour . if both buses travel indefinitely , what is the positive difference , in minutes , between the amount of time it takes bus b to cover the exact distance that bus a has covered and the amount of time it takes bus b to cover twice the distance that bus a has covered ?
Options: a ) 36 , b ) 72 , c ) 122 , d ) 144 , e ) 180
Rationale: "1 st part : - in 1 hr , bus a covers 30 miles . relative speed of bus abus b is ( 80 - 30 ) = 50 mph . so time required for bus b to cover the exact distance as a is 50 * t = 30 t = 3 / 5 = 36 min 2 nd part 80 * t = 2 d - b has to cover twice the distance 30 * ( t + 1 ) = d - a traveled 1 hr more and has to travel only only d so d / 30 - 2 d / 80 = 1 d = 120 t = 3 hrs = 180 min question asks for + ve difference between part 1 and part 2 in minutes = 180 - 36 = 122 min c"
Answer: c
Question (other): at a certain zoo , the ratio of sea lions to penguins is 4 to 11 . if there are 84 more penguins than sea lions at the zoo , how many sea lions are there ?
Options: a ) 24 , b ) 36 , c ) 48 , d ) 72 , e ) 132
Rationale: the ratio as mentioned = 4 / 11 also sea lion + 84 = penguins or , 4 x + 84 = 11 x x = 84 / 7 = 12 number of sea lions = 12 * 4 = 48 answer : c
Answer: c
Question (physics): two trains of equal length , running with the speeds of 60 and 40 kmph , take 36 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 10 sec , b ) 16 sec , c ) 19 sec , d ) 7.2 sec , e ) 13 sec
Rationale: rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 36 d = 36 * 100 / 18 = 200 rs = 60 + 40 = 100 * 5 / 18 t = 200 * 18 / 500 = 7.2 sec answer : d
Answer: d
Question (general): if x + y = 2 x + z , x - 2 y = 4 z and x + y + z = 21 , what is the value of y / z ?
Options: a ) - 4.5 . , b ) - 2 . , c ) - 1.7 . , d ) 3 . , e ) 6 .
Rationale: x + y = 2 x + 2 z y = x + 2 z - - - - - - - - - - 1 x - 2 y = 4 z x - 4 z = 2 y - - - - - - - - - 2 subtracting equation 1 from equation 2 - 6 z = y y / z = - 6 e is the answer
Answer: e
Question (gain): the bankers discount of a certain sum of money is rs . 36 and the true discount on the same sum for the same time is rs . 30 . the sum due is :
Options: a ) 140 , b ) 150 , c ) 160 , d ) 170 , e ) 180
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 36 * 30 ) / 36 - 30 ; 180 answer : e"
Answer: e
Question (general): 12 chess players take part in a tournament . every player plays twice with each of his opponents . how many games are to be played ?
Options: a ) 190 , b ) 132 , c ) 210 , d ) 220 , e ) 225
Rationale: "though 2 * ( 12 c 2 ) is the correct approcah to do this , but for people like me who find perm , comb n prob a nightmare , an easy approach can be used . the first guy has to play 2 matches with the rest of 11 , so he ' ll play 22 matches . similarly , second guy has to play with the rest of 10 as his 2 games with the first guy are already played . so he plays 20 matches . this continues like this and the total matches are 22 + 20 + 18 . . . + 2 22 + 20 + . . . + 2 = 2 ( 11 + 10 + . . . + 1 ) = 2 ( ( 11 * 12 ) / 2 ) = 11 * 12 = 132 . answer : b"
Answer: b
Question (physics): one hour after adrienne started walking the 60 miles from x to y , harold started walking from x to y as well . adrienne walks 3 miles per hour and harold walks 1 mile per hour faster than adrienne . how far from x will harold be when he catches up to adrienne ?
Options: a ) 8 miles , b ) 12 miles , c ) 10 miles , d ) 11 miles , e ) 14 miles
Rationale: first , determine how far adrienne has walked in the one hour . she has walked three miles which means she is three miles ahead of harold when he sets off . harold walks at four miles / hour which means that every hour , harold will get one mile closer to adrienne . if he gets one mile closer every hour , it will take him three hours to catch up to her which means he travels 3 hours * 4 miles / hour = 12 miles and she travels 4 hours * 3 miles / hour = 12 miles . he will be 12 miles from x when he catches up to her . a slightly different way to solve . . . we do n ' t know how long they will walk before they catch up to one another but we do know that a walks for one hour more than j . j = t and a = t + 1 . we are looking for the distance at which they meet up which means the distance will be the same . d = r * t so , r * t ( harold ) = r * t ( adrienne ) r * ( t ) = r * ( t + 1 ) 4 t = 3 t + 3 t = 3 d = r * t d = 4 * 3 d = 12 b ) 12 miles
Answer: b
Question (general): in a division , a student took 48 as divisor instead of 36 . his answer was 24 . the correct answer is -
Options: a ) 42 , b ) 32 , c ) 48 , d ) 28 , e ) 38
Rationale: "x / 48 = 24 . x = 24 * 48 . so correct answer would be , ( 24 * 48 ) / 36 = 32 . answer : b"
Answer: b
Question (physics): a man can row upstream at 20 kmph and downstream at 60 kmph , and then find the speed of the man in still water ?
Options: a ) 32 kmph , b ) 34 kmph , c ) 30 kmph , d ) 45 kmph , e ) 40 kmph
Rationale: "us = 20 ds = 60 m = ( 20 + 60 ) / 2 = 40 answer : e"
Answer: e
Question (other): two family reunions are happening at the same hotel , the dates reunion and the hall reunion . all 50 guests at the hotel attend at least one of the reunions . if 50 people attend the dates reunion and 60 people attend the hall reunion , how many people attend both reunions ?
Options: a ) 2 , b ) 5 , c ) 10 , d ) 16 , e ) 60
Rationale: no of people in dates reunion = 50 no of people in hall reunion = 60 attending both = x all guests attend at least one . therefore , 50 = 50 + 60 - ( both ) both = 60 answer e
Answer: e
Question (physics): a person travels equal distances with speeds of 6 km / hr , 12 km / hr , 18 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 1500 mts , c ) 1800 mts , d ) 2 km , e ) 1250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 6 ) + ( x / 12 ) + ( x / 18 ) = 11 / 60 x = 0.6 total distance = 3 * 0.6 = 1.8 km = 1800 meters correct option is c"
Answer: c
Question (physics): working alone at its constant rate , machine a produces x boxes in 10 minutes and working alone at its constant rate , machine b produces 2 x boxes in 5 minutes . how many minutes does it take machines a and b , working simultaneously at their respective constant rates , to produce 5 x boxes ?
Options: a ) 3 minutes , b ) 4 minutes , c ) 5 minutes , d ) 6 minutes , e ) 10 minutes
Rationale: "rate = work / time given rate of machine a = x / 10 min machine b produces 2 x boxes in 5 min hence , machine b produces 4 x boxes in 10 min . rate of machine b = 4 x / 10 we need tofind the combined time that machines a and b , working simultaneouslytakeat their respective constant rates let ' s first find the combined rate of machine a and b rate of machine a = x / 10 min + rate of machine b = 4 x / 10 = 5 x / 10 now combine time = combine work needs to be done / combine rate = 5 x / 5 x * 10 = 10 min ans : e"
Answer: e
Question (geometry): the volume of a cube is 1331 cc . find its surface .
Options: a ) 864 , b ) 726 , c ) 255 , d ) 287 , e ) 267
Rationale: "a 3 = 1331 = > a = 11 6 a 2 = 6 * 11 * 11 = 726 answer : b"
Answer: b
Question (general): if ( a – b ) is 11 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 11 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 11 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 11 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 11 = ( c – a ) – 3 = > 2 ( a – c ) = 8 = > ( a – c ) = 4 answer : d"
Answer: d
Question (physics): two trains 180 m and 160 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 ) 10.7 , b ) 10.9 , c ) 10.24 , d ) 12.24 , e ) 18.8
Rationale: "relative speed = 60 + 40 = 100 km / hr . = 100 * 5 / 18 = 250 / 9 m / sec . distance covered in crossing each other = 180 + 160 = 340 m . required time = 340 * 9 / 250 = 12.24 sec . answer : d"
Answer: d
Question (physics): a train passes a man standing on a platform in 8 seconds and also crosses the platform which is 267 metres long in 20 seconds . the length of the train ( in metres ) is :
Options: a ) 178 , b ) 176 , c ) 175 , d ) 96 , e ) none of these
Rationale: explanation : let the length of train be l m . acc . to question ( 267 + l ) / 20 = l / 8 2136 + 8 l = 20 l l = 2136 / 12 = 178 m answer a
Answer: a
Question (general): mixture a is 15 percent alcohol , and mixture b is 50 percent alcohol . if the two are poured together to create a 4 - gallon mixture that contains 30 percent alcohol , approximately how many gallons of mixture a are in the mixture ?
Options: a ) 1.5 , b ) 1.7 , c ) 2.3 , d ) 2.5 , e ) 3.0
Rationale: "ratio of a to b in the final mixture = 50 - 30 : 30 - 15 = 4 : 3 gallons of a used = 4 / 7 * 4 = 2.28 answer : c"
Answer: c
Question (general): on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 160 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 600 , b ) 320 , c ) 500 , d ) 520 , e ) 720
Rationale: "let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 160 ) = 2 + 2 ( extra ) = > 2 x - 320 = x = > x = 320 . answer : b"
Answer: b
Question (other): a certain store sold pens for $ 0.35 each and pencils for $ 0.25 each . if a customer purchased both pens and pencils from the store for a total of $ 3.00 , what total number of pens and pencils did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: answer : algebraically , the question looks like this : 3.0 = 0.35 x + 0.25 y there are six possible numbers of pens that fit that requirement : 1 pen : $ 0.35 2 pens : $ 0.70 3 pens : $ 1.05 4 pens : $ 1.40 5 pens : $ 1.75 balance 1.25 5 pencils cost $ 1.25 that ' s 5 pens and 5 pencils choice ( c ) is correct .
Answer: c
Question (general): what is the sum of natural numbers between 20 and 100
Options: a ) 4800 , b ) 4860 , c ) 5000 , d ) 5500 , e ) 5550
Rationale: "a = first number l = last number sn = n / 2 [ a + l ] between 20 and 100 numbers = 81 = > 100 - 20 = 80 + 1 = 81 sn = 81 / 2 × 120 = 81 × 60 = 4860 b )"
Answer: b
Question (gain): 4 weavers can weave 4 mats in 4 days . at the same rate , how many mats would be woven by 6 weavers in 6 days ?
Options: a ) 6 , b ) 9 , c ) 12 , d ) 15 , e ) 18
Rationale: 1 weaver can weave 1 mat in 4 days . 6 weavers can weave 6 mats in 4 days . 6 weavers can weave 9 mats in 6 days . the answer is b .
Answer: b
Question (general): a number whose fifth part increased by 6 is equal to its fourth part diminished by 6 is ?
Options: a ) 160 , b ) 180 , c ) 200 , d ) 240 , e ) none
Rationale: "answer let the number be n . then , ( n / 5 ) + 6 = ( n / 4 ) - 6 â ‡ ’ ( n / 4 ) - ( n / 5 ) = 12 â ‡ ’ ( 5 n - 4 n ) / 20 = 12 â ˆ ´ n = 240 option : d"
Answer: d
Question (general): if 3 a – 2 b – 4 c = 32 and √ 3 a - √ ( 2 b + 2 c ) = 4 , what is the value of a + b + c ?
Options: a ) 3 , b ) 9 , c ) 10 , d ) 12 , e ) 14
Rationale: "when we look at the two equations , we can relize some similarity , so lets work on it . . 3 a – 2 b – 2 c = 32 can be written as √ 3 a ^ 2 - √ ( 2 b + 2 c ) ^ 2 = 32 { √ 3 a - √ ( 2 b + 2 c ) } { √ 3 a + √ ( 2 b + 2 c ) } = 32 . . or 4 * √ 3 a + √ ( 2 b + 2 c ) = 32 . . or √ 3 a + √ ( 2 b + 2 c ) = 8 . . now lets work on these two equations 1 ) √ 3 a - √ ( 2 b + 2 c ) = 4 . . 2 ) √ 3 a + √ ( 2 b + 2 c ) = 8 . . a ) add the two eq . . √ 3 a + √ ( 2 b + 2 c ) + √ 3 a - √ ( 2 b + 2 c ) = 12 . . 2 √ 3 a = 12 . . or √ 3 a = 6 . . 3 a = 36 . . a = 12 . b ) subtract 1 from 2 . . √ 3 a + √ ( 2 b + 2 c ) - √ 3 a + √ ( 2 b + 2 c ) = 4 . . 2 √ ( 2 b + 2 c ) = 4 . . √ ( 2 b + 2 c ) = 2 . . 2 b + 2 c = 4 . . or b + c = 2 . . from a and b a + b + c = 12 + 2 = 14 . . d"
Answer: d
Question (general): find the product of the localvalue and absolutevalue of 3 in 20368 ?
Options: a ) 1000 , b ) 1100 , c ) 1200 , d ) 900 , e ) 10000
Rationale: "local value of 3 = 3 x 100 = 300 place value of 3 = 3 there fore = 3 x 300 = 900 d"
Answer: d
Question (physics): how many seconds will a train 120 meters long take to cross a bridge 200 meters long if the speed of the train is 36 kmph ?
Options: a ) 22 sec , b ) 32 sec , c ) 25 sec , d ) 24 sec , e ) 31 sec
Rationale: "explanation : d = 120 + 200 = 320 s = 36 * 5 / 18 = 10 mps t = 250 / 10 = 32 sec answer : option b"
Answer: b
Question (geometry): the difference of the areas of two squares drawn on two line segments of different lengths is 32 sq . cm . find the length of the greater line segment if one is longer than the other by 2 cm .
Options: a ) 6 cm , b ) 7 cm , c ) 9 cm , d ) 11 cm , e ) none
Rationale: "solution let the lengths of the line segments be x cm and ( x + 2 ) cm . then ( x + 2 ) 2 - x 2 = 32 < = > x 2 + 4 x + 4 - x 2 = 32 < = > 4 x = 28 therefore x = 7 . length of longer line segment = ( 7 + 2 ) cm = 9 cm . answer c"
Answer: c
Question (geometry): a cube of edge 6 cm is cut into cubes each of edge 3 cm . the ratio of the total surface area of one of the small cubes to that of the large cube is equal to :
Options: a ) 1 : 4 , b ) 1 : 25 , c ) 1 : 52 , d ) 1 : 522 , e ) none
Rationale: "sol . required ratio = 6 * 3 * 3 / 6 * 6 * 6 = 1 / 4 = 1 : 4 . answer a"
Answer: a
Question (general): robert ate 7 chocolates , nickel ate 3 chocolates . how many more chocolates did robert ate than nickel ?
Options: a ) 4 , b ) 7 , c ) 9 , d ) 5 , e ) 2
Rationale: 7 - 3 = 4 . answer is a
Answer: a
Question (physics): a car traveling at a certain constant speed takes 20 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 36 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 24 , b ) 26 , c ) 28 , d ) 30 , e ) 32
Rationale: "36 * t = 1 km = > t = 1 / 36 km / h v * ( t + 20 / 3600 ) = 1 v ( 1 / 36 + 20 / 3600 ) = 1 v ( 120 / 3600 ) = 1 v = 30 km / h the answer is d ."
Answer: d
Question (general): the product of x and y is a constant . if the value of x is increased by 50 % , by what percentage must the value of y be decreased ?
Options: a ) 50 % , b ) 40 % , c ) 33 1 ⁄ 3 % , d ) 25 % , e ) 12 1 ⁄ 2 %
Rationale: "product of x and y = xy if the value of x is increased by 50 % , value of y needs to be = xy / ( 1.5 x ) = 2 / 3 y decrease in value of y = y - 2 / 3 y = 1 / 3 y % decrease in value of y = ( 1 / 3 y ) / y * 100 % = 33 1 ⁄ 3 % answer c"
Answer: c