Cheukting/mathqa huggingface dataset:
Question (general): the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.2 kg . the weight of the new student is
Options: a ) 4 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 21 kg , e ) none of these
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.2 weight of the new student = ( 30 * 27.2 – 29 * 28 ) = 816 - 812 = 4 answer : a"
Answer: a
Question (general): the average expenditure of a labourer for 6 months was 80 and he fell into debt . in the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30 . his monthly income i
Options: a ) 70 , b ) 72 , c ) 75 , d ) 78 , e ) 80
Rationale: "income of 6 months = ( 6 × 80 ) – debt = 480 – debt income of the man for next 4 months = 4 × 60 + debt + 30 = 270 + debt ∴ income of 10 months = 750 average monthly income = 750 ÷ 10 = 75 answer c"
Answer: c
Question (geometry): the length of a rectangle is halved , whileits breadth is tripled . wat is the % change in area ?
Options: a ) 40 % , b ) 45 % , c ) 50 % , d ) 65 % , e ) 70 %
Rationale: "let original length = x and original breadth = y . original area = xy . new length = x . 2 new breadth = 3 y . new area = x x 3 y = 3 xy . 2 2 increase % = 1 xy x 1 x 100 % = 50 % . 2 xy c"
Answer: c
Question (general): a man saves 25 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 10 % , he is only able to save rs . 175 per month . what is his monthly salary ?
Options: a ) rs . 1000 , b ) rs . 2000 , c ) rs . 1500 , d ) rs . 3000 , e ) rs . 3100
Rationale: "income = rs . 100 expenditure = rs . 75 savings = rs . 25 present expenditure 75 + 75 * ( 10 / 100 ) = rs . 82.5 present savings = 100 – 82.50 = rs . 17.50 if savings is rs . 17.50 , salary = rs . 100 if savings is rs . 175 , salary = 100 / 17.5 * 175 = 1000 answer : a"
Answer: a
Question (gain): a 15 % stock yielding 12 % is quoted at :
Options: a ) s . 83.33 , b ) s . 110 , c ) s . 112 , d ) s . 125 , e ) s . 140
Rationale: "income of rs 12 on investment of rs 100 income of rs 15 on investment of ? = ( 15 * 100 ) / 12 = 125 answer : d"
Answer: d
Question (gain): on june 1 a bicycle dealer noted that the number of bicycles in stock had decreased by 2 for each of the past 5 months . if the stock continues to decrease at the same rate for the rest of the year , how many fewer bicycles will be in stock on september 1 than were in stock on january 1 ?
Options: a ) 18 , b ) 12 , c ) 20 , d ) 32 , e ) 36
Rationale: "jan 1 = c feb 1 = c - 2 march 1 = c - 4 april 1 = c - 8 may 1 = c - 10 june 1 = c - 12 july 1 = c - 14 aug 1 = c - 16 sept 1 = c - 18 difference between stock on september 1 than were in stock on january 1 will be - c - ( c - 18 ) = 18 hence answer will be ( a )"
Answer: a
Question (general): having received his weekly allowance , john spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.92 at the candy store . what is john ’ s weekly allowance ?
Options: a ) $ 2.55 , b ) $ 2.85 , c ) $ 3.15 , d ) $ 3.45 , e ) $ 3.75
Rationale: "x = 3 x / 5 + 1 / 3 * 2 x / 5 + 92 4 x / 15 = 92 x = 345 = $ 3.45 the answer is d ."
Answer: d
Question (general): a salesman ’ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1300 plus 2.5 % commission on all sales exceeding rs . 4000 . if his remuneration as per new scheme was rs . 600 more than that by the previous schema , his sales were worth ?
Options: a ) 12028 , b ) 12000 , c ) 12019 , d ) 12197 , e ) 18000
Rationale: [ 1300 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 18000 answer : c
Answer: c
Question (gain): a sum fetched a total simple interest of 4020.75 at the rate of 9 % . p . a . in 5 years . what is the sum ?
Options: a ) 5768 , b ) 8925 , c ) 2345 , d ) 6474 , e ) 8935
Rationale: "principal = ( 100 x 4020.75 ) / ( 9 x 5 ) = 402075 / 45 = 8935 . answer e"
Answer: e
Question (physics): two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 28 kmph and 21 kmph respectively . when they meet , it is found that one train has traveled 60 km more than the other one . the distance between the two stations is ?
Options: a ) 457 km , b ) 444 km , c ) 547 km , d ) 588 km , e ) 653 km
Rationale: "1 h - - - - - 5 ? - - - - - - 60 12 h rs = 28 + 21 = 49 t = 12 d = 49 * 12 = 588 answer : d"
Answer: d
Question (general): exactly 3 / 7 of the people in the room are under the age of 21 , and exactly 5 / 11 of the people in the room are over the age of 65 . if the total number of the people in the room is greater than 50 and less than 100 , how many people in the room are under the age of 21 ?
Options: a ) 21 , b ) 35 , c ) 33 , d ) 60 , e ) 65
Rationale: the total number of the people in the room must be a multiple of both 7 and 11 ( in order 3 / 7 and 5 / 11 of the number to be an integer ) , thus the total number of the people must be a multiple of lcm of 7 and 11 , which is 77 . since , the total number of the people in the room is greater than 50 and less than 100 , then there are 77 people in the room . therefore there are 3 / 7 * 77 = 33 people in the room under the age of 21 . answer : c .
Answer: c
Question (gain): one night 15 percent of the female officers on a police force were on duty . if 300 officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 90 , b ) 180 , c ) 270 , d ) 500 , e ) 1,000
Rationale: "let total number of female officers in the police force = f total number of officers on duty on that night = 300 number of female officers on duty on that night = 300 / 2 = 150 ( 15 / 100 ) * f = 150 = > f = 1000 answer e"
Answer: e
Question (general): with # andeach representing different digits in the problem below , the difference between # and # # is 801 . what is the value of ? # - # # ____ 812
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: 100 x - ( 10 x + x ) - - - - - - - - - - - 89 x = 801 x = 9 c
Answer: c
Question (other): a cat leaps 5 leaps for every 4 leaps of a dog , but 3 leaps of the dog are equal to 4 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?
Options: a ) 11 : 15 , b ) 15 : 11 , c ) 16 : 15 , d ) 15 : 16 , e ) 11 : 16
Rationale: "solution : given ; 3 dog = 4 cat ; or , dog / cat = 4 / 3 ; let cat ' s 1 leap = 3 meter and dogs 1 leap = 4 meter . then , ratio of speed of cat and dog = 3 * 5 / 4 * 4 = 15 : 16 . ' ' answer : option d"
Answer: d
Question (general): ( √ 97 + √ 486 ) / √ 54 = ?
Options: a ) 2 √ 2 , b ) 2 √ 3 , c ) 3 √ 2 , d ) 3 √ 3 , e ) 13 / 3
Rationale: "( √ 96 + √ 486 ) / √ 54 = ( 4 √ 6 + 9 √ 6 ) / 3 √ 6 = 13 √ 6 / 3 √ 6 = 13 / 3 hence , the correct answer is e ."
Answer: e
Question (physics): a secret can be told only 2 persons in 5 minutes . the same person tells to 2 more persons and so on . how long will take to tell it to 768 persons ?
Options: a ) 25 min , b ) 32 min , c ) 33 min , d ) 34 min , e ) 35 min
Rationale: at start one person will tell to 2 persons , it will take 5 min , now that 1 + 2 = 3 persons will tell this to next 6 persons , then 1 + 2 + 6 = 9 persons will tell to next 18 persons , then 1 + 2 + 6 + 18 = 27 persons to 54 similarly 1 + 2 + 6 + 18 + 54 = 81 persons will tell this to 162 persons similarly 1 + 2 + 6 + 18 + 54 + 162 = 243 persons will tell this to 486 persons , upto this step total persons who have listened this secret = 2 + 6 + 18 + 54 + 162 + 486 = 728 , and total time taken upto this step = 5 * 6 = 30 min , now next 5 min will be sufficient to tell this message to next 40 persons so total time taken = 35 min answer : e
Answer: e
Question (physics): in what time will a train 110 m long cross an electric pole , it its speed be 144 km / hr ?
Options: a ) 2.35 sec , b ) 2.85 sec , c ) 7.5 sec , d ) 2.75 sec , e ) 1.5 sec
Rationale: "speed = 144 * 5 / 18 = 40 m / sec time taken = 110 / 40 = 2.75 sec . answer : d"
Answer: d
Question (physics): 9 . on level farmland , two runners leave at the same time from the intersection of two country roads . one runner jogs due north at a constant rate of 6 miles per hour while the second runner jogs due east at a constant rate that is 2 miles per hour faster than the first runner ' s rate . how far apart , to the nearest mile , will they be after 1 / 2 hour ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 12 , e ) 14
Rationale: "if runner 1 is going north and runner 2 is going east they are like two sides of a 90 degree triangle . side 1 = 6 m / h - - > 3 m in 1 / 2 hr side 2 = 8 m / h - - > 4 m in 1 / 2 hr to complete this right angle triangle d ^ 2 = 4 ^ 2 + 3 ^ 2 d ^ 2 = 25 = 5 answer option c"
Answer: c
Question (general): find the smallest number which when divided by 13 and 15 leaves respective remainders of 2 and 4
Options: a ) 187 , b ) 197 , c ) 184 , d ) 219 , e ) 227
Rationale: let ' n ' is the smallest number which divided by 13 and 15 leaves respective remainders of 2 and 4 . required number = ( lcm of 13 and 15 ) - ( common difference of divisors and remainders ) = ( 195 ) - ( 11 ) = 184 . answer : c
Answer: c
Question (general): if sharon ' s weekly salary increased by 16 percent , she would earn $ 406 per week . if instead , her weekly salary were to increase by 20 percent , how much would she earn per week ?
Options: a ) $ 420 , b ) $ 382 , c ) $ 385 , d ) $ 392 , e ) $ 399
Rationale: "( 406 / 116 ) 120 = 420 in this case long division does not take much time . ( 406 / 116 ) = 3.5 35 * 12 = 420 ( 350 + 70 ) answer a"
Answer: a
Question (physics): two tains are running in opposite directions with the same speed . if the length of each train is 120 metres and they cross each other in 12 seconds , then the speed of each train ( in km / hr ) is :
Options: a ) 12 , b ) 24 , c ) 36 , d ) 48 , e ) 38
Rationale: sol . let the speed of each train be x m / sec . then , relative speed of the two trains = 2 x m / sec . so , 2 x = ( 120 + 120 ) / 12 ⇔ 2 x = 20 ⇔ x = 10 . ∴ speed of each train = 10 m / sec = [ 10 * 18 / 5 ] km / hr = 36 km / hr . answer c
Answer: c
Question (physics): a taxi company charges $ 2.5 for the first quarter of a mile and fifteen cents for each additional quarter of a mile . what is the maximum distance someone could travel with $ 4.90 ?
Options: a ) 4 miles , b ) 4 1 / 4 miles , c ) 4 3 / 4 miles , d ) 5 1 / 2 miles , e ) 6 1 / 4 miles
Rationale: "if we start out with $ 4.90 and have to spend $ 2.5 for the first quarter - mile , we will have $ 2.40 left to spend on quarter - mile intervals . since $ 2.40 / $ 0.15 = 16 , we can buy 16 more quarter - miles , and will travel 17 quarter miles in all : 17 × 1 / 4 = 4 1 / 4 miles . the correct answer is choice ( b ) ."
Answer: b
Question (general): a student has to obtain 60 % of the total marks to pass . he got 160 marks and failed by 20 marks . the maximum marks are ?
Options: a ) 210 , b ) 280 , c ) 300 , d ) 320 , e ) 340
Rationale: "let the maximum marks be x then , 60 % of x = 160 + 20 60 x / 100 = 180 60 x = 180 * 100 = 18000 x = 300 answer is c"
Answer: c
Question (general): in a renowned city , the average birth rate is 7 people every two seconds and the death rate is 2 people every two seconds . estimate the size of the population net increase that occurs in one day .
Options: a ) 215,000 , b ) 216,000 , c ) 217,000 , d ) 218,000 , e ) 219,000
Rationale: this question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds . for this particular question : increase in the population every 2 seconds = 7 - 2 = 5 people . total 2 second interval in a day = 24 * 60 * 60 / 2 = 43,200 population increase = 43,200 * 5 = 216,000 . hence b .
Answer: b
Question (general): two trains of equal are running on parallel lines in the same direction at 46 km / hr and 36 km / hr . the faster train passes the slower train in 36.00001 sec . the length of each train is ?
Options: a ) 50 , b ) 99 , c ) 77 , d ) 26 , e ) 23
Rationale: "let the length of each train be x m . then , distance covered = 2 x m . relative speed = 46 - 36 = 10 km / hr . = 10 * 5 / 18 = 25 / 9 m / sec . 2 x / 36 = 25 / 9 = > x = 50 . answer : a"
Answer: a
Question (physics): two numbers n and 14 have lcm = 56 and gcf = 10 . find n .
Options: a ) 24 , b ) 40 , c ) 44 , d ) 54 , e ) 64
Rationale: "the product of two integers is equal to the product of their lcm and gcf . hence . 14 × n = 56 × 10 n = 56 × 10 / 14 = 40 correct answer b"
Answer: b
Question (gain): how many liters of water must be evaporated from 50 liters of a 2 percent sugar solution to get a 4 percent sugar solution ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 35 , e ) 40
Rationale: "let x be the amount that needs to be evaporated . 0.02 ( 50 ) = 0.04 ( 50 - x ) 0.04 x = 2 - 1 x = 1 / 0.04 = 25 liters the answer is b ."
Answer: b
Question (general): a batsman scored 60 runs which included 2 boundaries and 2 sixes . what percent of his total score did he make by running between the wickets .
Options: a ) 30 % , b ) 33.33 % , c ) 40 % , d ) 60 % , e ) 50 %
Rationale: "explanation : number of runs made by running = 60 - ( 2 x 4 + 2 x 6 ) = 60 - ( 20 ) = 20 now , we need to calculate 20 is what percent of 60 . = > 20 / 60 * 100 = 33.33 % option b"
Answer: b
Question (physics): if 3 people can do 3 times of a particular work in 3 days , then how many days would it take 5 people to do 5 times of that particular work ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 8
Rationale: 3 people can do the work one time in one day . 1 person can do 1 / 3 of the work in one day . 5 people can do 5 / 3 of the work in one day . 5 people can do 5 times the work in 3 days . the answer is c .
Answer: c
Question (gain): what is the value of â ˆ š 64 % ?
Options: a ) 80 % , b ) 20 % , c ) 40 % , d ) 90 % , e ) 26 %
Rationale: "explanation : br > â ˆ š 64 % = â ˆ š 64 / â ˆ š 100 = 8 / 10 = 80 / 100 = 80 % correct answer is a ) 80 %"
Answer: a
Question (gain): tom opened a shop investing rs . 500 . jose joined him 2 months later , investing rs . 350 . they earned a profit of rs . 1720 after completion of one year . what will be jose ' s share of profit ?
Options: a ) 80 , b ) 20 , c ) 30 , d ) 41 , e ) 15
Rationale: "sol = ~ s - so anju ’ s share = [ 5 / 9 ] x 1720 = 80 a"
Answer: a
Question (physics): the sides of a rectangular field are in the ratio 3 : 4 . if the area of the field is 8748 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 . 94.50 , e ) none of these
Rationale: "solution let length = ( 3 x ) metres and breadth = ( 4 x ) metres . then , 3 x × 4 x = 8748 ⇔ 12 x 2 = 8748 ⇔ x 2 = 729 ⇔ x = 27 . so , length = 81 m and breadth = 108 m . perimeter = [ 2 ( 81 + 108 ) ] m = 378 m . ∴ cost of fencing = rs . ( 0.25 × 378 ) = rs . 94.50 . answer d"
Answer: d
Question (physics): the angle between the minute hand and the hour hand of a clock when the time is 4.20 , is :
Options: a ) 10 d , b ) 0 d , c ) 15 d , d ) 5 d , e ) 20 d
Rationale: "angle traced hr 13 / 3 = ( 360 / 12 * 13 / 3 ) = 130 traced by min hand 20 min = ( 360 / 60 * 20 ) = 120 req = ( 130 - 120 ) = 10 d answer a"
Answer: a
Question (general): the positive numbers w , x , y , and z are such that x is 40 percent greater than y , y is 20 percent greater than z , and w is 20 percent less than x . what percent greater than z is w ?
Options: a ) 15.2 % , b ) 16.0 % , c ) 20.0 % , d ) 23.2 % , e ) 24.8 %
Rationale: "my strategy is same as thedobermanbut instead take z = 100 , which makes life a bit easy . as : z = 100 y = 120 ( 20 % greater than z ) z = 144 ( 20 % greater than y ) now calculate w 20 % less than z = 144 * 80 / 100 = 115.2 now by just looking , relation between w and z : w - z / z * 100 = 23.2 - answer d"
Answer: d
Question (physics): if 10 men do a work in 80 days , in how many days will 20 men do it ?
Options: a ) 18 days , b ) 38 days , c ) 40 days , d ) 48 days , e ) 50 days
Rationale: "10 * 80 = 20 * x x = 40 days answer : c"
Answer: c
Question (physics): a trader sells 60 meters of cloth for rs . 8400 at the profit of rs . 12 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 128 , b ) 140 , c ) 123 , d ) 110 , e ) 150
Rationale: "sp of 1 m of cloth = 8400 / 60 = rs . 140 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 140 - rs . 12 = rs . 128 . answer : a"
Answer: a
Question (general): 48 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 ) 42 , d ) 27 , e ) 21
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 48 = 21 answer : e"
Answer: e
Question (physics): a car covers a distance of 624 km in 6 â ½ hours . find its speed ?
Options: a ) 104 , b ) 190 , c ) 109 , d ) 278 , e ) 211
Rationale: explanation : 624 / 6 = 104 kmph answer : c
Answer: c
Question (general): when average age of 23 members are 0 , how many members greater than 0 ?
Options: a ) 17 , b ) 22 , c ) 21 , d ) 24 , e ) 25
Rationale: "average of 23 numbers = 0 . sum of 23 numbers ( 0 x 23 ) = 0 . it is quite possible that 22 of these numbers may be positive and if their sum is a then 23 rd number is ( - a ) answer is 22 ( b )"
Answer: b
Question (general): if 2 : 9 : : x : 18 , then find the value of x
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "explanation : treat 2 : 9 as 2 / 9 and x : 18 as x / 18 , treat : : as = so we get 2 / 9 = x / 18 = > 9 x = 36 = > x = 4 option c"
Answer: c
Question (general): during the first two weeks of january , the total rainfall in springdale was 35 inches . if the rainfall during the second week was 1.5 times the rainfall during the first week , what was the rainfall during the second week of january ?
Options: a ) 5 inches , b ) 6 inches , c ) 9 inches , d ) 10 inches , e ) 21 inches
Rationale: total rainfall in 2 weeks = 35 inches . assume the rainfall in second week = 1 . x rainfall in first week = x total rainfall = 2.5 x = 35 inches x = 14 and 1.5 x = 21 rainfall during second week = 21 inches option e
Answer: e
Question (probability): if you roll one fair 6 - sided die , what is the probability that the number is even or less than 3 ?
Options: a ) 2 / 3 , b ) 1 / 2 , c ) 3 / 4 , d ) 5 / 6 , e ) 1 / 3
Rationale: the numbers which satisfy the conditions are 1 , 2 , 4 , and 6 . the probability is 4 / 6 = 2 / 3 the answer is a .
Answer: a
Question (general): a fifth of arun â € ™ s marks in mathematics exceed a third of his marks in english by 20 . if he got 260 marks in two subjects together how many marks did he got in english ?
Options: a ) 12080 , b ) 18060 , c ) 20060 , d ) 20040 , e ) none of them
Rationale: let arun â € ™ s marks in mathematics and english be x and y then ( 1 / 5 ) x - ( 1 / 3 ) y = 20 3 x - 5 y = 300 â € ¦ â € ¦ > ( 1 ) x + y = 260 â € ¦ â € ¦ . > ( 2 ) solving ( 1 ) and ( 2 ) x = 200 and y = 60 answer is c .
Answer: c
Question (other): in a colony of 70 residents , the ratio of the number of men and women is 4 : 3 . among the women , the ratio of the educated to the uneducated is 1 : 4 . if the ratio of the number of education to uneducated persons is 8 : 27 , then find the ratio of the number of educated and uneducated men in the colony ?
Options: a ) 1 : 7 , b ) 1 : 1 , c ) 1 : 2 , d ) 1 : 9 , e ) 1 : 3
Rationale: "number of men in the colony = 4 / 7 ( 70 ) = 40 number of women in the colony = 3 / 7 ( 70 ) = 30 number of educated women in the colony = 1 / 5 ( 30 ) = 6 number of uneducated women in the colony = 4 / 5 ( 30 ) = 24 number of educated persons in the colony = 8 / 35 ( 70 ) = 16 as 6 females are educated , remaining 10 educated persons must be men . number of uneducated men in the colony = 40 - 10 = 30 number of educated men and uneducated men are in the ratio 10 : 30 = > 1 : 3 answer : e"
Answer: e
Question (general): 40 persons like apple . 7 like orange and mango dislike apple . 10 like mango and apple and dislike orange . 4 like all . how many people like apple ?
Options: a ) 47 , b ) 46 , c ) 54 , d ) 58 , e ) 62
Rationale: "orange + mango - apple = 7 mango + apple - orange = 10 apple = 40 orange + mango + apple = 4 40 + 10 + 4 - 7 = 47 like apple answer : a"
Answer: a
Question (general): one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 50,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 30000 , b ) 60000 , c ) 50000 , d ) 90000 , e ) 70000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 150000 - x ) respectively . then , ( 1 / 3 ) x = ( 1 / 2 ) ( 150000 - x ) ( x / 3 ) + ( x / 2 ) = 75000 5 x / 6 = 75000 x = 75000 x 6 / 5 = 90000 savings in public provident fund = rs . ( 150000 - 90000 ) = rs . 60000 answer is b ."
Answer: b
Question (physics): a girl goes to her school from her house at a speed of 6 km / hr and returns at a speed of 4 km / hr . if she takes 10 hours in going and coming back , the distance between her school and house is
Options: a ) 12 kms , b ) 16 kms , c ) 20 kms , d ) 24 kms , e ) none of above
Rationale: let distance be d 10 = d / 4 + d / 6 answer : d
Answer: d
Question (general): if x = - 6 and y = - 3 , what is the value of 4 ( x - y ) ^ 2 - xy ?
Options: a ) 20 , b ) 18 , c ) 17 , d ) 22 , e ) 23
Rationale: x = - 6 and y = - 3 x - y = - 6 - ( - 3 ) = - 6 + 3 = - 3 x * y = - 6 * - 3 = 18 now we apply it in the equation 4 ( x - y ) ^ 2 - xy = 4 ( - 3 ) ^ 2 - 18 = = > 4 * 9 - 18 = 36 - 18 = 18 answer : b
Answer: b
Question (general): if the sum of the 4 th term and the 12 th term of an arithmetic progression is 12 , what is the sum of the first 15 terms of the progression ?
Options: a ) 90 , b ) 80 , c ) 70 , d ) 60 , e ) 50
Rationale: "4 th term + 12 th term = 12 i . e . , ( a + 3 d ) + ( a + 11 d ) = 12 now , sum of first 15 terms = ( 15 / 2 ) * [ 2 a + ( 15 - 1 ) d ] = ( 15 / 2 ) * [ 2 a + 14 d ] = ( 15 / 2 ) * 12 - - - - - - - - - - - - - - - from ( 1 ) = 90 answer : a"
Answer: a
Question (general): ( 51 + 52 + 53 + . . . + 100 ) = ?
Options: a ) 2525 , b ) 2975 , c ) 3225 , d ) 3775 , e ) 2753
Rationale: "explanation : this is an a . p . in which a = 51 , l = 100 and n = 50 . sum = n ( a + l ) = 50 x ( 51 + 100 ) = ( 25 x 151 ) = 3775 . 2 2 answer : d"
Answer: d
Question (physics): the edges of a cuboid are 2 cm , 5 cm and 8 cm . find the volume of the cuboid ?
Options: a ) 90 , b ) 80 , c ) 40 , d ) 120 , e ) 70
Rationale: "2 * 5 * 8 = 80 answer : b"
Answer: b
Question (general): a car was driving at 50 km / h for 30 minutes , and then at 40 km / h for another 30 minutes . what was its average speed ?
Options: a ) 80 . , b ) 75 . , c ) 70 . , d ) 65 . , e ) 54 .
Rationale: "driving at 50 km / h for 30 minutes , distance covered = 50 * 1 / 2 = 25 km driving at 40 km / h for 30 minutes , distance covered = 40 * 1 / 2 = 20 km average speed = total distance / total time = 45 / 1 = 45 km / h answer : a"
Answer: a
Question (physics): a and b walk around a circular track . they start at 9 a . m . from the same point in the opposite directions . a and b walk at a speed of 2 rounds per hour and 3 rounds per hour respectively . how many times shall they cross each other before 11 : 00 a . m . ?
Options: a ) 8 , b ) 7 , c ) 6 , d ) 15 , e ) 3
Rationale: "sol . relative speed = ( 2 + 3 ) = 5 rounds per hour . so , they cross each other 5 times in an hour . hence , they cross each other 15 times before 11 : 00 a . m . answer d"
Answer: d
Question (physics): a can do a work in 21 days and b alone can do it 28 days , they begin the work together , but a left after some days . b completed the remaining work in 21 days . after how many days did a leave ?
Options: a ) 10 , b ) 8 , c ) 3 , d ) 15 , e ) 16
Rationale: explanation : ( a + b ) 1 day work = { 1 / 21 + 1 / 28 } = 1 / 12 = 12 days is required for a & b b ’ s 1 day work = 1 / 28 b ’ s 21 days work = 21 / 28 1 - 21 / 28 = 7 / 28 - 1 / 4 1 / 4 * 12 = 3 days answer : option c
Answer: c