Cheukting/mathqa huggingface dataset:
Question (general): 4 athletes , wendy , michelle , brenda , and jamal , scored in a soccer ( football ) game . if michelle scored 1 more goal than brenda did , jamal scored 3 less than wendy did , and wendy scored 3 more than michelle did , how many fewer goals did brenda score than jamal ?
Options: a ) - 8 , b ) - 6 , c ) - 2 , d ) - 1 , e ) - 3
Rationale: in this word problem , the first key is to turn the story into equations : michelle scored 1 more than brenda did : m = 1 + b jamal scored 3 less than wendy did : j = w - 3 wendy scored 3 more than michelle did : w = 3 + m then , in classic gmat style , the problem does n ' t ask you to solve for a single variable , but instead to solve for the difference between b and j ( how many more goals did brenda score than jamal did ? ) . this means that your goal is to get the equations in terms of b and j so that you can solve for the expression b - j . taking the first equation and solving for b , you have b = m - 1 . taking the second equation and solving for j you have j = w - 3 , and then with the third equation you can replace w with 3 + m so that both b and j are in terms of m : j = ( 3 + m ) - 3 . so if b = m - 1 and j = m , then : b - j = ( m - 1 ) - ( m ) b - j = m - 1 - m ( remove the parentheses by distributing the multiplication ) b - j = - 1 , so the answer is d .
Answer: d
Question (physics): a bus trip of 550 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: the time is the distance / speed . the time difference is 1 hour . 550 / v - 550 / ( v + 5 ) = 1 550 ( v + 5 ) - 550 v = ( v ) ( v + 5 ) 2750 = ( v ) ( v + 5 ) 50 * 55 = ( v ) ( v + 5 ) v = 50 mph the answer is c .
Answer: c
Question (physics): the sum of the squares of 3 consecutive natural number is 2030 . what is the middle number ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: let the numbers be x , x + 1 and x + 2 x 2 + ( x + 1 ) 2 + ( x + 2 ) 2 = 2030 3 x 2 + 6 x - 2025 = 0 ( x + 27 ) ( x - 25 ) = 0 x = 25 the middle number is 26 answer b 26
Answer: b
Question (general): ( √ 112 + √ 567 ) / √ 175 = ?
Options: a ) 2 √ 2 , b ) 13 / 5 , c ) 3 √ 2 , d ) 3 √ 3 , e ) √ 2
Rationale: ( √ 112 + √ 567 ) / √ 175 = ( 4 √ 7 + 9 √ 7 ) / 5 √ 7 = 13 / 5 hence , the correct answer is b .
Answer: b
Question (gain): a statue is being carved by a sculptor . the original piece of marble weighed 250 kg . in the first week 30 percent is cut away . in the second week 20 percent of the remainder is cut away . in the third week the statue is completed when 25 percent of the remainder is cut away . what is the weight of the final statue ?
Options: a ) 105 kg , b ) 103 kg , c ) 108 kg , d ) 125 kg , e ) 117 kg
Rationale: "a 105 kg 250 × 0.7 × 0.8 × 0.75 = 105 kg ."
Answer: a
Question (physics): dan can do a job alone in 12 hours . annie , working alone , can do the same job in just 9 hours . if dan works alone for 8 hours and then stops , how many hours will it take annie , working alone , to complete the job ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: dan can complete 1 / 12 of the job per hour . in 8 hours , dan completes 8 ( 1 / 12 ) = 2 / 3 of the job . annie can complete 1 / 9 of the job per hour . to complete the job , annie will take 1 / 3 / 1 / 9 = 3 hours . the answer is b .
Answer: b
Question (physics): two cars start from the opposite places of a main road , 105 km apart . first car runs for 25 km and takes a right turn and then runs 15 km . it then turns left and then runs for another 25 km and then takes the direction back to reach the main road . in the mean time , due to minor break down the other car has run only 35 km along the main road . what would be the distance between two cars at this point ?
Options: a ) 65 , b ) 38 , c ) 20 , d ) 28 , e ) 21
Rationale: answer : c ) 20 km
Answer: c
Question (probability): 4 dice are thrown simultaneously on the board . find the probability show the same face ?
Options: a ) 2 / 113 , b ) 1 / 215 , c ) 1 / 216 , d ) 3 / 113 , e ) 4 / 113
Rationale: "the total number of elementary events associated to the random experiments of throwing four dice simultaneously is : = 6 × 6 × 6 × 6 = 64 = 6 × 6 × 6 × 6 = 64 n ( s ) = 64 n ( s ) = 64 let xx be the event that all dice show the same face . x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } x = { ( 1,1 , 1,1 , ) , ( 2,2 , 2,2 ) , ( 3,3 , 3,3 ) , ( 4,4 , 4,4 ) , ( 5,5 , 5,5 ) , ( 6,6 , 6,6 ) } n ( x ) = 6 n ( x ) = 6 hence required probability , = n ( x ) n ( s ) = 664 = n ( x ) n ( s ) = 664 = 1 / 216 c"
Answer: c
Question (general): every disk in a bag is either blue , yellow or green . the ratio of blue disks to yellow disks to green disks in this bag is 3 : 7 : 8 . if the total number of disks in the bag is 126 , how many more green disks than blue disks are in the bag ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 40
Rationale: let b : y : g = 3 x : 7 x : 8 x . 3 x + 7 x + 8 x = 18 x = 126 - - > x = 7 . g - b = 8 x - 3 x = 5 x = 35 . the answer is d .
Answer: d
Question (general): ben left a job paying $ 75000 per year to accept a sales job paying $ 45000 per year plus 15 percent commission . if each of his sales is for $ 750 , what is the least number of sales he must make per year if he is not to lose money because of the change ?
Options: a ) 40 , b ) 200 , c ) 266 , d ) 267 , e ) 600
Rationale: in order not to lose money because of the change ben ' s total commission must beat least $ 75,000 - $ 45,000 = $ 30,000 , so total sales must beat least $ 30,000 / 0.15 = $ 200,000 . which means that he must makeat least $ 200,000 / 750 = 800 / 3 = 266.6 sales , so 267 sales . answer : d .
Answer: d
Question (physics): if there are 86 workers in a factory , and on a certain day , 72 were present . calculate the percentage that showed up for work ? ( round to the nearest tenth ) .
Options: a ) 82.7 % , b ) 81.7 % , c ) 83.7 % , d ) 89.7 % , e ) 88.7 %
Rationale: "72 / 86 * 100 = 83.72 83.7 % correct answer c"
Answer: c
Question (physics): x does a work in 20 days . y does the same work in 40 days . in how many days they together will do the same work ?
Options: a ) 10 , b ) 12 , c ) 20 , d ) 30 , e ) 13.33
Rationale: x ' s 1 day ' s work = 1 / 20 y ' s 1 day ' s work = 1 / 40 ( x + y ) ' s 1 day ' s work = ( 1 / 20 + 1 / 40 ) = 1 / 13.33 both together will finish the work in 13.33 days . correct option is e
Answer: e
Question (other): in a school the ratio of boys and girls are in the ration 5 : 6 . 25 % of boys will get scholar ship and 20 % of girls will get scholar ship what % of students wont get scholarship ?
Options: a ) 60 % , b ) 78 % , c ) 88 % , d ) 98 % , e ) 99 %
Rationale: boys : girls = > 5 x : 6 x total no . of students including boys nd girls = 5 x + 6 x = 11 x 25 % of boys = > 5 x * 25 / 100 = 5 x / 4 20 % of girls = > 6 x * 20 / 100 = 6 x / 5 no . of students who are getting scholarship = > 5 x / 4 + 6 x / 5 = 49 x / 20 no . of students who are not getting scholarship = 11 x - 49 x / 20 = 171 x / 20 % of students not getting scolorship = > 171 x / 20 / 11 x * 100 = > 100 * 171 x / 220 x = 77.7 % answer : b
Answer: b
Question (physics): a start walking from a place at a uniform speed of 7 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
Options: a ) 4.7 kmph , b ) 7.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph
Rationale: distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 7 + 5 / 9 = 7.55 answer b
Answer: b
Question (general): find large number from below question the difference of two numbers is 1355 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1235 , b ) 1345 , c ) 1678 , d ) 1767 , e ) 1623
Rationale: "let the smaller number be x . then larger number = ( x + 1355 ) . x + 1355 = 6 x + 15 5 x = 1340 x = 268 large number = 268 + 1355 = 1623 e"
Answer: e
Question (general): six persons standing in queue with different age group , after two years their average age will be 43 and seventh person joined with them . hence the current average age has become 45 . find the age of the 7 th person .
Options: a ) 69 , b ) 70 , c ) 71 , d ) 72 , e ) 73
Rationale: "let ‘ x ’ be the average of 6 persons since there are 6 after 2 years the age will be increased by 2 for each . so 6 * 2 = 12 after two years age will be = x + 12 average age is 43 that is ( x + 12 ) / 6 = 43 = > x = 246 let ‘ y ’ be the 7 th person age ( x + y ) / 7 = 45 ( 246 + y ) / 7 = 45 y = ( 45 * 7 ) - 246 y = 69 answer a"
Answer: a
Question (general): solve below question 2 x + 1 = - 13
Options: a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 7
Rationale: "2 x + 1 = - 13 x = - 7 e"
Answer: e
Question (physics): car a is 16 miles behind car b , which is traveling in the same direction along the same route as car a . car a is traveling at a constant speed of 58 miles per hour and car bis traveling at a constant speed of 50 miles per hour . how many hours will it take for car a to overtake and drive 8 miles ahead of car b ?
Options: a ) 1.5 , b ) 2.0 , c ) 2.5 , d ) 3.0 , e ) 3.5
Rationale: relative speed of car a is 58 - 50 = 8 miles per hour , to catch up 16 miles and drive 8 miles ahead so to drive 24 miles it ' ll need 24 / 8 = 3 hours . answer : d
Answer: d
Question (general): if x + y = 290 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 245 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 290 x - y = 200 2 x = 90 x = 45 y = 245 answer is b"
Answer: b
Question (general): for all positive integers m , [ m ] = 3 m when m is odd and [ m ] = ( 1 / 2 ) * m when m is even . what is [ 5 ] * [ 8 ] equivalent to ?
Options: a ) [ 40 ] , b ) [ 60 ] , c ) [ 80 ] , d ) [ 120 ] , e ) [ 150 ]
Rationale: "[ 5 ] * [ 8 ] = 15 * 4 = 60 = ( 1 / 2 ) ( 120 ) = [ 120 ] the answer is d ."
Answer: d
Question (other): if log 10 2 = 0.3010 , the value of log 10 80 is :
Options: a ) 1.5252 , b ) 1.903 , c ) 3.9252 , d ) 3.903 , e ) 2.5252
Rationale: "= log 10 8 + log 10 10 = log 10 ( 23 ) + 1 = 3 log 10 2 + 1 = ( 3 x 0.3010 ) + 1 = 1.9030 . answer b"
Answer: b
Question (gain): the bankers discount of a certain sum of money is rs . 18 and the true discount on the same sum for the same time is rs . 15 . the sum due is :
Options: a ) 89 , b ) 90 , c ) 91 , d ) 92 , e ) 93
Rationale: "sum = ( b . d * t . d ) / ( b . d - t . d ) ( 18 * 15 ) / 18 - 15 ; 90 answer : b"
Answer: b
Question (general): the mean of 50 observations is 200 . but later he found that there is decrements of 34 from each observations . what is the the updated mean is ?
Options: a ) 165 , b ) 166 , c ) 190 , d ) 198 , e ) 199
Rationale: "166 answer is b"
Answer: b
Question (general): the sum of first 45 natural numbers is
Options: a ) 1035 , b ) 1280 , c ) 2070 , d ) 2140 , e ) none
Rationale: solution we know that ( 1 + 2 + 3 + . . . . . + 45 ) = n ( n + 1 ) / 2 therefore ( 1 + 2 + 3 + . . . . + 45 ) = ( 45 × 46 / 2 ) = 1035 . answer a
Answer: a
Question (general): what is the dividend . divisor 13 , the quotient is 17 and the remainder is 1
Options: a ) 222 , b ) 224 , c ) 226 , d ) 228 , e ) 230
Rationale: "a = d * q + r a = 13 * 17 + 1 a = 221 + 1 a = 222"
Answer: a
Question (general): a man performs 3 / 5 of the total journey by rail , 17 / 20 by bus and the remaining 6.5 km on foot . his total journey is :
Options: a ) 125 km , b ) 130 km , c ) 135 km , d ) 140 km , e ) none
Rationale: "sol . let the total journey be x km . then 3 x / 5 + 7 x / 20 + 6.5 = x ⇔ 12 x + 7 x + 20 * 6.5 = 20 x ⇔ x = 130 km . answer b"
Answer: b
Question (general): there are 300 female managers in a certain company . find the total number of female employees in the company , if 2 / 5 of all the employees are managers and 2 / 5 of all male employees are managers .
Options: a ) 650 , b ) 700 , c ) 750 , d ) 800 , e ) none of these
Rationale: as per question stem 2 / 5 m ( portion of men employees who are managers ) + 200 ( portion of female employees who are managers ) = 2 / 5 t ( portion of total number of employees who are managers ) , thus we get that 2 / 5 m + 300 = 2 / 5 t , or 2 / 5 ( t - m ) = 300 , from here we get that t - m = 750 , that would be total number of female employees and the answer ( c )
Answer: c
Question (general): of the seven - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ?
Options: a ) 24 , b ) 36 , c ) 72 , d ) 152409600 , e ) 216
Rationale: "of the seven - digit positive integers that have no digits equal to zero , how many have two digits that are equal to each other and the remaining digit different from the other two ? a . 24 b . 36 c . 72 d . 144 e . 216 choosing the digit for p - 9 ways ; choosing the digit for q - 8 ways ; choosing the digit for r - 7 ways ; choosing the digit for s - 6 ways ; choosing the digit for t - 5 ways ; choosing the digit for u - 4 ways ; # of permutations of 3 digits in ppqrstu - 7 ! / 2 ! total : 9 * 8 * 7 * 6 * 5 * 4 * 7 ! / 2 ! = 152409600 . answer : d ."
Answer: d
Question (gain): the true discount on a bill of rs . 2260 is rs . 360 . what is the banker ' s discount ?
Options: a ) rs . 428 , b ) rs . 422 , c ) rs . 412 , d ) rs . 442 , e ) none of these
Rationale: "explanation : f = rs . 2260 td = rs . 360 pw = f - td = 2260 - 360 = rs . 1900 true discount is the simple interest on the present value for unexpired time = > simple interest on rs . 1900 for unexpired time = rs . 360 banker ' s discount is the simple interest on the face value of the bill for unexpired time = simple interest on rs . 2260 for unexpired time = 360 / 1900 × 2260 = 0.19 × 2260 = rs . 428 answer : option a"
Answer: a
Question (gain): in the first 20 overs of a cricket game , the run rate was only 4.8 . what should be the run rate in the remaining 30 overs to reach the target of 302 runs ?
Options: a ) 5 , b ) 6.25 , c ) 6.75 , d ) 6.87 , e ) 7.25
Rationale: required run rate = 302 - ( 4.8 x 20 ) / 30 = 206 / 30 = 6.87 option d
Answer: d
Question (physics): a trader sells 85 meters of cloth for rs . 8500 at the profit of rs . 15 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 80 , b ) rs . 85 , c ) rs . 90 , d ) rs . 95 , e ) none of these
Rationale: "sp of 1 m of cloth = 8500 / 85 = rs . 105 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 100 - rs . 15 = rs . 85 . answer : b"
Answer: b
Question (general): anne bought doughnuts for a class breakfast party . she bought 9 chocolate doughnuts , 7 coconut doughnuts , and 9 jam - filled doughnuts . how many doughnuts did anne buy in all ?
Options: a ) 25 , b ) 36 , c ) 39 , d ) 21 , e ) 11
Rationale: "add the numbers of doughnuts . 9 + 7 + 9 = 25 . answer is a ."
Answer: a
Question (geometry): the length of a rectangle i s two - fifths of the radius of a circle . the radius of the circle is equal to the side of the square , whose area is 1225 sq . units . what is the area ( in sq . units ) of the rectangle if the rectangle if the breadth is 10 units ?
Options: a ) 140 sq . units
b ) 149
c ) 148
d ) 17
e ) 143
Rationale: given that the area of the square = 1225 sq . units = > side of square = √ 1225 = 35 units the radius of the circle = side of the square = 35 units length of the rectangle = 2 / 5 * 35 = 14 units given that breadth = 10 units area of the rectangle = lb = 14 * 10 = 140 sq . units answer : option a
Answer: a
Question (physics): a cyclist bikes x distance at 8 miles per hour and returns over the same path at 10 miles per hour . what is the cyclist ' s average rate for the round trip in miles per hour ?
Options: a ) 8.1 , b ) 8.9 , c ) 8.6 , d ) 8.3 , e ) 9.0
Rationale: distance = d 1 = x miles speed = s 1 = 8 miles per hour time = t 1 = distance / speed = x / 8 2 . going from b to a distance = d 2 = x miles speed = s 2 = 10 miles per hour time = t 2 = distance / speed = x / 10 3 . average speed = total distance / total time total distance = x + x = 2 x total time = x / 10 + x / 8 = x ( 1 / 10 + 1 / 8 ) = = 9 x / 40 speed = 2 x / ( 9 x / 40 ) = 80 / 9 = 8.9 answer : b
Answer: b
Question (other): sandy is younger than molly by 6 years . if their ages are in the respective ratio of 7 : 9 , how old is molly ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 36 , e ) 45
Rationale: "s = m - 6 s / m = 7 / 9 9 s = 7 m 9 ( m - 6 ) = 7 m m = 27 the answer is c ."
Answer: c
Question (general): the average weight of 25 persons sitting in a boat had some value . a new person added to them whose weight was 46 kg only . due to his arrival , the average weight of all the persons decreased by 5 kg . find the average weight of first 25 persons ?
Options: a ) 55 kg , b ) 48 kg , c ) 52 kg , d ) none , e ) 55 kg
Rationale: "answer : option d 25 x + 46 = 26 ( x â € “ 5 ) x = 176"
Answer: d
Question (other): right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 38 years . what is molly ' s age right now ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: now , sandy is 38 - 6 = 32 molly ' s age is ( 3 / 4 ) * 32 = 24 the answer is d .
Answer: d
Question (physics): a hexagon is formed abcdef which perimeter 36 cm . a polygon is formed by joining the points ae & bd . find the area of the polygon abde ?
Options: a ) 34 √ 3 cm 2
b ) 35 √ 3 cm 2
c ) 36 √ 3 cm 2
d ) 37 √ 3 cm 2
e ) 38 √ 3 cm 2
Rationale: a regular hexagon consist of 6 equilateral triangle . each of side 6 cm . so the area of 1 equilateral triangle is = ¼ ( √ 3 a 2 ) = 9 √ 3 cm 2 the figure formed by joining polygon abde consist of 2 equilateral triangle and 4 half equilateral triangle which employs area of 4 equilateral triangle . so , the area of polygon abde = 4 * ( area of equilateral traingle ) = 4 * 9 √ 3 = 36 √ 3 cm 2 answer : c
Answer: c
Question (general): 10 , 1000 , 100000 , 10000000 . . . .
Options: a ) 100 , 000,000 , b ) 1,000 , 000,000 , c ) 1 , 000,000 , 000,000 , d ) 100 , e ) 1 , 000,000
Rationale: "each number in this sequence is multiplied by 100 . with multiples of ten , it is easiest to remember that you can just transfer all the zeroes on the end of the end of any number . example : 10 x 100 = 1,000 . add two digits to the end of 10 , 000,000 and you get 1,000 , 000,000 . answer is b"
Answer: b
Question (gain): an investor deposited $ 10,000 to open a new savings account that earned 12 percent annual interest , compounded quarterly . if there were no other transactions in the account , what was the amount of money in the account 6 months after the account was opened ?
Options: a ) $ 10,300 , b ) $ 10,303 , c ) $ 10,600 , d ) $ 10,609 , e ) $ 10,900
Rationale: "the amount in the account after 6 months is 1.03 * 1.03 ( $ 10,000 ) = $ 10,609 . the answer is d ."
Answer: d
Question (general): in a survey of parents , exactly 5 / 6 of the mothers and 3 / 4 of the fathers held full - time jobs . if 40 percent of the parents surveyed were women , what percent of the parents did not hold full - time jobs ?
Options: a ) 10 % , b ) 12 % , c ) 15 % , d ) 18 % , e ) 22 %
Rationale: "fathers without full - time jobs are 1 / 4 * 3 / 5 = 3 / 20 of all the parents surveyed . mothers without full - time jobs are 1 / 6 * 2 / 5 = 1 / 15 of all the parents surveyed . the percent of parents without full - time jobs is 3 / 20 + 1 / 15 = 13 / 60 which is about 22 % the answer is e ."
Answer: e
Question (general): a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 500 and $ 300 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 8
Rationale: "the smallest amount that the company can spend is the lcm of 500 and 300 , which is 1500 for each , which is total 3000 . the number of 1 st type of computers which costing $ 500 = 1500 / 500 = 3 . the number of 2 nd type of computers which costing $ 300 = 1500 / 300 = 3 . total = 3 + 3 = 6 answer is d ."
Answer: d
Question (general): 212 : 436 : : 560 : ?
Options: a ) 786 , b ) 682 , c ) 784 , d ) 688 , e ) 622
Rationale: "2 + 2 = 4 1 + 2 = 3 2 + 4 = 6 like that , 5 + 2 = 7 6 + 2 = 8 0 + 4 = 4 answer c"
Answer: c
Question (physics): circular gears p and q start rotating at the same time at constant speeds . gear p makes 10 revolutions per minute and gear q makes 40 revolutions per minute . how many seconds after the gears start rotating will gear q have made exactly 45 more revolutions than gear p ?
Options: a ) 45 , b ) 80 , c ) 90 , d ) 100 , e ) 120
Rationale: "gear q makes 30 more revolutions each 60 seconds . the time to make 45 = 30 * 1.5 more revolutions is 60 * 1.5 = 90 seconds . the answer is c ."
Answer: c
Question (general): for the symbol , m ” n = n ^ 2 − m for all values of m and n . what is the value of 6 ” 3 ?
Options: a ) 5 , b ) 3 , c ) 2 , d ) 1 , e ) 0
Rationale: 6 ” 3 = 9 - 6 = 3 answer : b
Answer: b
Question (geometry): the sides of a square region , measured to the nearest centimeter , are 4 centimeters long . the least possible value of the actual area of the square region is
Options: a ) 15.25 sq cm , b ) 18.25 sq cm , c ) 12.25 sq cm , d ) 21.25 sq cm , e ) 25.25 sq cm
Rationale: "though there might be some technicalities concerning the termnearest ( as 3.5 is equidistant from both 3 and 4 ) the answer still should be : 3.5 ^ 2 = 12.25 . answer : c"
Answer: c
Question (gain): what sum of money will produce rs . 80 as simple interest in 4 years at 3 1 / 2 percent ?
Options: a ) 263 , b ) 571.4 , c ) 367 , d ) 368 , e ) 339
Rationale: "80 = ( p * 4 * 7 / 2 ) / 100 p = 571.4 answer : b"
Answer: b
Question (general): two - third of a positive number and 144 / 216 of its reciprocal are equal . the number is :
Options: a ) 5 / 12 , b ) 12 / 5 , c ) 25 / 144 , d ) 144 / 25 , e ) 1
Rationale: "let the number be x . then , 2 / 3 x = 144 / 216 * 1 / x x 2 = 144 / 216 * 3 / 2 = 144 / 144 x = 1 answer : e"
Answer: e
Question (other): from a container having pure milk , 20 % is replaced by water and the process is repeated thrice . at the end of the third operation , the milk is ?
Options: a ) 45 % , b ) 49.6 % , c ) 51.2 % , d ) 55 % , e ) 60.3 %
Rationale: let the total quantity of original milk = 1000 gm milk after 1 st operation = 80 % of 1000 = 800 gm milk after second operation = 80 % of 800 = 640 gm milk after third operation = 80 % of 640 = 512 gm strength of final mixture = 51.2 % answer is c
Answer: c
Question (general): after 6 games , team b had an average of 70 points per game . if it got only 47 points in game 7 , how many more points does it need to score to get its total above 500 ?
Options: a ) 85 , b ) 74 , c ) 67 , d ) 33 , e ) 28
Rationale: "( 6 * 70 ) + 47 + x > 500 420 + 47 + x > 500 467 + x > 500 = > x > 33 option d"
Answer: d
Question (general): if a ' s height is 40 % less than that of b , how much percent b ' s height is more than that of a ?
Options: a ) 66.66 % , b ) 66.68 % , c ) 66.766 % , d ) 86.66 % , e ) 66.65 %
Rationale: "excess of b ' s height over a ' s = [ ( 40 / ( 100 - 40 ) ] x 100 % = 66.66 % answer : a ) 66.66 %"
Answer: a
Question (gain): how long will a boy take to run round a square field of side 35 meters , if he runs at the rate of 9 km / hr ?
Options: a ) 22 , b ) 38 , c ) 37 , d ) 56 , e ) 28
Rationale: answer : d ) 56 sec
Answer: d
Question (gain): a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 40 to incur a loss 20 % ?
Options: a ) 20 , b ) 36 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 40 * ( 100 % + 20 % ) = $ 48 number of articles to be sold for $ 48 to incur a 20 % loss : $ 48 / $ 2.40 = 20 thus , solution a is correct ."
Answer: a