Cheukting/mathqa huggingface dataset:
Question (physics): a person travels equal distances with speeds of 3 km / hr , 4 km / hr , 5 km / hr . and takes a total time of 47 minutes . find the total distance ?
Options: a ) 3 , b ) 2 , c ) 5 , d ) 4 , e ) 6
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 3 ) + ( x / 4 ) + ( x / 5 ) = 47 / 60 x = 1 total distance = 3 * 1 = 3 km correct option is a"
Answer: a
Question (general): the product of a and b is equal to 11 more than twice the sum of a and b . if b = 5 , what is the value of b - a ?
Options: a ) - 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35
Rationale: "ab = 11 + 2 ( a + b ) 5 a = 11 + 2 a + 10 3 a = 21 a = 7 b - a = 5 - 7 = - 2 a is the answer"
Answer: a
Question (gain): in town x , 64 percent of the population are employed , and 48 percent of the population are employed males . what percent of the employed people in town x are females ?
Options: a ) 16 % , b ) 25 % , c ) 32 % , d ) 40 % , e ) 52 %
Rationale: "let population be 100 total employed people = 64 % of the population = 64 employed males = 48 % of the population = 48 employed females = 16 % of the population = 16 employed females % in terms of employed people = ( 16 / 64 ) * 100 = 25 % answer is b ."
Answer: b
Question (general): if s is a positive integer , and if the units ' digit of s ^ 2 is 4 and the units ' digit of ( s + 1 ) ^ 2 is 1 , what is the units ' digit of ( s + 2 ) ^ 2 ?
Options: a ) 0 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: a for me . _ 1 ² = _ 1 _ 2 ² = _ 4 _ 3 ² = _ 9 _ 4 ² = _ 6 _ 5 ² = _ 5 _ 6 ² = _ 6 _ 7 ² = _ 9 _ 8 ² = _ 4 _ 9 ² = _ 1 _ 0 ² = _ 0 on the list , the only number that squared has the units digit = 4 preceding a number that squared has the units digit = 1 is the _ 8 . so , s = _ 8 , that has square 4 . the next square is 1 andnext nextsquare is 0 .
Answer: a
Question (other): in a group of 65 people , 40 like cricket , 10 like both cricket and tennis . how many like tennis ?
Options: a ) 30 , b ) 35 , c ) 40 , d ) 45 , e ) 50
Rationale: "make a venn diagram , and enter your data . let the number of people who like only tennis be x x + 10 + 30 = 65 x = 25 so number who like tennis = 10 + 25 = 35 answer b"
Answer: b
Question (general): the arithmetic mean and standard deviation of a certain normal distribution are 14.0 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: "the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 14.0 - 2 * 1.5 = 11 . answer : b ."
Answer: b
Question (general): if a * b denotes the greatest common divisor of a and b , then ( ( 16 * 20 ) * ( 18 * 24 ) ) = ?
Options: a ) 24 , b ) 12 , c ) 6 , d ) 4 , e ) 2
Rationale: the greatest common divisor of 16 and 20 is 4 . hence 16 * 20 = 4 ( note that * here denotes the function not multiplication ) . the greatest common divisor of 18 and 24 is 6 . hence 18 * 24 = 6 . hence ( ( 16 * 20 ) * ( 18 * 24 ) ) = 4 * 6 . the greatest common divisor of 4 and 6 is 2 . answer ; e .
Answer: e
Question (general): the average weight of a group of boys is 30 kg . after a boy of weight 39 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 ) a ) 4 , b ) b ) 8 , c ) c ) 6 , d ) d ) 2 , e ) e ) 1
Rationale: "let the number off boys in the group originally be x . total weight of the boys = 30 x after the boy weighing 39 kg joins the group , total weight of boys = 30 x + 39 so 30 x + 39 = 31 ( x + 1 ) = > x = 8 . answer : b"
Answer: b
Question (gain): by selling a book for 260 , 20 % profit was earned . what is the cost price of the book ?
Options: a ) a ) 215 , b ) b ) 216 , c ) c ) 230 , d ) d ) 235 , e ) e ) 240
Rationale: "sp = 120 % of cp ; : . cp = 260 × 100 / 120 = 216 option ' b '"
Answer: b
Question (physics): a man sitting in a train which is traveling at 60 kmph observes that a goods train , traveling in opposite direction , takes 12 seconds to pass him . if the goods train is 300 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 30 kmph , e ) 34 kmph
Rationale: "explanation : relative speed = 300 / 12 m / sec = ( ( 300 / 12 ) × ( 18 / 5 ) ) kmph = 90 kmph . speed of goods train = ( 90 - 60 ) kmph = 30 kmph answer : option d"
Answer: d
Question (gain): solution p is 20 percent lemonade and 80 percent carbonated water by volume ; solution q is 45 percent lemonade and 55 percent carbonated water by volume . if a mixture of pq contains 65 percent carbonated water , what percent of the volume of the mixture is p ?
Options: a ) 20 % , b ) 40 % , c ) 50 % , d ) 60 % , e ) 80 %
Rationale: "65 % is 15 % - points below 80 % and 10 % - points above 55 % . so the ratio of solution p to solution q is 2 : 3 . mixture p is 2 / 5 = 40 % of the volume of mixture pq . the answer is b ."
Answer: b
Question (general): in a class of 40 students , 2 students did not borrow any books from the library , 12 students each borrowed 1 book , 12 students each borrowed 2 books , and the rest borrowed at least 3 books . if the average number of books per student was 2 , what is the maximum number of books any single student could have borrowed ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the class borrowed a total of 40 * 2 = 80 books . the 26 students who borrowed 0 , 1 , or 2 books borrowed a total of 12 + 12 * 2 = 36 . to maximize the number of books borrowed by 1 student , let ' s assume that 13 students borrowed 3 books and 1 student borrowed the rest . 80 - 36 - 3 * 13 = 5 the maximum number of books borrowed by any student is 5 . the answer is c ."
Answer: c
Question (gain): shop offered 40 % offer for every shirt , smith bought a shirt at rs . 560 . and what was the shop ' s original selling price ?
Options: a ) 500 , b ) 550 , c ) 600 , d ) 933 , e ) 750
Rationale: "sp * ( 60 / 100 ) = 560 sp = 9.33 * 100 = > cp = 933 answer : d"
Answer: d
Question (general): the average score of a cricketer for 12 matches is 48 runs . if the average for first 8 matches is 40 , then average for last 4 matches is
Options: a ) 33.25 , b ) 89 , c ) 64 , d ) 68 , e ) 90
Rationale: explanation : = ( 48 × 12 ) − ( 40 × 8 ) / 4 = ( 576 − 320 ) / 4 = 64 answer : option c
Answer: c
Question (general): the average of 40 results is 30 and the average of other 30 results is 40 . what is the average of all the results ?
Options: a ) 34 , b ) 25 , c ) 48 , d ) 50 , e ) none
Rationale: answer sum of 70 result = sum of 40 result + sum of 30 result . = 40 x 30 + 30 x 40 = 2400 / 70 correct option : a
Answer: a
Question (gain): a candidate got 35 % of the votes polled and he lost to his rival by 2340 votes . how many votes were cast ?
Options: a ) 7500 , b ) 3388 , c ) 2665 , d ) 7800 , e ) 2661
Rationale: "35 % - - - - - - - - - - - l 65 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 30 % - - - - - - - - - - 2340 100 % - - - - - - - - - ? = > 7800 answer : d"
Answer: d
Question (gain): a and b started a business in partnership investing rs . 20,000 and rs . 15,000 respectively . after 6 months , c joined them with rs . 20,000 . whatwill be b ' s share in total profit of rs . 25,000 earned at the end of 2 years from the startingof the business ?
Options: a ) rs . 5,000 , b ) rs . 5,500 , c ) rs . 5,700 , d ) rs . 6,500 , e ) rs . 7,500
Rationale: "a : b : c = ( 20,000 x 24 ) : ( 15,000 x 24 ) : ( 20,000 x 18 ) = 4 : 3 : 3 . b ' s share = rs . 25000 x 3 / 10 = rs . 7,500 . e"
Answer: e
Question (general): in a box of 12 pens , a total of 4 are defective . if a customer buys 2 pens selected at random from the box , what is the probability that neither pen will be defective ?
Options: a ) 1 / 6 , b ) 2 / 33 , c ) 14 / 33 , d ) 9 / 16 , e ) 3 / 44
Rationale: "method - 1 there are 9 fine pieces of pen and 4 defective in a lot of 12 pens i . e . probability of first pen not being defective = ( 8 / 12 ) i . e . probability of second pen not being defective = ( 7 / 11 ) [ 11 pen remaining with 8 defective remaining considering that first was defective ] probability of both pen being non - defective = ( 8 / 12 ) * ( 7 / 11 ) = 14 / 33 answer : option c"
Answer: c
Question (gain): a bowl was filled with 10 ounces of water , and 0.007 ounce of the water evaporated each day during a 50 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.004 % , b ) 0.04 % , c ) 0.40 % , d ) 4 % , e ) 3.5 %
Rationale: "total amount of water evaporated each day during a 50 - day period = . 007 * 50 = . 007 * 100 / 2 = . 7 / 2 = . 35 percent of the original amount of water evaporated during this period = ( . 35 / 10 ) * 100 % = 3.5 % answer e"
Answer: e
Question (general): the price of a certain painting increased by 30 % during the first year and decreased by 20 % during the second year . the price of the painting at the end of the 2 - year period was what percent of the original price ?
Options: a ) 102 % , b ) 105 % , c ) 120 % , d ) 135 % , e ) 104 %
Rationale: "easiest thing to do : assume that price is 100 price at the end of yr 1 : 100 + 30 = 130 price at the end of year 2 = 130 - 130 * 0.20 = 130 * 0.80 = 104 hence required answer = ( 104 / 100 ) * 100 % = 104 % answer is e ."
Answer: e
Question (other): the least whole number which when subtracted from both the terms of the ratio 6 : 7 to give a ra ɵ o less than 16 : 21 , is
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: explanation : let x is subtracted . then , ( 6 − x ) ( 7 − x ) < 162121 ( 6 � x ) < 16 ( 7 � x ) = > 5 x > 14 = x > 2.8 least such number is 3 answer : a
Answer: a
Question (physics): in what time will a train 134 m long cross an electric pole , it its speed be 169 km / hr ?
Options: a ) 2.5 , b ) 2.7 , c ) 2.9 , d ) 2.3 , e ) 2.1
Rationale: "speed = 169 * 5 / 18 = 46.9 m / sec time taken = 134 / 46.9 = 2.9 sec . answer : c"
Answer: c
Question (physics): a train 75 m long passes a man , running at 5 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 28 , b ) 50 , c ) 88 , d ) 22 , e ) 32
Rationale: "speed of the train relative to man = ( 75 / 10 ) m / sec = ( 15 / 2 ) m / sec . [ ( 15 / 2 ) * ( 18 / 5 ) ] km / hr = 27 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 5 ) km / hr . x - 5 = 27 = = > x = 32 km / hr . answer : e"
Answer: e
Question (physics): a train 200 m long crosses a platform 150 m long in 20 sec ; find the speed of the train ?
Options: a ) 73 , b ) 63 , c ) 65 , d ) 70 , e ) 83
Rationale: "d = 200 + 150 = 350 t = 20 s = 350 / 20 * 18 / 5 = 63 kmph . answer : b"
Answer: b
Question (general): if ( 5 ^ 13 ) ( 9 ^ 7 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: ( 5 ^ 13 ) ( 9 ^ 7 ) = 3 ( 15 ^ x ) = > 5 ^ 13 * 3 ^ 14 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 13 * 3 ^ 14 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 13 answer d
Answer: d
Question (physics): in one hour , a boat goes 19 km / hr along the stream and 11 km / hr against the stream . the speed of the boat in still water ( in km / hr ) is :
Options: a ) 12 kmph , b ) 13 kmph , c ) 14 kmph , d ) 15 kmph , e ) 16 kmph
Rationale: "explanation : let the speed downstream be a km / hr and the speed upstream be b km / hr , then speed in still water = 1 / 2 ( a + b ) km / hr rate of stream = 1 / 2 ( a − b ) km / hr speed in still water = 1 / 2 ( 19 + 11 ) kmph = 15 kmph . answer : option d"
Answer: d
Question (probability): a , b , c , d , e , f , g , h sitting in a row what is the probability that a , b , d are sitting together ?
Options: a ) 1 / 5 , b ) 3 / 28 , c ) 1 / 7 , d ) 1 / 14 , e ) 5 / 28
Rationale: "total number of arrangement is = 8 ! = 40320 favorable event i . e a , b and d can be arranged in 3 ! and the remaining can be arranged in 6 ! since abd can be in any of the six positions . so 3 ! * 6 ! / 8 ! = 3 / 28 answer : b"
Answer: b
Question (general): the divisor is 21 , the quotient is 14 and the remainder is 7 . what is the dividend ?
Options: a ) 201 , b ) 394 , c ) 302 , d ) 301 , e ) 294
Rationale: d = d * q + r d = 21 * 14 + 7 d = 294 + 7 d = 301
Answer: d
Question (physics): tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 6 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4 mph , e ) 0.5 mph
Rationale: "( 1 mph + 6 mph ) / 2 = 3.5 mph correct option is : c"
Answer: c
Question (gain): what annual payment will discharge a debt of rs . 1050 due in 2 years at the rate of 5 % compound interest ?
Options: a ) 993.2 , b ) 551.25 , c ) 534.33 , d ) 543.33 , e ) 564.69
Rationale: "explanation : let each installment be rs . x . then , x / ( 1 + 5 / 100 ) + x / ( 1 + 5 / 100 ) 2 = 1050 820 x + 1050 * 441 x = 564.69 so , value of each installment = rs . 564.69 answer : option e"
Answer: e
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 880 grams per kg , what is his percent ?
Options: a ) 15 % , b ) 13.6 % , c ) 65 % , d ) 45 % , e ) 35 %
Rationale: "explanation : 880 - - - 120 100 - - - ? = > 13.6 % answer : b"
Answer: b
Question (general): the number of positive integer solutions for the equation x + y + z + t = 21 is
Options: a ) 1140 , b ) 1145 , c ) 1240 , d ) 1340 , e ) 15640
Rationale: "the number of positive integer solutions for the equatio fx 1 + x 2 + ⋯ + xn = k ( k - 1 ) c ( n - 1 ) - where k is the number and n is number of variable in the equation . 21 - 1 c 4 - 1 = 20 c 3 = 1140 answer : a"
Answer: a
Question (gain): a shopkeeper buys mangoes at the rate of 6 a rupee and sells them at 5 a rupee . find his net profit or loss percent ?
Options: a ) 34 % , b ) 33 % , c ) 20 % , d ) 35 % , e ) 30 %
Rationale: "the total number of mangoes bought by the shopkeeper be 30 . if he buys 6 a rupee , his cp = 5 he selling at 5 a rupee , his sp = 6 profit = sp - cp = 6 - 5 = 1 profit percent = 1 / 5 * 100 = 20 % answer : c"
Answer: c
Question (gain): machine p and machine q are each used to manufacture 330 sprockets . it takes machine p 10 hours longer to produce 330 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 3 , d ) 95 , e ) 125
Rationale: "p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 330 / x = 330 / 1.1 x + 10 1.1 ( 330 ) = 330 + 11 x 11 x = 33 x = 3 the answer is c ."
Answer: c
Question (general): at veridux corporation , there are 250 employees . of these , 90 are female , and the rest are males . there are a total of 40 managers , and the rest of the employees are associates . if there are a total of 160 male associates , how many female managers are there ?
Options: a ) 40 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: 250 employees : 90 male , 160 female 40 managers , 210 associates 160 male associates implies 50 female associates which means the remaining 40 females must be managers a . 40
Answer: a
Question (general): think of a number , divide it by 5 and add 8 to it . the result is 61 . what is the number thought of ?
Options: a ) 24 , b ) 77 , c ) 297 , d ) 265 , e ) 29
Rationale: "explanation : 61 - 6 = 53 53 x 5 = 265 answer : d"
Answer: d
Question (other): the ratio by weight , measured in pounds , of books to clothes to electronics in a suitcase initially stands at 7 : 4 : 3 . someone removes 8 pounds of clothing from the suitcase , thereby doubling the ratio of books to clothes . how many pounds do the electronics in the suitcase weigh ?
Options: a ) 6 , b ) 8 , c ) 10 , d ) 12 , e ) 14
Rationale: the weights of the items in the suitcase are 7 k , 4 k , and 3 k . if removing 8 pounds of clothes doubles the ratio of books to clothes , then 8 pounds represents half the weight of the clothes . 2 k = 8 pounds and then k = 4 pounds . the electronics weigh 3 ( 4 ) = 12 pounds . the answer is d .
Answer: d
Question (physics): the radius of a semi circle is 2.1 cm then its perimeter is ?
Options: a ) 32.5 , b ) 11.12 , c ) 32.1 , d ) 10.8 , e ) 32.3
Rationale: "36 / 7 r = 2.1 = 10.80 answer : d"
Answer: d
Question (geometry): the dimensions of a rectangular solid are 4 inches , 5 inches , and 10 inches . if a cube , a side of which is equal to one of the dimensions of the rectangular solid , is placed entirely within thespherejust large enough to hold the cube , what the ratio of the volume of the cube to the volume within thespherethat is not occupied by the cube ?
Options: a ) 10 : 17 , b ) 2 : 5 , c ) 10 : 19 , d ) 25 : 7 , e ) 32 : 25
Rationale: answer : c .
Answer: c
Question (general): which number should replace both the asterisks in ( * / 21 ) x ( * / 189 ) = 1 ?
Options: a ) 21 , b ) 63 , c ) 3969 , d ) 147 , e ) 167
Rationale: "answer let ( y / 21 ) x ( y / 189 ) = 1 then , y 2 = 21 x 189 = 21 x 21 x 9 ∴ y = ( 21 x 3 ) = 63 . option : b"
Answer: b
Question (gain): a tank contains 10,000 gallons of a solution that is 6 percent sodium chloride by volume . if 6,000 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 15 %
Rationale: "the remaining solution will be approximately what percent sodium chloride ? means : what percent of the remaining solution is sodium chloride . now , since the remaining solution is 10,000 - 6,000 = 4,000 gallons and sodium chloride is 600 gallons ( 6 % of initial solution of 10,000 gallons ) then sodium chloride is 600 / 4,000 * 100 = 15 % of the remaining solution of 4,000 gallons . answer : e ."
Answer: e
Question (physics): two pipes a and b can fill a cistern in 12 and 20 minutes respectively , and a third pipe c can empty it in 30 minutes . how long will it take to fill the cistern if all the three are opened at the same time ?
Options: a ) 15 min , b ) 13 min , c ) 12 min , d ) 10 min , e ) 17 min
Rationale: "1 / 12 + 1 / 20 - 1 / 30 = 1 / 10 10 / 1 = 10 answer : d"
Answer: d
Question (gain): two tests had the same maximum mark . the pass percentages in the first and the second test were 40 % and 45 % respectively . a candidate scored 231 marks in the second test and failed by 48 marks in that test . find the pass mark in the first test ?
Options: a ) 768 , b ) 243 , c ) 246 , d ) 625 , e ) 248
Rationale: "let the maximum mark in each test be m . the candidate failed by 48 marks in the second test . pass mark in the second test = 231 + 48 = 279 45 / 100 m = 279 pass mark in the first test = 40 / 100 m = 40 / 45 * 279 = 248 . answer : e"
Answer: e
Question (physics): trains a and b start simultaneously from stations 200 miles apart , and travel the same route toward each other on adjacent parallel tracks . if train a and train b travel at a constant rate of 20 miles per hour and 20 miles per hour , respectively , how many miles will train a have traveled when the trains pass each other , to the nearest mile ?
Options: a ) 100 , b ) 133 , c ) 150 , d ) 167 , e ) 188
Rationale: "since we know the distance ( 200 ) and the combined rate ( 40 ) , we plug it into the formula : distance = rate * time 200 = 40 * time we can solve for the time they will meet cause we added the rate of train a and train b together . so the time will be 200 / 40 from dividing 40 on both sides to isolate time in the equation above . time will be 5 hours so now you can plug that in for train a ’ s distance . distance = rate * time distance = 20 * 5 distance = 100 according to answer choice a ."
Answer: a
Question (general): x = 13.165 y = 7.686 z = 11.545 the number a is obtained by first rounding the values of x , y , and z to the hundredths place and then adding the resulting values . the number b is obtained by first adding the values of x , y , and z and then rounding the sum to the hundredths place . what is the value of a – b ?
Options: a ) 0.01 , b ) 0.02 , c ) 0.03 , d ) 0.1 , e ) 0.2
Rationale: rounding off the values : x = 13.17 y = 7.69 z = 11.55 a = 13.17 + 7.69 + 11.55 = 32.41 x + y + z = 13.165 + 7.686 + 11.545 = 32.206 b = 32.21 a - b = 0.2 option e
Answer: e
Question (geometry): the area of a square is 144 m ² . find its perimeter .
Options: a ) 18 m
b ) 28 m
c ) 38 m
d ) 42 m
e ) 48 m
Rationale: area of square = side × side given ; area of square = 144 m ² therefore , side ² = 144 m ² therefore , side = √ ( 144 m ² ) = √ ( 2 × 2 × 2 × 2 × 3 × 3 ) m ² = 2 × 2 × 3 m = 12 m now , the perimeter of the square = 4 x side = 4 × 12 m = 48 m answer : e
Answer: e
Question (gain): how is 1 % expressed as a decimal fraction ?
Options: a ) 0.1 , b ) 0.001 , c ) 0.01 , d ) 0.0001 , e ) 1
Rationale: "1 / 100 = 0.01 answer : c"
Answer: c
Question (general): salesperson a ' s compensation for any week is $ 350 plus 6 percent of the portion of a ' s total sales above $ 1,000 for that week . salesperson b ' s compensation for any week is 8 percent of a ' s total sales for that week . for what amount of total weekly sales would both salepeople earn the same compensation ?
Options: a ) $ 21,000 , b ) $ 18,000 , c ) $ 15,000 , d ) $ 14,500 , e ) $ 4,000
Rationale: "sometime , setting up an equation is an easy way to go with : 350 + 0.06 ( x - 1000 ) = 0.08 x x = 14,500 ans : d"
Answer: d
Question (general): a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2430 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 820 , d ) s . 900 , e ) s . 920
Rationale: "2430 * 1 / 3 = 810 option b"
Answer: b
Question (physics): a person walks at a speed of 4 km / hr and runs at a speed of 8 km / hr . how many hours will the person require to cover a distance of 8 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 0.5 , b ) 1.5 , c ) 2.5 , d ) 3.5 , e ) 4.5
Rationale: "time = 4 / 4 + 4 / 8 = 12 / 8 = 1.5 hours the answer is b ."
Answer: b
Question (general): dacid obtained 45 , 35 , 52 , 47 and 55 marks ( out of 100 ) in english , mathematics , physics , chemistry and biology . what are his average marks ?
Options: a ) 79 , b ) 99 , c ) 47 , d ) 89 , e ) 45
Rationale: average = ( 45 + 35 + 52 + 47 + 55 ) / 5 = 234 / 5 = 47 . answer : c
Answer: c
Question (geometry): if anangletis defined as 1 percent of 1 degree , then how many anglets are there in a quarter circle ?
Options: a ) 0.36 , b ) 3.6 , c ) 9000 , d ) 3,600 , e ) 36,000
Rationale: "1 degree * 1 / 100 = 1 anglet so 1 degree = 100 anglets = > 90 degrees = 9000 anglets answer - c"
Answer: c
Question (general): the product of a and b is equal to 10 more than twice the sum of a and b . if b = 9 , what is the value of b - a ?
Options: a ) 2 , b ) 5 , c ) 7 , d ) 24 , e ) 35
Rationale: "ab = 10 + 2 ( a + b ) 9 a = 10 + 2 a + 18 7 a = 28 a = 4 b - a = 9 - 4 = 5 b is the answer"
Answer: b
Question (general): how many times digit 2 is used while writing numbers from 400 to 700 ?
Options: a ) 150 , b ) 190 , c ) 250 , d ) 80 , e ) 130
Rationale: "in 400 to 500 there are 50 two ' s in 500 to 600 there are 50 two ' s in 600 to 700 there are 50 two ' s so total is 150 two ' s correct option : a"
Answer: a
Question (physics): lionel left his house and walked towards walt ' s house , 48 miles away . two hours later , walt left his house and ran towards lionel ' s house . if lionel ' s speed was 2 miles per hour and walt ' s 6 miles per hour , how many miles had lionel walked when he met walt ?
Options: a ) 12 , b ) 15 , c ) 20 , d ) 24 , e ) 28
Rationale: in the first 2 hours lionel at the rate of 2 miles per hour covered distance = rate * time = 2 * 2 = 4 miles . so , the distance between him and walt was 48 - 4 = 44 miles when walt left his house . now , their combined rate to cover this distance was 2 + 6 = 8 miles per hour , hence they will meet ( they will cover that distance ) in time = distance / rate = 44 / 8 = 5.5 hours . total time that lionel was walking is 2 + 5.5 = 7.5 hours , which means that he covered in that time interval distance = rate * time = 2 * 7.5 = 15 miles . answer : b .
Answer: b