Cheukting/mathqa huggingface dataset:
Question (general): a sum of money is to be divided among ann , bob and chloe . first , ann receives $ 4 plus one - half of what remains . next , bob receives $ 4 plus one - third of what remains . finally , chloe receives the remaining $ 32 . how much money n did bob receive ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 52
Rationale: "notice that we need not consider ann ' s portion in the solution . we can just let k = the money remaining after ann has received her portion and go from there . our equation will use the fact that , once we remove bob ' s portion , we have $ 32 for chloe . so , we getk - bob ' s $ = 32 bob received 4 dollars plus one - third of what remained once bob receives $ 4 , the amount remaining is k - 4 dollars . so , bob gets a 1 / 3 of that as well . 1 / 3 of k - 4 is ( k - 4 ) / 3 so altogether , bob receives 4 + ( k - 4 ) / 3 so , our equation becomes : k - [ 4 + ( k - 4 ) / 3 ] = 32 simplify to get : k - 4 - ( k - 4 ) / 3 = 32 multiply both sides by 3 to get : 3 k - 12 - k + 4 = 96 simplify : 2 k - 8 = 96 solve : k = 52 plug this k - value intok - bob ' s $ = 32 to get : 52 - bob ' s $ = 32 so , bob ' s $ n = 20 answer : b"
Answer: b
Question (physics): two trains leave a station traveling the same direction . train a leaves the station traveling at a constant speed of 60 mph , and train b leaves the station traveling at a constant speed of 80 mph . if both trains maintain constant speeds , in how many minutes will train b overtake train a if train a left 40 minutes prior to train b ?
Options: a ) 90 , b ) 100 , c ) 110 , d ) 120 , e ) 130
Rationale: we can use d = rt [ distance = rate * time ] train a will have traveled for 40 minutes longer than train b when b overtakes a , so time of train a : t + 40 minutes = t + ( 2 / 3 ) hours ( use hours since the rate is in hours ) time of train b : t rate of train a : 60 mph rate of train b : 80 mph the distances traveled by each will be equal when train b overtakes train a , so we can set the right sides of d = rt equal for the two trains ( rate of train a ) * ( time of train a ) = ( rate of train b ) * ( time of train b ) 60 * ( t + 2 / 3 ) = 80 * t 60 t + 40 = 80 t 40 = 20 t 2 = t 2 hours = 120 minutes d
Answer: d
Question (general): if the average of 5 positive integers is 50 and the difference between the largest and the smallest of these 5 numbers is 10 , what is the maximum value possible for the largest of these 5 integers ?
Options: a ) 50 , b ) 58 , c ) 49 , d ) 48 , e ) 44
Rationale: sum of 5 integer ( a , b , c , d , e ) = 5 * 50 = 250 e - a = 10 i . e . e = a + 10 for e to be maximum remaining 4 must be as small as possible since smallest of 5 numbers is a so to minimize other numbers we can take them equal to the smallest of 5 numbers i . e . a + a + a + a + ( a + 10 ) = 250 i . e . 5 a = 240 i . e . a = 48 i . e . largest e = 48 + 10 = 58 answer : option b
Answer: b
Question (general): what is the smallest number which , when increased by 7 , is divisible by 8 , 11 , and 24 ?
Options: a ) 264 , b ) 257 , c ) 269 , d ) 270 , e ) 282
Rationale: "lcm ( 8 , 11,24 ) = 24 x 11 = 264 so the least divisible number is 264 , and the number we are looking for is 264 - 7 = 257 . the answer is b ."
Answer: b
Question (other): in a college the ratio of the numbers of boys to the girls is 8 : 5 . if there are 210 girls , the total number of students in the college is ?
Options: a ) 562 , b ) 356 , c ) 452 , d ) 416 , e ) 546
Rationale: "let the number of boys and girls be 8 x and 5 x then , 5 x = 210 x = 42 total number of students = 13 x = 13 * 42 = 546 answer is e"
Answer: e
Question (general): the grade point average of one third of the classroom is 15 ; the grade point average of the rest is 18 . what is the grade point average of the whole class ?
Options: a ) 17 , b ) 19 , c ) 21 , d ) 23 , e ) 25
Rationale: "let n = total students in class total points for 1 / 3 class = 15 n / 3 = 5 n total points for 2 / 3 class = 18 * 2 n / 3 = 12 n total points for whole class = 5 n + 12 n = 17 n 17 n total class points / n total students = 17 grade point average for total class answer : a"
Answer: a
Question (general): arjun started a business with rs . 10,000 and is joined afterwards by anoop with rs . 40 , 000 . after how many months did anoop join if the profits at the end of the year are divided equally ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "suppose anoop joined after 3 months . then , 10000 * 12 = 40000 * ( 12 – x ) = > x = 9 . answer : e"
Answer: e
Question (general): if the operation @ is defined for all a and b by the equation a @ b = ( a - b ) / 5 , then ( 3 @ - 2 ) @ 6 = ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) - 2 , e ) - 1
Rationale: work within the parenthesis first so solve ( 3 @ - 2 ) first ( 3 @ - 2 ) = ( 3 - ( - 2 ) ) / 5 = ( 3 + 2 ) / 5 = 1 now take 1 plug back into equation and solve the rest ( 1 @ 6 ) = ( 1 - 6 ) / 5 = - 5 / 5 = - 1 so - 1 is the answer . . . . this question is merely testing order of operations remember pemdas answer is option : e
Answer: e
Question (general): what is the ratio of 5 / 7 to the product 3 * ( 7 / 3 ) ?
Options: a ) 3 : 7 , b ) 1 : 3 , c ) 5 : 49 , d ) 1 : 7 , e ) 3 : 49
Rationale: "3 / 7 / 21 / 3 = 5 / 49 . . . imo option c ."
Answer: c
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 250 m long platform in 15 sec . what is the length of the goods train ?
Options: a ) 299 , b ) 277 , c ) 276 , d ) 270 , e ) 50
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 15 sec . let the length of the train be x meters . then , ( x + 250 ) / 15 = 20 x = 50 m . answer : e"
Answer: e
Question (physics): a goods train runs at the speed of 72 km / hr and crosses a 290 m long platform in 26 sec . what is the length of the goods train ?
Options: a ) 278 , b ) 166 , c ) 151 , d ) 230 , e ) 109
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . time = 26 sec . let the length of the train be x meters . then , ( x + 290 ) / 26 = 20 x = 230 m . answer : d"
Answer: d
Question (general): the contents of a certain box consist of 24 oranges and 30 kiwis . how many kiwis must be added to the box so that exactly 30 % of the pieces of fruit in the box will be oranges ?
Options: a ) 24 , b ) 26 , c ) 30 , d ) 46 , e ) 50
Rationale: oranges = ( oranges + kiwi + x ) * 0.3 24 = ( 30 + 24 + x ) * 0.3 x = 26 . answer : b .
Answer: b
Question (general): if s is the sum of reciprocals of a list of consecutive integers from 55 to 64 , inclusive , s is approximately equal to
Options: a ) 0.16 , b ) 0.2 , c ) 0.3 , d ) 0.4 , e ) 0.5
Rationale: we need to find the approximate value of 1 / 55 + 1 / 56 + 1 / 57 + 1 / 58 + 1 / 59 + 1 / 60 + 1 / 61 + 1 / 62 + 1 / 63 + 1 / 64 . now , the sum of these 10 terms will be very close to 10 times 1 / 60 , which is 0.016 * 10 = 0.16 . answer : a .
Answer: a
Question (physics): the sector of a circle has radius of 28 cm and central angle 135 o . find its perimeter ?
Options: a ) 122 cm , b ) 92.2 cm , c ) 28.9 cm , d ) 29.2 cm , e ) 98.2 cm
Rationale: "perimeter of the sector = length of the arc + 2 ( radius ) = ( 135 / 360 * 2 * 22 / 7 * 28 ) + 2 ( 28 ) = 66 + 56 = 122 cm answer : a"
Answer: a
Question (physics): a swimmer swims downstream 55 km and upstream 10 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 4.6 , b ) 4.5 , c ) 4.4 , d ) 4.3 , e ) 4.2
Rationale: 55 - - - 5 ds = 11 ? - - - - 1 10 - - - - 5 us = 2 ? - - - - 1 s = ? s = ( 11 - 2 ) / 2 = 4.5 answer : b
Answer: b
Question (general): what is the sum of the greatest common factor and the lowest common multiple of 16 and 72 ?
Options: a ) 142 , b ) 152 , c ) 124 , d ) 160 , e ) 184
Rationale: "prime factorization of 16 = 2 x 2 x 2 x 2 . prime factorization of 72 = 2 x 2 x 2 x 3 x 3 gcf = 8 lcm = 144 sum = 152 . answer b ."
Answer: b
Question (physics): a is half good a work man as b and together they finish a job in 13 days . in how many days working alone b finish the job ?
Options: a ) 23 , b ) 22 , c ) 39 / 2 , d ) 36 , e ) 48
Rationale: c 39 / 2 wc = 1 : 2 2 x + x = 1 / 13 = > x = 1 / 39 2 x = 2 / 39 = > 39 / 2 days
Answer: c
Question (physics): 33 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 11 , c ) 13 , d ) 18 , e ) 19
Rationale: let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 33 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 33 x 5 x 12 x = ( 33 x 5 x 12 ) / ( 30 x 6 ) x = 11 answer b
Answer: b
Question (geometry): the diagonal of a rectangle is √ 41 cm and its area is 20 sq . cm . the perimeter of the rectangle must be :
Options: a ) 18
b ) 28
c ) 38
d ) 48
e ) 58
Rationale: explanation : l 2 + b 2 = 41 also , lb = 20 ( l + b ) 2 = l 2 + b 2 + 2 lb = 41 + 40 = 81 ( l + b ) = 9 perimeter = 2 ( l + b ) = 18 cm . answer : a
Answer: a
Question (physics): the pilot of a small aircraft with a 60 - gallon fuel tank wants to fly to cleveland , which is 480 miles away . the pilot recognizes that the current engine , which can fly only 10 miles per gallon , will not get him there . by how many miles per gallon must the aircraft ’ s fuel efficiency be improved to make the flight to cleveland possible ?
Options: a ) 5 , b ) 12 , c ) 2 , d ) 4 , e ) 6
Rationale: "actual miles / gallon is = 480 / 60 = 8 miles / gallon . current engine miles / gallon is 10 miles / gallon . additional 2 miles / gallon is required to match the actual mileage . answer : c"
Answer: c
Question (geometry): there is a square with sides of 12 . what is the circumference of the biggest circle that can be cut out of this square ?
Options: a ) 75.4
b ) 31.42
c ) 36
d ) 18.85
e ) 37.7
Rationale: circumference of a circle = c = 2 ï € r square is 12 wide , so circle ' s diameter would be 12 , and radius would be 6 c = 2 ï € 6 which is approximately 37.7 answer is e
Answer: e
Question (physics): convert 0.36 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 17 / 50 , d ) 9 / 25 , e ) none
Rationale: "answer 0.36 = 36 / 100 = 9 / 25 correct option : d"
Answer: d
Question (general): a box contain the number of balls which is as much greater than 44 is less than 70 . the number of balls is ?
Options: a ) 47 , b ) 114 , c ) 74 , d ) 67 , e ) 57
Rationale: answer let the number be x . then , x - 44 = 70 - x â ‡ ’ 2 x = 70 + 44 = 114 â ‡ ’ 2 x = 114 â ˆ ´ x = 57 correct option : e
Answer: e
Question (general): robert ' s salary was decreased by 20 % and subsequently increased by 20 % . how much percentage does he lose ?
Options: a ) 4 % , b ) 20 % , c ) 25 % , d ) 30 % , e ) 50 %
Rationale: "let original salary be $ 100 salary after decreasing 20 % = 100 - 100 x 20 / 100 = $ 80 salary after increasing 20 % on $ 80 = 80 + 80 x 20 / 100 = $ 96 percentage of loss = 100 - 96 = 4 % answer : a"
Answer: a
Question (general): the average of temperatures at noontime from monday to friday is 55 ; the lowest one is 45 , what is the possible maximum range of the temperatures ?
Options: a ) 20 , b ) 25 , c ) 40 , d ) 45 , e ) 75
Rationale: "there are 5 days so the sum of temperature can be 55 * 5 = 275 lowest is 45 . to find the maximum range we can say the temperature was the lowest for 4 of the 5 days so 4 * 45 = 180 . on the fifth day it is 275 - 180 = 95 range is therefore 95 - 45 = 40 answer c"
Answer: c
Question (general): 12 . what is the dividend . divisor 17 , the quotient is 9 and the remainder is 6 .
Options: a ) 150 , b ) 152 , c ) 154 , d ) 159 , e ) 144
Rationale: "d = d * q + r d = 17 * 9 + 6 d = 153 + 6 d = 159 answer d"
Answer: d
Question (probability): what is the probability that the sum of two dice will yield a 5 , and then when both are thrown again , their sum will again yield a 5 ? assume that each die has 4 sides with faces numbered 1 to 4 .
Options: a ) 1 / 144 , b ) 1 / 36 , c ) 1 / 12 , d ) 1 / 16 , e ) 1 / 3
Rationale: "solution - rolling dices is an independent event . the combinations to get 5 are ( 1,4 ) , ( 4,1 ) , ( 2,3 ) , ( 3,2 ) , and total combinations of both dices is 16 . the probability of getting 5 in first attempt is 4 / 16 = 1 / 4 . probability of getting 5 again in second attempt = ( 1 / 4 ) * ( 1 / 4 ) = 1 / 16 . 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 . 2400 ?
Options: a ) s . 800 , b ) s . 810 , c ) s . 820 , d ) s . 900 , e ) s . 920
Rationale: "2400 * 1 / 3 = 800 option a"
Answer: a
Question (gain): yesterday ' s closing prices of 2,420 different stocks listed on a certain stock exchange were all different from today ' s closing prices . the number of stocks that closed at a higher price today than yesterday was 20 percent greater than the number that closed at a lower price . how many of the stocks closed at a higher price today than yesterday ?
Options: a ) 484 , b ) 726 , c ) 1,100 , d ) 1,320 , e ) 1,694
Rationale: "lets consider the below - the number of stocks that closed at a higher price = h the number of stocks that closed at a lower price = l we understand from first statement - > h + l = 2420 - - - - ( 1 ) we understand from second statement - > h = ( 120 / 100 ) l = > h = 1.2 l - - - - ( 2 ) solve eq ( 1 ) & ( 2 ) to get h = 1320 . d is answer ."
Answer: d
Question (gain): a shopkeeper sells 200 metres of cloth for rs . 12000 at a loss of rs . 12 per metre . find his cost price for one metre of cloth ?
Options: a ) s . 59 , b ) s . 72 , c ) s . 62 , d ) s . 50 , e ) s . 13
Rationale: "sp per metre = 12000 / 200 = rs . 60 loss per metre = rs . 12 cp per metre = 60 + 12 = rs . 72 answer : b"
Answer: b
Question (general): before 7 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 54 , d ) 60 , e ) 70
Rationale: "a - 7 = 4 ( b - 7 ) - - > a - 4 b = - 21 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 29 - - > a = 3 ( 22 ) = 99 a - b = 99 - 29 = 70 answer : e"
Answer: e
Question (physics): a pipe can empty 2 / 3 rd of a cistern in 12 mins . in 6 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 3 / 7 , c ) 4 / 9 , d ) 3 / 8 , e ) 1 / 3
Rationale: "2 / 3 - - - - 12 ? - - - - - 6 = = > 1 / 3 e"
Answer: e
Question (general): a grocer has a sale of rs . 5420 , rs . 5660 , rs . 6200 , rs . 6350 and rs . 6500 for 5 consecutive months . find the sale he should have in the sixth month , so that he gets an average sale of rs . 6400 ?
Options: a ) rs . 5870 , b ) rs . 8270 , c ) rs . 6020 , d ) rs . 6850 , e ) none of these
Rationale: "explanation : total sale for 5 months = rs . ( 5420 + 5660 + 6200 + 6350 + 6500 ) = rs . 30,130 therefore , required sale = rs . [ ( 6400 * 6 ) – 30,130 ] = rs . ( 38400 – 30,130 ) = rs . 8270 answer b"
Answer: b
Question (general): 1401 x 1401 = ?
Options: a ) 1962800 , b ) 1962801 , c ) 1960000 , d ) 1951611 , e ) 1951613
Rationale: "1401 x 1401 = ( 1401 ) 2 = ( 1400 + 1 ) 2 = ( 1400 ) 2 + ( 1 ) 2 + ( 2 x 1400 x 1 ) = 1960000 + 1 + 2800 = 1960001 + 2800 = 1962801 . b )"
Answer: b
Question (general): the sum of first n consecutive odd integers is n ^ 2 . what is the sum of all odd integers between 9 and 39 inclusive .
Options: a ) 351 , b ) 384 , c ) 410 , d ) 424 , e ) 450
Rationale: "we ' re dealing with a sequence of consecutive odd integers : 9 to 39 , inclusive . we ' re asked for the sum of this group . 1 ) start with the sum of the smallest and the biggest : 9 + 39 = 48 2 ) now look at the ' next smallest ' and the ' next biggest ' : 11 + 37 = 48 now we have proof that there is no middle term . we have 8 bunches of 48 8 ( 48 ) = 384 b"
Answer: b
Question (geometry): huey ' s hip pizza sells two sizes of square pizzas : a small pizza that measures 12 inches on a side and costs $ 10 , and a large pizza that measures 18 inches on a side and costs $ 20 . if two friends go to huey ' s with $ 30 apiece , how many more square inches of pizza can they buy if they pool their money than if they each purchase pizza alone ?
Options: a ) 5 square inches , b ) 36 square inches , c ) 15 square inches , d ) 25 square inches , e ) 350 square inches
Rationale: "in the first case each can buy one pizza of $ 10 and one pizza of $ 20 . in square inches that would be ( 12 * 12 = 144 ) for the small pizza and ( 18 * 18 = 324 ) for the large pizza . in total sq inches that would be ( 144 + 324 ) * 2 = 936 sq inches . in the second case if they pool their money together they can buy 3 large pizzas . in terms of square inches that would be 3 * 324 = 972 sq inches . hence , the difference is 36 square inches more ( 972 - 936 ) . the correct answer is b"
Answer: b
Question (physics): two goods trains each 75 m long are running in opposite directions on parallel tracks . their speeds are 45 km / hr and 30 km / hr respectively . find the time taken by the slower train to pass the driver of the faster one ?
Options: a ) 2.3 sec , b ) 4.2 sec , c ) 48 sec , d ) 7.2 sec , e ) 9 sec
Rationale: "relative speed = 45 + 30 = 75 km / hr . 75 * 5 / 18 = 125 / 6 m / sec . distance covered = 75 + 75 = 150 m . required time = 150 * 6 / 125 = 7.2 sec . answer : d"
Answer: d
Question (general): if each participant of a chess tournament plays exactly one game with each of the remaining participants , then 153 games will be played during the tournament . find the number of participants .
Options: a ) 15 , b ) 16 , c ) 17 , d ) 18 , e ) 19
Rationale: "if the number of participants is 3 ( say a , b , c ) the number of games played will be 2 ( a plays against b and c ) + 1 ( b plays against c ) = 3 using the same logic , if the number of participants is n , the number of games played will be ( n - 1 ) + ( n - 2 ) + ( n - 3 ) + . . . 3 + 2 + 1 given that this sum = 153 = 1 + 2 + 3 + . . . ( n - 1 ) sum of first m positive integers is given by m ( m + 1 ) / 2 . so sum of first ( n - 1 ) positive integers is ( n - 1 ) * n / 2 153 = ( n - 1 ) * n / 2 ( n - 1 ) * n = 306 17 * 18 = 306 ( we know that 15 ^ 2 = 225 so the two consecutive numbers must be greater than 15 . also , 20 ^ 2 = 400 so the two numbers must be less than 20 . the pair of numbers in between 15 and 20 whose product ends with 6 is 17 and 18 ) so n = 18 answer ( d )"
Answer: d
Question (general): find the ones digit of 73 ^ 340
Options: a ) 3 , b ) 5 , c ) 6 , d ) 7 , e ) 9
Rationale: "cyclicity of 3 is 3,9 , 7,1 after 4 multiplication again the cycle repeats . so divide 340 by 4 and we get 87 as quotient and 2 as remainder . so cycle will run for 87 times and then 2 times more . so pick up the 2 nd item from the cycle . hence answer a ."
Answer: a
Question (gain): if a lends rs . 2000 to b at 15 % per annum and b lends the same sum to c at 17 % per annum then the gain of b in a period of 4 years is ?
Options: a ) 155 , b ) 162 , c ) 157.5 , d ) 160 , e ) 157.12
Rationale: "( 2000 * 2 * 4 ) / 100 = > 160 answer : d"
Answer: d
Question (physics): how much time will a train of length 400 m moving at a speed of 72 kmph take to cross another train of length 300 m , moving at 36 kmph in the same direction ?
Options: a ) 40 sec , b ) 50 sec , c ) 60 sec , d ) 70 sec , e ) 80 sec
Rationale: "the distance to be covered = sum of their lengths = 400 + 300 = 700 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 700 / 10 = 70 sec . answer : d"
Answer: d
Question (physics): length of a rectangular plot is 26 mtr more than its breadth . if the cost of fencin gthe plot at 26.50 per meter is rs . 5300 , what is the length of the plot in mtr ?
Options: a ) 53 m , b ) 63 m , c ) 73 m , d ) 83 m , e ) 93 m
Rationale: "let breadth = x metres . then , length = ( x + 26 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 26 ) + x ] = 200 2 x + 26 = 100 2 x = 74 x = 37 hence , length = x + 26 = 63 m b"
Answer: b
Question (physics): on a map the distance between two mountains is 312 inches . the actual distance between the mountains is 136 km . ram is camped at a location that on the map is 34 inch from the base of the mountain . how many km is he from the base of the mountain ?
Options: a ) 14.83
b ) 14.81
c ) 14.8
d ) 14.82
e ) 14.12
Rationale: explanation : since 312 inch = 136 km so 1 inch = 136 / 312 km so 34 inch = ( 136 × 34 ) / 312 = 14.82 km answer : d
Answer: d
Question (general): the sum of the present ages of a father and his son is 42 years . 6 years ago , father ' s age was 4 times the age of the son . after 6 years , son ' s age will be :
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: let the present ages of son and father be x and ( 42 - x ) years respectively . then , ( 42 - x ) - 6 = 4 ( x - 6 ) 36 - x = 4 x - 24 x = 12 the son ' s age after 6 years will be 18 . the answer is c .
Answer: c
Question (physics): two trains a and b starting from two points and travelling in opposite directions , reach their destinations 9 hours and 16 hours respectively after meeting each other . if the train a travels at 80 kmph , find the rate at which the train b runs .
Options: a ) 40 , b ) 160 , c ) 120 , d ) 80 , e ) 100
Rationale: "if two objects a and b start simultaneously from opposite points and , after meeting , reach their destinations in ‘ a ’ and ‘ b ’ hours respectively ( i . e . a takes ‘ a hrs ’ to travel from the meeting point to his destination and b takes ‘ b hrs ’ to travel from the meeting point to his destination ) , then the ratio of their speeds is given by : sa / sb = √ ( b / a ) i . e . ratio of speeds is given by the square root of the inverse ratio of time taken . sa / sb = √ ( 4 / 16 ) = 2 / 4 = 1 / 2 this gives us that the ratio of the speed of a : speed of b as 1 : 2 . since speed of a is 80 kmph , speed of b must be 80 * ( 2 / 1 ) = 160 kmph b"
Answer: b
Question (general): a recipe requires 2 1 / 2 ( mixed number ) cups of flour 2 3 / 4 ( mixed number ) cups of sugar and 1 1 / 3 ( mixed number ) cups of milk to make one cake . victor has 15 cups if flour , 16 cups of sugar and 8 cups of milk . what is the greatest number of cakes tom can make using this recipe ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: less work up front : go through each item and see what the greatest number of cakes you can make with each . the lowest of these will be the right answer . flour : 15 cups , we need 2.5 cups each . just keep going up the line to see how many cakes we can make : that means i can make 2 cakes with 5 cups , so 6 cakes overall with 15 cups . i ' ve already got the answer narrowed to either a or b . sugar : 16 cups , we need 2.75 cups each . same principle . i can make 2 cups with 5.5 cups , so to make 6 cakes i ' d need 16.5 cups . i do n ' t have that much sugar , so we ' re limited to 5 cakes . no need to even do milk because we ' re already at 5 . sugar will be the limiting factor . answer is a
Answer: a
Question (gain): the c . p of 10 pens is equal to the s . p of 5 pens . find his gain % or loss % ?
Options: a ) 50 % , b ) 40 % , c ) 30 % , d ) 60 % , e ) 20 %
Rationale: 10 cp = 5 sp 10 - - - 5 cp gain 100 - - - ? = > 50 % ( gain ) answer : a
Answer: a
Question (general): the average of 6 no . ' s is 3.95 . the average of 2 of them is 4.2 , while the average of theother 2 is 3.85 . what is the average of the remaining 2 no ' s ?
Options: a ) 4.2 , b ) 4.4 , c ) 4.6 , d ) 3.8 , e ) 5.7
Rationale: "sum of the remaining two numbers = ( 3.95 * 6 ) - [ ( 4.2 * 2 ) + ( 3.85 * 2 ) ] = 7.60 . required average = ( 7.6 / 2 ) = 3.8 . d"
Answer: d