Cheukting/mathqa huggingface dataset:
Question (general): a man engaged a servant on the condition that he would pay him rs . 600 and a uniform after one year service . he served only for 9 months and received uniform and rs . 400 , find the price of the uniform ?
Options: a ) s . 80 , b ) s . 85 , c ) s . 90 , d ) s . 100 , e ) s . 200
Rationale: 9 / 12 = 3 / 4 * 600 = 450 400 - - - - - - - - - - - - - 50 1 / 4 - - - - - - - - 50 1 - - - - - - - - - ? = > rs . 200 answer : e
Answer: e
Question (general): find the value of y from ( 12 ) ^ 1 x 6 ^ 4 ÷ 432 = y ?
Options: a ) 2134 , b ) 2234 , c ) 2540 , d ) 2560 , e ) 36
Rationale: "36 e"
Answer: e
Question (general): find the least number which when divided by 20 , 25,35 and 40 leaves remainders 14 , 19,29 and 34 respectively .
Options: a ) 1394 , b ) 1294 , c ) 1194 , d ) 1094 , e ) none of them
Rationale: "here , ( 20 - 14 ) = 6 , ( 25 – 19 ) = 6 , ( 35 - 29 ) = 6 and ( 40 - 34 ) = 6 . therefore , required number = ( l . c . m . of 20,25 , 35,40 ) – 6 = 1394 . answer is a ."
Answer: a
Question (general): if 1 / 8 of a pencil is black , 1 / 2 of the remaining is white and the remaining 3 1 / 2 cm is blue , find the total length of the pencil .
Options: a ) 12 , b ) 9 , c ) 8 , d ) 6 , e ) 5
Rationale: let the total length of the pencil be x cm . black part is 1 / 8 of the length so x / 8 . so the remaining part is x - x / 8 = = > 8 x / 8 - x / 8 = = > 7 x / 8 cm . white part = 1 / 2 * 7 x / 8 = 7 x / 16 cm . so the remaining part is 7 x / 8 - 7 x / 16 = = > 14 x / 16 - 7 x / 16 = 7 x / 16 which is equal to 3 1 / 2 . 7 x / 16 = 7 / 2 cross multiply and we get x = 16 / 2 = 8 cm . so the total length of the pencil is 8 cm . the correct answer is option c ) 8 .
Answer: c
Question (general): marcella has 25 pairs of shoes . if she loses 9 individual shoes , what is the greatest number of matching pairs she could have left ?
Options: a ) 21 , b ) 20 , c ) 19 , d ) 16 , e ) 15
Rationale: "greatest number of paired shoes means greatest number of lost pairs 9 shoes have 4 pairs and 1 extra shoes of a pair . so a otal of 5 pairs she loses leftover pair = 20 answer : b"
Answer: b
Question (physics): the radius of a wheel is 22.4 cm . what is the distance covered by the wheel in making 180 resolutions ?
Options: a ) 724 m , b ) 704 m , c ) 287 m , d ) 278 m , e ) 253.4 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 180 resolutions . = 180 * 2 * 22 / 7 * 22.4 = 25344 cm = 253.4 m answer : e"
Answer: e
Question (physics): if a motorist had driven 1 hour longer on a certain day and at an average rate of 5 miles per hour faster , he would have covered 80 more miles than he actually did . how many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that day ?
Options: a ) 100 , b ) 120 , c ) 140 , d ) 150 , e ) 160
Rationale: "case 1 : let rate = r , time = t , and distance = d so d = rt case 2 : ( d + 80 ) = ( r + 5 ) ( t + 1 ) case 3 : ( d + x ) = ( r + 10 ) ( t + 2 ) x = 160 ans e"
Answer: e
Question (gain): a reduction of 20 % in the price of oil enables a house wife to obtain 10 kgs more for rs . 1500 , what is the reduced price for kg ?
Options: a ) rs . 20 , b ) rs . 25 , c ) rs . 30 , d ) rs . 35 , e ) rs . 40
Rationale: "explanation : 1500 * ( 20 / 100 ) = 300 - - - - 10 ? - - - - 1 = > rs . 30 answer : c"
Answer: c
Question (physics): a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 99 km / hr . what is the length of the platform ?
Options: a ) 440 , b ) 488 , c ) 477 , d ) 426 , e ) 422
Rationale: "speed = 99 * 5 / 18 = 27.5 m / sec . length of the train = 27.5 * 20 = 550 m . let the length of the platform be x m . then , ( x + 550 ) / 36 = 27.5 = > x = 440 m . answer : a"
Answer: a
Question (general): 100 white and black tiles will be used to form a 20 x 20 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?
Options: a ) 75 , b ) 70 , c ) 85 , d ) 90 , e ) 95
Rationale: "answer = b please refer diagram below 90 - 20 = 70"
Answer: b
Question (general): two numbers a and b are such that the sum of 6 % of a and 4 % of b is two - third of the sum of 6 % of a and 8 % of b . find the ratio of a : b .
Options: a ) 2 : 3 , b ) 1 : 2 , c ) 4 : 3 , d ) 1 : 1 , e ) 3 : 2
Rationale: "explanation : 6 % of a + 4 % of b = 2 / 3 ( 6 % of a + 8 % of b ) 6 a / 100 + 4 b / 100 = 2 / 3 ( 6 a / 100 + 8 b / 100 ) ⇒ 6 a + 4 b = 2 / 3 ( 6 a + 8 b ) ⇒ 18 a + 12 b = 12 a + 16 b ⇒ 6 a = 4 b ⇒ ab = 4 / 6 = 2 / 3 ⇒ a : b = 2 : 3 answer : option a"
Answer: a
Question (general): if the sum of the first n positive integers is s , what is the sum of the first n negative even integers , in terms of s ?
Options: a ) s / 2 , b ) s , c ) 2 s , d ) 2 s + 2 , e ) 4 s
Rationale: answer is c given sum of - 1 - 2 - 3 . . . . . - n = s sum of - 2 , - 4 , - 6 . . . . - 2 n = 2 [ sum ( - 1 - 2 - 3 . . . . n ) ] = 2 s
Answer: c
Question (general): if you add all the numbers on your mobile phone except 9 , what is the answer ?
Options: a ) 45 , b ) 28 , c ) 65 , d ) 36 , e ) 42
Rationale: "we have to add 0 to 8 to find the answer . therefore 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 answer is d"
Answer: d
Question (general): a fruit drink is made of orange , watermelon , and grape juice , where 25 percent of the drink is orange juice and 40 percent is watermelon juice . if the drink is made with 70 ounces of grape juice , how many ounces is the drink total ?
Options: a ) 125 , b ) 160 , c ) 200 , d ) 250 , e ) 320
Rationale: "let the total number of ounces in the drink be x . % of orange = 25 % % of watermelon = 40 % % of grape = 100 % - 65 % = 35 % 0.35 x = 70 x = 200 therefore there are a total of 200 ounces in the drink . the answer is c ."
Answer: c
Question (general): the wages earned by robin is 30 % more than that earned by erica . the wages earned by charles is 60 % more than that earned by erica . how much percent is the wages earned by charles more than that earned by robin ?
Options: a ) 18.75 % , b ) 23 % , c ) 30 % , d ) 50 % , e ) 100 %
Rationale: let wage of erica = 10 wage of robin = 1.3 * 10 = 13 wage of charles = 1.6 * 10 = 16 percentage by which wage earned by charles is more than that earned by robin = ( 16 - 13 ) / 13 * 100 % = 3 / 13 * 100 % = 23 % answer b
Answer: b
Question (geometry): find the surface area of a cuboid 12 m long , 14 m broad and 7 m high
Options: a ) 868 sq . cm
b ) 600 sq . cm
c ) 700 sq . cm
d ) 900 sq . cm
e ) none of these
Rationale: explanation : surface area = [ 2 ( 12 x 14 + 14 x 7 + 12 x 7 ) ] cm 2 = ( 2 x 350 ) cm 2 = 700 cm 2 . answer : c
Answer: c
Question (physics): the speed of a boat in still water in 42 km / hr and the rate of current is 7 km / hr . the distance travelled downstream in 44 minutes is :
Options: a ) 86.6 km , b ) 46.6 km , c ) 35.9 km , d ) 35.6 km , e ) 26.6 km
Rationale: "speed downstream = ( 42 + 7 ) = 49 kmph time = 44 minutes = 44 / 60 hour = 11 / 15 hour distance travelled = time × speed = 11 / 15 × 49 = 35.9 km answer : c"
Answer: c
Question (general): what is the remainder when 750 * 810 * 830 * 790 is divided by 13 ?
Options: a ) 4 , b ) 9 , c ) 10 , d ) 8 , e ) 6
Rationale: "oa is ' c ' . oe : take the remainder from each of 750 / 15 , 810 / 15 and so on . . 750 / 13 gives remainder = 9 810 / 13 gives remainder = 4 830 / 13 gives remainder = 11 790 / 13 gives remainder = 10 the net remainder is the product of above individual remainders . i . e = 9 * 4 * 11 * 10 break them into pairs 9 * 4 / 13 gives remainder 10 and 11 * 10 / 13 gives remainder 6 so 10 * 6 / 13 gives remainder 8 . answer : c"
Answer: c
Question (physics): sides of a rectangular park are in the ratio 2 : 5 and its area is 3750 sq m , the cost of fencing it at 50 ps per meter is ?
Options: a ) s . 122 , b ) s . 129 , c ) s . 125 , d ) s . 120 , e ) s . 130.64
Rationale: "2 x * 5 x = 3750 = > x = 19.36 2 ( 80.64 + 50 ) = 261.28 m 261.28 * 1 / 2 = rs . 130.64 answer : e"
Answer: e
Question (general): the sum of ages of 5 children born at the intervals of 3 years each is 60 years . what is the age of the youngest child ?
Options: a ) 3 years , b ) 4 years , c ) 6 years , d ) 7 years , e ) 8 years
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 60 5 x = 30 x = 6 . age of the youngest child = x = 6 years . c )"
Answer: c
Question (general): a 100 - litre mixture of milk and water contains 36 litres of milk . ' x ' litres of this mixture is removed and replaced with an equal quantum of water . if the process is repeated once , then the concentration of the milk stands reduced at 9 % . what is the value of x ?
Options: a ) 57.5 litres , b ) 56.67 litres , c ) 57.67 litres , d ) 56.5 litres , e ) 50 litres
Rationale: "working formula . . . initial concentration * initial volume = final concentration * final volume . let x is the part removed from 100 lts . 36 % ( 1 - x / 100 ) ^ 2 = 9 % * 100 % ( 1 - x / 100 ) ^ 2 = 9 / 36 - - - - - - > ( 1 - x / 100 ) ^ 2 = ( 3 / 6 ) ^ 2 100 - x = 300 / 6 x = 50 ans e"
Answer: e
Question (geometry): the length of each side of an equilateral triangle having an area of 4 √ 3 cm 2 is ?
Options: a ) 3 : 4
b ) 3 : 9
c ) 3 : 7
d ) 3 : 1
e ) 3 : 2
Rationale: let the speed of the train be x km / hr and that of the car be y km / hr . then , 120 / x + 480 / y = 8 or 1 / x + 4 / y = 1 / 15 - - - ( i ) and , 200 / x + 400 / y = 25 / 3 or 1 / x + 2 / y = 1 / 24 - - - ( ii ) solving ( i ) and ( ii ) , we get x = 60 and y = 80 ratio of speeds = 60 : 80 = 3 : 4 answer : a
Answer: a
Question (physics): length of a rectangular plot is 24 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 ) 52 m , b ) 62 m , c ) 72 m , d ) 82 m , e ) 92 m
Rationale: "let breadth = x metres . then , length = ( x + 24 ) metres . perimeter = 5300 m = 200 m . 26.50 2 [ ( x + 24 ) + x ] = 200 2 x + 24 = 100 2 x = 76 x = 38 . hence , length = x + 24 = 62 m b"
Answer: b
Question (general): if x is real , find the maximum value of the expression - 2 x ^ 2 + 7 x + 9 .
Options: a ) 6.125 , b ) 9.125 , c ) 12.125 , d ) 15.125 , e ) 18.125
Rationale: "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 7 x + 9 = ( - 2 x + 9 ) ( x + 1 ) the roots are 9 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 1.75 the maximum value is - 2 ( 1.75 ) ^ 2 + 7 ( 1.75 ) + 9 = 15.125 the answer is d ."
Answer: d
Question (general): the average monthly salary of 20 employees in an organisation is rs . 1500 . if the manager ' s salary is added , then the average salary increases by rs . 150 . what is the manager ' s monthly salary ?
Options: a ) rs . 6003 , b ) rs . 6029 , c ) rs . 4650 , d ) rs . 6108 , e ) rs . 6011
Rationale: "explanation : manager ' s monthly salary rs . ( 1650 * 21 - 1500 * 20 ) = rs . 4650 . answer : c"
Answer: c
Question (other): the probability of two events a and b are 0.25 and 0.30 respectively . the probability that both a and b occur is 0.15 . the probability that neither a nor b occur is _________
Options: a ) 0.45 , b ) 0.4 , c ) 0.5 , d ) 0.05 , e ) 0.6
Rationale: we are apply that formula . . . . . . . . . . . . . . p ( aorb ) = p ( a ) + p ( b ) - p ( a and b ) = . 25 + . 30 - . 15 = . 40 but the probability of neither a nor b = 1 - . 40 = 0.60 answer : e
Answer: e
Question (geometry): the size of a flat - screen tablet is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 6 - inch flat - screen tablet than a square 5 - inch flat - screen tablet ?
Options: a ) 5.0
b ) 6.0
c ) 6.8
d ) 5.8
e ) 5.5
Rationale: if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 6 - inch flat - screen television the diagonal ( hypotenuse ) = 6 so , we can apply the pythagorean theorem to get x ² + x ² = 6 ² simplify : 2 x ² = 6 ² divide both sides by 2 to get : x ² = 6 ² / 2 since the area of the square = x ² , we can see that the area of this square is 6 ² / 2 square 5 - inch flat - screen television the diagonal ( hypotenuse ) = 5 so , we can apply the pythagorean theorem to get x ² + x ² = 5 ² simplify : 2 x ² = 5 ² divide both sides by 2 to get : x ² = 5 ² / 2 since the area of the square = x ² , we can see that the area of this square is 5 ² / 2 difference in areas = 6 ² / 2 - 5 ² / 2 = ( 6 ² - 5 ² ) / 2 = ( 36 - 25 ) / 2 = 11 / 2 = 5.5 e
Answer: e
Question (physics): the sum of 4 consecutive even numbers is 140 . what would be the largest number ?
Options: a ) 33 , b ) 38 , c ) 70 , d ) 123 , e ) 12
Rationale: let the four consecutive even numbers be 2 ( x - 2 ) , 2 ( x - 1 ) , 2 x , 2 ( x + 1 ) their sum = 8 x - 4 = 140 = > x = 18 smallest number is : 2 ( x + 1 ) = 38 . answer : b
Answer: b
Question (gain): in a sample of college students , 50 percent are third year students and 70 percent are not second - year students . what fraction of those students who are not third - year students are second - year students ?
Options: a ) 2 / 3 , b ) 1 / 4 , c ) 2 / 5 , d ) 3 / 7 , e ) 2 / 9
Rationale: required answer = 40 / 60 . = 2 / 3 answer is a
Answer: a
Question (general): a camera lens filter kit containing 5 filters sells for $ 75.50 . if the filters are purchased individually , 3 of them are priced at $ 7.35 each , 3 at $ 12.05 each , 1 at $ 12.50 . the amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually ?
Options: a ) 5.35 % , b ) 6.35 % , c ) 7.35 % , d ) 8.35 % , e ) 9.35 %
Rationale: "cost of kit = $ 75.50 if filters are purchased individually - $ 7.35 * 3 + $ 12.05 * 3 + $ 12.50 = $ 70.70 amount saved = $ 75.50 - $ 70.70 = $ 4.80 required % age = ( $ 4.80 / $ 75.50 ) * 100 = 6.35 % so , the correct answer is b ."
Answer: b
Question (general): if a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20 , what is the probability e that this product will be a multiple of 45 ?
Options: a ) 1 / 32 , b ) 1 / 28 , c ) 1 / 24 , d ) 1 / 16 , e ) 1 / 14
Rationale: "there are 3 single digit multiple of 3 , that is , 3 , 6,9 . there are 8 prime nos less than 20 - 2,3 , 5,7 , 11,13 , 17,19 total outcome - 8 * 3 = 24 favourable outcome = 1 ( 9 * 5 ) hence required probability e = 1 / 24 . answer c ."
Answer: c
Question (general): when positive integer n is divided by positive integer j , the remainder is 16 . if n / j = 204.04 , what is value of j ?
Options: a ) 100 , b ) 120 , c ) 400 , d ) 260 , e ) 380
Rationale: "when a number is divided by another number , we can represent it as : dividend = quotient * divisor + remainder so , dividend / divisor = quotient + remainder / divisor given that n / j = 204.04 here 204 is the quotient . given that remainder = 16 so , 204.04 = 204 + 16 / j so , j = 400 answer : c"
Answer: c
Question (general): find the lowest common multiple of 24 , 36 and 40 .
Options: a ) 360 , b ) 420 , c ) 510 , d ) 320 , e ) 280
Rationale: "lcm = 2 * 2 * 2 * 3 * 3 * 5 = 360 . answer is a"
Answer: a
Question (gain): 14 is what percent of 70 ?
Options: a ) 0.2 % , b ) 2 % , c ) 5 % , d ) 20 % , e ) 500 %
Rationale: "14 = x * 70 / 100 x = 20 % ans ; d"
Answer: d
Question (physics): the perimeter of a semi circle is 140 cm then the radius is ?
Options: a ) 27 , b ) 28 , c ) 19 , d ) 11 , e ) 12
Rationale: "36 / 7 r = 140 = > r = 27 answer : a"
Answer: a
Question (general): among the members of the malmo family , there are 3 times as many members who do not wear glasses as members who do . half of the malmo family members have blue eyes , and 4 / 5 of the family members who have blue eyes do not wear glasses . what percent of the malmo family members wear glasses and do not have blue eyes ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 35
Rationale: number in black are given and in red are calculated . now , since x + 3 x = 100 , then x = 25 and therefore = 25 − 10 = 15 answer : b .
Answer: b
Question (physics): a train passes a station platform in 20 sec and a man standing on the platform in 12 sec . if the speed of the train is 72 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 140 , c ) 160 , d ) 120 , e ) 171
Rationale: "speed = 72 * 5 / 18 = 20 m / sec . length of the train = 20 * 12 = 240 m . let the length of the platform be x m . then , ( x + 240 ) / 20 = 20 = > x = 160 m . answer : c"
Answer: c
Question (physics): the distance between two cities a and b is 870 km . a train starts from a at 8 a . m . and travel towards b at 60 km / hr . another train starts from b at 9 a . m and travels towards a at 75 km / hr . at what time do they meet ?
Options: a ) 09 pm , b ) 07 pm , c ) 03 pm , d ) 05 am , e ) 03 am
Rationale: "explanation : suppose they meet x hrs after 8 a . m then , [ distance moved by first in x hrs ] + [ distance moved by second in ( x - 1 ) hrs ] = 870 . therefore , 60 x + 75 ( x - 1 ) = 870 . = > x = 7 . so , they meet at ( 8 + 7 ) i . e , 15 = > 3 pm answer : c )"
Answer: c
Question (general): apple , orange , mango . mango + apple = 12 . mango + orange = 10 . mango + apple + orange = 38 . calculate the no of mango ?
Options: a ) - 8 , b ) - 9 , c ) - 10 , d ) - 12 , e ) - 16
Rationale: mango + apple = 12 . . . . . . . . . . . . . ( a ) mango + orange = 10 . . . . . . . . . . ( b ) adding a and b 2 mango + apple + orange = 22 but mango + apple + orange = 38 . . . . given which is not possible . in this case , no of mangoes is negative ( - 16 ) answer : d
Answer: d
Question (general): a theater charges $ 12 for seats in the orchestra and $ 8 for seats in the balcony . on a certain night , a total of 360 tickets were sold for a total cost of $ 3,320 . how many more tickets were sold that night for seats in the balcony than for seats in the orchestra ?
Options: a ) 90 , b ) 110 , c ) 120 , d ) 140 , e ) 220
Rationale: "orchestra seats - a balcony seats - b a + b = 360 and 12 a + 8 b = 3320 solving equations simultaneously ( multiply equation 1 with 8 and subtract from second equation ) 4 a = 3320 - 8 * 360 = 3320 - 2880 = 440 i . e . a = 110 and b = 360 - 110 = 250 more seats in balcony than orchestra = b - a = 250 - 110 = 140 answer : option d"
Answer: d
Question (physics): a train running at the speed of 36 km / hr crosses a pole in 9 seconds . what is the length of the train ?
Options: a ) 120 metres , b ) 180 metres , c ) 324 metres , d ) 90 metres , e ) 100 meters
Rationale: "speed = 36 x 5 / 18 m / sec = 30 / 3 m / sec . length of the train = ( speed x time ) . length of the train = 30 / 3 x 9 m = 90 m . answer : d"
Answer: d
Question (general): tough and tricky questions : arithmetic . ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 =
Options: a ) 4 , b ) 18 , c ) 29 , d ) 8 , e ) 116
Rationale: ans is 8 my approach was : ( 56 ^ 2 + 56 ^ 2 ) / 28 ^ 2 = 56 ( 56 + 56 ) / 28 * 28 = 56 * 112 / 28 * 28 = 2 * 4 = 8 d
Answer: d
Question (general): a boy has rs . 480 in the denominations of one - rupee notes , 5 - rupee notes and 10 - rupee notes . the number of notes of each denomination is equal . what is the total number of notes that he has ?
Options: a ) 90 , b ) 110 , c ) 140 , d ) 130 , e ) 120
Rationale: let number of notes of each denomination be x . then x + 5 x + 10 x = 480 16 x = 480 x = 30 . hence , total number of notes = 3 x = 90 . a
Answer: a
Question (physics): glen and hannah drive at constant speeds toward each other on a highway . glen drives at a constant speed of 37 km per hour . at a certain time they pass by each other , and then keep driving away from each other , maintaining their constant speeds . if glen is 130 km away from hannah at 6 am , and also 130 km away from hannah at 11 am , then how fast is hannah driving ( in kilometers per hour ) ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: glen and hannah complete 260 km / 5 hours = 52 km / hour hannah ' s speed is 52 - 37 = 15 km / hour the answer is d .
Answer: d
Question (general): the output of a factory was increased by 10 % to keep up with rising demand . to handle the holiday rush , this new output was increased by 20 % . by approximately what percent would the output now have to be decreased in order to restore the original output ?
Options: a ) 20 % , b ) 24 % , c ) 30 % , d ) 32 % , e ) 79 %
Rationale: "let initial output is o then after 10 % increase it will be 1.1 o and after 20 % increase on this new output the latest output will be 1.1 o * 1.20 = 1.32 o now we have to decrease the output by some percentage so that the new output is same as the starting output ( o ) so , 1.32 o * ( 1 - x / 100 ) = o = > x = 24.24 % so , answer will be b"
Answer: b
Question (general): integer d is the product of the integers a , b , and c and 1 < a < b < c . if the remainder when 233 is divided by d is 79 , what is the value of a + c ?
Options: a ) 7 , b ) 9 , c ) 13 , d ) 14 , e ) 18
Rationale: 79 is the remainder , therefore the number ( a * b * c ) or multiple of the number we need is 79 less than 233 hence 233 - 79 = 154 therefore , 154 is either a number we want or it is a multiple of the number we want but the largest factor of 154 is 77 because 77 * 2 = 154 but 77 is less than 79 hence it can not be a number thus 154 is the number we want a * b * c = 154 now factorize 154 = 1 * 2 * 7 * 11 all are prime also we know 1 < a < b < c thus a = 2 and c = 11 therefore a + c = 2 + 11 = 13 answer : c
Answer: c
Question (general): each of the 20 boxes in a certain shipment weighs either 10 pounds or 20 pounds , and the average ( arithmetic mean ) weight of the boxes in the shipment is 18 pounds . if the average weight of the boxes in the shipment is to be reduced to 15 pounds by removing some of the 20 - pound boxes , how many 20 - pound boxes must be removed ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: "if the average of 10 - pound and 20 - pound boxes is 18 , the ratio of 10 - pound boxes : 20 - pound boxes is 1 : 4 . so out of 20 boxes , 4 are 10 - pound boxes and 16 are 20 - pound boxes . if the average of 10 and 20 - pound boxes is to be 15 , the ratio of 10 - pound boxes : 20 - pound boxes should be 1 : 1 . the number of 10 pound boxes remains the same so we still have 4 of them . to get a ratio of 1 : 1 , the number of 20 - pound boxes must be 4 . we need to remove 12 of the 20 - pound boxes . the answer is b ."
Answer: b
Question (geometry): the monthly rent of a shop of dimension 18 feet × 20 feet is rs . 3600 . what is the annual rent per square foot of the shop ?
Options: a ) 120 , b ) 56 , c ) 68 , d ) 87 , e ) 92
Rationale: "sol . monthly rent per square feet = 3600 / ( 18 * 20 ) = 10 & annual rent per square feet = 12 * 10 = 120 answer : a"
Answer: a
Question (physics): a van takes 6 hours to cover a distance of 378 km . how much should the speed in kmph be maintained to cover the same direction in 3 / 2 th of the previous time ?
Options: a ) 50 kmph , b ) 60 kmph , c ) 70 kmph , d ) 42 kmph , e ) 90 kmph
Rationale: "time = 6 distence = 378 3 / 2 of 6 hours = 6 * 3 / 2 = 9 hours required speed = 378 / 9 = 42 kmph d"
Answer: d
Question (general): country x taxes each of its citizens an amount equal to 14 percent of the first $ 40,000 of income , plus 20 percent of all income in excess of $ 40,000 . if a citizen of country x is taxed a total of $ 8,000 , what is her income ?
Options: a ) $ 40,000 , b ) $ 52,000 , c ) $ 64,000 , d ) $ 66,667 , e ) $ 80,000
Rationale: "equation is correct , so math must be a problem . 0.14 * 40,000 + 0.2 * ( x - 40,000 ) = 8,000 - - > 5,600 + 0.2 x - 8,000 = 8,000 - - > 0.2 x = 10,400 - - > x = 52,000 . answer : b ."
Answer: b