Cheukting/mathqa huggingface dataset:
Question (general): 8900 ÷ 6 ÷ 4 = ?
Options: a ) 349 , b ) 541.75 , c ) 224.37 , d ) 370.833 , e ) none of these
Rationale: explanation : given exp . 8900 * 1 / 6 * 1 / 4 = 370.833 answer : d
Answer: d
Question (general): the markup on a box of apples is 10 percent of the cost . the markup is what percent of the selling price ? ( markup = selling price - cost )
Options: a ) 9.09 % , b ) 10 % , c ) 12 1 / 2 % , d ) 15 % , e ) 16 2 / 3 %
Rationale: mp = 0.1 cp sp = cp + 0.1 cp = 1.1 cp hence mp = 0.1 / 1.1 sp = 1 / 1 sp . hence mp is 9.09 % of sp answer a
Answer: a
Question (physics): a train speeds past a pole in 15 seconds and a platform 100 m long in 40 seconds . its length is ?
Options: a ) 188 m , b ) 876 m , c ) 251 m , d ) 100 m , e ) 145 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 15 = > y = x / 15 x + 100 / 40 = x / 15 x = 100 m . answer : d"
Answer: d
Question (physics): a train running at the speed of 30 km / hr crosses a pole in 12 seconds . what is the length of the train ?
Options: a ) 70 , b ) 80 , c ) 90 , d ) 100 , e ) 110
Rationale: "speed = ( 30 x ( 5 / 18 ) m / sec = ( 25 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 25 / 3 ) x 12 ) m = 100 m d"
Answer: d
Question (other): three numbers are in the ratio 3 : 4 : 5 and their l . c . m is 2400 . their h . c . f is :
Options: a ) 40 , b ) 80 , c ) 120 , d ) 200 , e ) 220
Rationale: "let the numbers be 3 x , 4 x and 5 x . then , their l . c . m = 60 x . so , 60 x = 2400 or x = 40 . the numbers are ( 3 * 40 ) , ( 4 * 40 ) and ( 5 * 40 ) . hence , required h . c . f = 40 . answer : a"
Answer: a
Question (general): how many positive integers less than 9999 are such that the product of their digits is 210 .
Options: a ) 24 , b ) 58 , c ) 26 , d ) 34 , e ) 25
Rationale: "the prime factorization of 210 is 2 * 3 * 5 * 7 . so one way to make the right kind of number is to use those four digits , in any of the 4 ! = 24 orders you can put them in . notice though that we can also get 210 as a product by multiplying 5 , 6 and 7 . so we can make some 3 - digit numbers with the right product : 3 ! = 6 of them to be exact . but we can also get the right product using the digit 1 along with the digits 5 , 6 , and 7 . again we can arrange those digits in 4 ! = 24 orders . a"
Answer: a
Question (physics): two stations p and q are 65 km apart on a straight track . one train starts from p at 7 a . m . and travels towards q at 20 kmph . another train starts from q at 8 a . m . and travels towards p at a speed of 25 kmph . at what time will they meet ?
Options: a ) 9 am , b ) 12 am , c ) 10.30 am , d ) 12.30 am , e ) 11 am
Rationale: assume both trains meet after x hours after 7 am distance covered by train starting from p in x hours = 20 x km distance covered by train starting from q in ( x - 1 ) hours = 25 ( x - 1 ) total distance = 65 = > 20 x + 25 ( x - 1 ) = 65 = > 45 x = 90 = > x = 2 means , they meet after 2 hours after 7 am , ie , they meet at 9 am answer is a .
Answer: a
Question (general): a store reported total sales of $ 385 million for february of this year . if the total sales for the same month last year was $ 320 million , approximately what was the percent increase w in sales ?
Options: a ) 2 % , b ) 17 % , c ) 20 % , d ) 65 % , e ) 83 %
Rationale: "last year ' s sales = $ 320 million ; this year ' s sales = $ 385 million ; increase w = $ 65 million . now , 20 % of $ 320 million is $ 64 million , which is very close to actual increase of $ 65 million . answer : c ."
Answer: c
Question (general): a man saves 10 % of his monthly salary . if an account of dearness of things he is to increase his monthly expenses by 5 % , he is only able to save rs . 400 per month . what is his monthly salary ?
Options: a ) rs . 6500 , b ) rs . 7500 , c ) rs . 7200 , d ) rs . 7273 , e ) rs . 6300
Rationale: "income = rs . 100 expenditure = rs . 90 savings = rs . 10 present expenditure 90 + 90 * ( 5 / 100 ) = rs . 94.5 present savings = 100 – 94.5 = rs . 5.50 if savings is rs . 5.50 , salary = rs . 100 if savings is rs . 400 , salary = 100 / 5.5 * 400 = 7273 answer : d"
Answer: d
Question (physics): working individually , emma can wrap presents for 6 hours and troy can wrap presents in 8 hours . if emma and troy work together but independently at the task for 2 hours , at which point troy leaves , how many remaining hours will it take emma to complete the task alone ?
Options: a ) 30 / 12 , b ) 5 / 12 , c ) 3 / 4 , d ) 2 / 12 , e ) 3 / 5
Rationale: in first 2 hrs troy will finish 2 / 8 = 1 / 4 of work and emma will finish 2 / 6 work so total 1 / 4 + 1 / 3 = 7 / 12 work is finished and 1 - 7 / 12 = 5 / 12 work remaining . now emma will take ( 5 / 12 ) * 6 = 30 / 12 hrs to finish it . so answer is a .
Answer: a
Question (physics): the length of a rectangular plot is 20 metres more than its breadth . if the cost of fencing the plot @ rs . 26.50 per metre is rs . 8480 , what is the length of the plot in metres ?
Options: a ) 20 , b ) 200 , c ) 300 , d ) 90 , e ) 140
Rationale: "let length of plot = l meters , then breadth = l - 20 meters and perimeter = 2 [ l + l - 20 ] = [ 4 l - 40 ] meters [ 4 l - 40 ] * 26.50 = 8480 [ 4 l - 40 ] = 8480 / 26.50 = 320 4 l = 360 l = 360 / 4 = 90 meters . answer : d"
Answer: d
Question (general): find the last digit of ( 1021 ^ 3921 ) + ( 3081 ^ 3921 )
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "last digit of 1 st expression is 1 and second expression is also 1 as , 1 raised to any power will be 1 itself so , 1 + 1 = 2 so the last digit will be 2 answer : c"
Answer: c
Question (physics): a certain electric - company plan offers customers reduced rates for electricity used between 8 p . m . and 8 a . m . weekdays and 24 hours a day saturdays and sundays . under this plan , the reduced rates z apply to what fraction of a week ?
Options: a ) 1 / 2 , b ) 5 / 8 , c ) 9 / 14 , d ) 16 / 21 , e ) 9 / 10
Rationale: number of hours between 8 pm to 8 am = 12 number of hours with reduced rates = ( 12 * 5 ) + ( 24 * 2 ) hours with reduced rates z / total number of hours in a week = ( 12 * 5 ) + ( 24 * 2 ) / ( 24 * 7 ) = 108 / ( 24 * 7 ) = 9 / 14 answer : c
Answer: c
Question (geometry): the ratio of the volumes of two cubes is 125 : 216 . what is the ratio of their total surface areas ?
Options: a ) 13 : 18 , b ) 8 : 12 , c ) 1 : 12 , d ) 8 : 17 , e ) 1 : 11
Rationale: "ratio of the sides = ³ √ 125 : ³ √ 216 = 5 : 6 ratio of surface areas = 52 : 62 = 13 : 18 answer : a"
Answer: a
Question (general): the average weight of d , e and f is 42 kg . if the average weight of d and e be 35 kg and that of e and f be 41 kg , what is the weight of e ?
Options: a ) 23 kg , b ) 24 kg , c ) 25 kg , d ) 26 kg , e ) 27 kg
Rationale: let the weight of d , e and f are a , b and c respectively . average weight of d , e and f = 42 a + b + c = 42 × 3 = 126 - - - equation ( 1 ) average weight of d and e = 35 a + b = 35 × 2 = 70 - - - equation ( 2 ) average weight of e and f = 41 b + c = 41 × 2 = 82 - - - equation ( 3 ) equation ( 2 ) + equation ( 3 ) - equation ( 1 ) = > a + b + b + c - ( a + b + c ) = 70 + 82 - 126 = > b = 152 - 126 = 26 weight of b = 26 kg answer : d
Answer: d
Question (physics): two trains 121 meters and 165 meters in length respectively are running in opposite directions , one at the rate of 75 km and the other at the rate of 65 kmph . in what time will they be completely clear of each other from the moment they meet ?
Options: a ) 7.19 , b ) 7.17 , c ) 7.2 , d ) 7.35 , e ) 7.11
Rationale: "t = ( 121 + 165 ) / ( 75 + 65 ) * 18 / 5 t = 7.35 answer : d"
Answer: d
Question (general): find the smallest number which when divided by 12 and 15 leaves respective remainders of 8 and 11 .
Options: a ) 87 , b ) 97 , c ) 27 , d ) 21 , e ) 56
Rationale: "let ' n ' is the smallest number which divided by 12 and 15 leaves respective remainders of 8 and 11 . required number = ( lcm of 12 and 15 ) - ( common difference of divisors and remainders ) = ( 60 ) - ( 4 ) = 56 . answer : e"
Answer: e
Question (gain): a merchant marks his goods up by 20 % and then offers a discount of 10 % on the marked price . what % profit does the merchant make after the discount ?
Options: a ) 8 % , b ) 10 % , c ) 21 % , d ) 15 % , e ) 17 %
Rationale: "let the price be 100 . the price becomes 120 after a 20 % markup . now a discount of 10 % on 120 . profit = 108 - 100 8 % answer a"
Answer: a
Question (general): a batsman in his 20 th innings makes a score of 90 , and thereby increases his average by 2 . what is his average after the 20 th innings ? he had never been ’ not out ’ .
Options: a ) 52 , b ) 37 , c ) 39 , d ) 43 , e ) 42
Rationale: "average score before 20 th innings = 90 - 2 × 20 = 50 average score after 20 th innings = > 50 + 2 = 52 answer : a"
Answer: a
Question (general): s ( n ) is a n - digit number formed by attaching the first n perfect squares , in order , into one integer . for example , s ( 1 ) = 1 , s ( 2 ) = 14 , s ( 3 ) = 149 , s ( 4 ) = 14916 , s ( 5 ) = 1491625 , etc . how many digits are in s ( 99 ) ?
Options: a ) 350 , b ) 353 , c ) 354 , d ) 356 , e ) 357
Rationale: "focus on the points where the number of digits in squares change : 1 , 2 , 3 - single digit squares . first 2 digit number is 10 . 4 , 5 , . . . 9 - two digit squares . to get 9 , the last number with two digit square , think that first 3 digit number is 100 which is 10 ^ 2 . so 9 ^ 2 must be the last 2 digit square . 10 , 11 , 12 , . . . 31 - three digit squares . to get 31 , think of 1000 - the first 4 digit number . it is not a perfect square but 900 is 30 ^ 2 . 32 ^ 2 = 2 ^ 10 = 1024 , the first 4 digit square . 32 - 99 - four digit squares . to get 99 , think of 10,000 - the first 5 digit number which is 100 ^ 2 . so number of digits in s ( 99 ) = 3 * 1 + 6 * 2 + 22 * 3 + 68 * 4 = 3 + 12 + 66 + 272 = 353 ; answer : b"
Answer: b
Question (other): the h . c . f . of two numbers is 23 and the other two factors of their l . c . m . are 10 and 12 . the larger of the two numbers is :
Options: a ) 276 , b ) 295 , c ) 322 , d ) 345 , e ) 354
Rationale: "clearly , the numbers are ( 23 x 10 ) and ( 23 x 12 ) . larger number = ( 23 x 12 ) = 276 . answer : option a"
Answer: a
Question (general): how many figures are required to number the pages the pages of a book containing 1210 pages ?
Options: a ) 3533 , b ) 3833 , c ) 3333 , d ) 3633 , e ) 3733
Rationale: "1 to 9 = 9 * 1 = 9 10 to 99 = 90 * 2 = 180 100 to 999 = 900 * 3 = 2700 1000 to 1210 = 211 * 4 = 844 - - - - - - - - - - - 3733 answer : e"
Answer: e
Question (general): the average weight of a , b and c is 75 kg . if the average weight of a and b be 88 kg and that of b and c be 72 kg , then the weight of b is :
Options: a ) 60 kg , b ) 59 kg , c ) 62 kg , d ) 63 kg , e ) 61 kg
Rationale: "explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 75 x 3 ) = 225 â € ¦ . ( i ) a + b = ( 88 x 2 ) = 176 â € ¦ . ( ii ) b + c = ( 72 x 2 ) = 144 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 288 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 63 . b â € ™ s weight = 63 kg . answer d"
Answer: d
Question (general): a and b are mixed together in the ratio 9 : 11 . what is the weight of mixture , if 26.1 kg of a has been consumed in it ?
Options: a ) 56 , b ) 45 , c ) 58.2 , d ) 58 , e ) 46
Rationale: explanation : for 9 kg a , mixture = ( 9 + 11 ) kg . for 26.1 kg a , mixture = ( ( 20 / 9 ) x 26.1 ) kg = 58 kg . answer : d
Answer: d
Question (general): find the constant k so that : - x 2 - ( k + 12 ) x - 8 = - ( x - 2 ) ( x - 4 )
Options: a ) 11 , b ) 12 , c ) 18 , d ) 14 , e ) 15
Rationale: "- x 2 - ( k + 12 ) x - 8 = - ( x - 2 ) ( x - 4 ) : given - x 2 - ( k + 12 ) x - 8 = - x 2 + 6 x - 8 - ( k + 12 ) = 6 : two polynomials are equal if their corresponding coefficients are equal . k = - 18 : solve the above for k correct answer c"
Answer: c
Question (general): last year , company x paid out a total of $ 1 , 050,000 in salaries to its 31 employees . if no employee earned a salary that is more than 20 % greater than any other employee , what is the lowest possible salary that any one employee earned ?
Options: a ) $ 10,000 , b ) $ $ 28 , 378.37 , c ) $ 42,000 , d ) $ 50,000 , e ) $ 60,000
Rationale: "employee 1 earned $ x ( say ) employee 2 will not earn more than $ 1.2 x therfore , to minimize the salary of any one employee , we need to maximize the salaries of the other 30 employees ( 1.2 x * 30 ) + x = 1 , 050,000 solving for x = $ 28 , 378.37 answer b"
Answer: b
Question (general): if n is a positive integer and the product of all integers from 1 to n , inclusive , is a multiple of 350 , what is the least possible value of n ?
Options: a ) 5 , b ) 7 , c ) 12 , d ) 13 , e ) 14
Rationale: "350 = 2 * 5 * 5 * 7 so the least value forncan be 7 . b"
Answer: b
Question (other): the duplicate ratio of 2 : 3 is ?
Options: a ) 4 : 9 , b ) 1 : 4 , c ) 1 : 8 , d ) 1 : 18 , e ) 1 : 13
Rationale: "2 ^ 2 : 3 ^ 2 = 4 : 9 answer : a"
Answer: a
Question (geometry): the water level in a rectangular swimming pool measuring 40 feet by 25 feet is to be lowered by 6 inches . how many gallons of water must be removed ? ( 1 cu ft = 7.5 gallons )
Options: a ) 100 , b ) 250 , c ) 750 , d ) 3750 , e ) 5625
Rationale: "6 inches = 1 / 2 feet ( there are 12 inches in a foot . ) , so 40 * 25 * 1 / 2 = 500 feet ^ 3 of water must be removed , which equals to 500 * 7.5 = 3750 gallons . answer : d ."
Answer: d
Question (general): 3 maths classes : a , b and c take an algebra test . the average score of class a is 83 . the average score of class b is 76 . the average score of class c is 85 . the average score of class a and b is 79 and average score of class b and c is 81 . what is the average score of classes a , b , c ?
Options: a ) 81.8 , b ) 81.1 , c ) 81.2 , d ) 81.5 , e ) 81.9
Rationale: let the number of students in classes a , b and c be p , q and r respectively . then , total score of a = 83 p , total score of b = 76 q , total score of c = 85 r . also given that , ( 83 p + 76 q ) / ( p + q ) = 79 = > 4 p = 3 q . ( 76 q + 85 r ) / ( q + r ) = 81 = > 4 r = 5 q , = > q = 4 p / 3 and r = 5 p / 3 therefore , average score of a , b , c = ( 83 p + 76 q + 85 r ) / ( p + q + r ) = 978 / 12 = 81.5 answer : d
Answer: d
Question (physics): at a certain resort , each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants . the 3 restaurants are the family buffet , the dining room , and the snack bar . exactly 19 employees are trained to work in the family buffet , 18 are trained to work in the dining room , and 12 are trained to work in the snack bar . if 4 employees are trained to work in exactly 2 restaurants , how many employees are trained to work in all 3 restaurants ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "39 = 19 + 18 + 12 - 4 - 2 x 2 x = 19 + 18 + 12 - 4 - 39 = 45 - 39 = 6 x = 3 answer : b"
Answer: b
Question (geometry): the volume of a cube is 1728 cc . find its surface .
Options: a ) 864 , b ) 556 , c ) 255 , d ) 287 , e ) 267
Rationale: "a 3 = 1728 = > a = 12 6 a 2 = 6 * 12 * 12 = 864 answer : a"
Answer: a
Question (geometry): the length of rectangle is thrice its breadth and its perimeter is 40 m , find the area of the rectangle ?
Options: a ) 432 , b ) 212 , c ) 75 , d ) 992 , e ) 212
Rationale: "2 ( 3 x + x ) = 40 l = 15 b = 5 lb = 15 * 5 = 75 answer : c"
Answer: c
Question (geometry): a 25 cm wide path is to be made around a circular garden having a diameter of 4 meters . approximate area of the path is square meters is ?
Options: a ) 3.34 sq m , b ) 98.8 sq m , c ) 67.8 sq m , d ) 27.9 sq m , e ) 19.9 sq m
Rationale: "area of the path = area of the outer circle - area of the inner circle = ∏ { 4 / 2 + 25 / 100 } 2 - ∏ [ 4 / 2 ] 2 = ∏ [ 2.252 - 22 ] = ∏ ( 0.25 ) ( 4.25 ) { ( a 2 - b 2 = ( a - b ) ( a + b ) } = ( 3.14 ) ( 1 / 4 ) ( 17 / 4 ) = 53.38 / 16 = 3.34 sq m answer : a"
Answer: a
Question (physics): a train is 700 meter long is running at a speed of 21 km / hour . in what time will it pass a bridge of 130 meter length ?
Options: a ) 142.286 , b ) 251.228 , c ) 34 , d ) 200 , e ) 150.627
Rationale: "speed = 21 km / hr = 21 * ( 5 / 18 ) m / sec = 35 / 6 m / sec total distance = 700 + 130 = 830 meter time = distance / speed = 830 * ( 6 / 35 ) = 142.286 seconds . answer : a"
Answer: a
Question (probability): a coin is tossed 4 times . what is the probability of getting exactly 3 heads ?
Options: a ) 1 / 2 , b ) 1 / 4 , c ) 1 / 8 , d ) 1 / 16 , e ) 3 / 16
Rationale: the number of possible outcomes is 2 ^ 4 = 16 there are 4 ways to get exactly 3 heads . p ( exactly 3 heads ) = 4 / 16 = 1 / 4 the answer is b .
Answer: b
Question (other): the ratio of pens to pencils is 5 to 6 . there are 4 more pencils than pens . how many pencils are there ?
Options: a ) 12 , b ) 16 , c ) 20 , d ) 24 , e ) 28
Rationale: "let the number of pens be 5 x and the number of pencils be 6 x . 6 x - 5 x = 4 x = 4 the number of pencils is 24 . the answer is d ."
Answer: d
Question (physics): a train passes a station platform in 42 sec and a man standing on the platform in 12 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 227 , b ) 450 , c ) 460 , d ) 480 , e ) 171
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 12 = 180 m . let the length of the platform be x m . then , ( x + 180 ) / 42 = 15 = > x = 450 m . answer : b"
Answer: b
Question (physics): how many pieces of 75 cm can be cut from a rope 45 meters long ?
Options: a ) 30 , b ) 40 , c ) 60 , d ) none , e ) can not be determined
Rationale: "explanation : total pieces of 75 cm that can be cut from a rope of 45 meters long is = ( 45 meters ) / ( 75 cm ) = ( 45 meters ) / ( 0.75 meters ) = 60 answer : c"
Answer: c
Question (other): in what ratio mental a at rs . 68 per kg be mixed with another metal at rs . 96 per kg so that cost of alloy ( mixture ) is rs . 75 per kg ?
Options: a ) 5 : 8 , b ) 3 : 1 , c ) 3 : 7 , d ) 9 : 5 , e ) 9 : 8
Rationale: "( 96 - 75 ) / ( 75 - 68 ) = 21 / 7 = 3 / 1 answer : b"
Answer: b
Question (gain): a shopkeeper fixes the marked price of an item 30 % above its cost price . the percentage of discount allowed to gain 6 % is
Options: a ) 18.45 % , b ) 18.46 % , c ) 18.47 % , d ) 18.48 % , e ) none of these
Rationale: "explanation : let the cost price = rs 100 then , marked price = rs 130 required gain = 6 % , so selling price = rs 106 discount = 130 - 106 = 24 discount % = ( 24 / 130 ) * 100 = 18.46 % option b"
Answer: b
Question (general): the product of two numbers is 120 and the sum of their squares is 289 . find the sum ?
Options: a ) 23 , b ) 20 , c ) 15 , d ) 26 , e ) 28
Rationale: "nos a and b ab = 120 and a 2 + b 2 = 289 ( a + b ) 2 = 529 a + b = root ( 529 ) = 23 answer a"
Answer: a
Question (general): find the sum of first 26 natural numbers
Options: a ) 470 , b ) 468 , c ) 465 , d ) 351 , e ) 485
Rationale: "explanation : sum of n natural numbers = n ( n + 1 ) / 2 = 26 ( 26 + 1 ) / 2 = 26 ( 27 ) / 2 = 351 answer : option d"
Answer: d
Question (geometry): in an electric circuit , two resistors with resistances m and n are connected in parallel . in this case , if p is the combined resistance of these two resistors , then the reciprocal of p is equal to the sum of the reciprocals of m and n . what is p in terms of m and n ?
Options: a ) ( n - m )
b ) mn / ( m + n )
c ) ( nm )
d ) ( n - m ) / ( m + n )
e ) none of these
Rationale: the wording is a bit confusing , though basically we are told that 1 / p = 1 / m + 1 / n , from which it follows that p = mn / ( m + n ) . answer : b
Answer: b
Question (general): x + ( 1 / x ) = 3 find x ^ 2 + ( 1 / x ^ 2 )
Options: a ) 2.25 , b ) 7 , c ) 4.25 , d ) 5.25 , e ) 6.25
Rationale: "squaring on both sides ( x + 1 / x ) ^ 2 = 3 ^ 2 x ^ 2 + 1 / x ^ 2 = 9 - 2 x ^ 2 + 1 / x ^ 2 = 7 answer : b"
Answer: b
Question (general): a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 8 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 8 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 443 , b ) 450 , c ) 465 , d ) 468 , e ) 475
Rationale: "total number of installments = 52 payment per installment for the first 8 installments = 410 payment per installment for the remaining 32 installments = 410 + 65 = 475 average = ( 8 * 410 + 44 * 475 ) / 52 = 465 answer c"
Answer: c
Question (general): the sum of the fourth and twelfth term of an arithmetic progression is 20 . what is the sum of the first 20 terms of the arithmetic progression ?
Options: a ) 300 , b ) 120 , c ) 150 , d ) 170 , e ) 200
Rationale: "n th term of a . p . is given by a + ( n - 1 ) d 4 th term = a + 3 d 12 th term = a + 11 d given a + 3 d + a + 11 d = 20 - - > 2 a + 14 d = 20 - - > a + 7 d = 10 sum of n term of a . p = n / 2 [ 2 a + ( n - 1 ) d ] subsitiuing n = 20 . . . we get 20 / 2 [ 2 a + 14 d ] = 20 [ a + 7 d ] = 20 * 10 = 200 . . . answer is e . . ."
Answer: e
Question (physics): a alone can finish a work in 10 days which b alone can finish in 15 days . if they work together and finish it , then out of a total wages of rs . 3100 , a will get :
Options: a ) rs . 1200 , b ) rs . 1500 , c ) rs . 1860 , d ) rs . 2000 , e ) none of these
Rationale: explanation : ratio of working days of a : b = 10 : 15 therefore , their wages ratio = reverse ratio = 15 : 10 therefore , a will get 15 units of ratio total ratio = 25 1 unit of ratio = 3100 / 25 = 124 so , a ’ s amount = 124 × 15 = rs . 1860 . answer : option c
Answer: c
Question (general): crazy eddie has a key chain factory . eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price , and thus increased the profit from the sale of each key chain from 40 % of the selling price to 50 % of the selling price . if the manufacturing cost is now $ 50 , what was it before the decrease ?
Options: a ) $ 20 , b ) $ 40 , c ) $ 50 , d ) $ 80 , e ) $ 60
Rationale: "deargoodyear 2013 , i ' m happy to help . this is a relatively straightforward problem , not very challenging . btw , crazy eddiewas the actually name of an electronics chain on the east coast of the usa back in the 1970 s . manufacturing now is $ 50 . they now are making a 50 % profit , so the selling price must be $ 100 . they had this same selling price , $ 100 , before they made the change , and had a profit of 40 % , so the manufacturing must have been $ 60 . answer = ( e ) ."
Answer: e
Question (physics): while driving from a - ville to b - town , harriet drove at a constant speed of 110 kilometers per hour . upon arriving in b - town , harriet immediately turned and drove back to a - ville at a constant speed of 140 kilometers per hour . if the entire trip took 5 hours , how many minutes did it take harriet to drive from a - ville to b - town ?
Options: a ) 138 , b ) 148 , c ) 150 , d ) 162 , e ) 168
Rationale: "5 hr = 300 min . if harriet spend equal hrs on each leg she will spend 150 min on each . since speed a - b is less than speed b - a and distance on each leg is the same , time spent on a - b is more than 150 min , which mean we can eliminate ans . a , b and c . now let plug in ans . d or e and verify which one give same distance on each leg . e . t = 168 min * leg a - b - - - > d = 110.168 / 60 = 18480 / 60 * leg b - a - - - - > d = 140 * 132 / 60 = 18480 / 60 so the correct ans . ise"
Answer: e
Question (general): if the average of 1 , 2 , 4 , 5 , 6 , 9 , 9 , 10 , 12 and x is 7 , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 12 , e ) 13
Rationale: "sum of the deviations of the numbers in the set from the mean is always zero 1 , 2 , 4 , 5 , 6 , 9 , 9 , 10 , 12 mean is 7 so the list is - 6 - 5 - 3 - 2 - 1 + 2 + 2 + 3 + 5 . . . this shud total to zero but this is - 5 , hence we need a number that is 5 more than the mean to get a + 5 and make it zero hence the answer is 7 + 5 = 12 d"
Answer: d