Cheukting/mathqa huggingface dataset:
Question (physics): mr and mrs a are opposite to each other . the distance between mr a and mrs a are 120 km . the speed of mr a and mrs a are 30 kmph , 10 kmph respectively . one bee is running between mr a nose to mrs a nose and returning back to mr a nose . the speed of bee is 60 kmph . then how far bee traveled ?
Options: a ) 160 km , b ) 170 km , c ) 180 km , d ) 190 km , e ) 130 km
Rationale: 30 x + 10 x = 120 x = 3 hrs speed of bee = 60 kmph distance traveled by bee = speed * time taken = 60 * 3 = 180 km answer : c
Answer: c
Question (general): each machine of type a has 2 steel parts and 3 chrome parts . each machine of type b has 3 steel parts and 5 chrome parts . if a certain group of type a and type b machines has a total of 40 steel parts and 32 chrome parts , how many machines are in the group
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: look at the below representation of the problem : steel chrome total a 2 3 40 > > no . of type a machines = 40 / 5 = 8 b 3 5 32 > > no . of type b machines = 32 / 8 = 4 so the answer is 12 i . e a . hope its clear .
Answer: a
Question (gain): because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 4 times as much as mork did , what was their combined tax rate ?
Options: a ) 32 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 38 %
Rationale: "let x be mork ' s income , then mindy ' s income is 4 x . the total tax paid is 0.4 x + 1.2 x = 1.6 x 1.6 x / 5 x = 0.32 the answer is a ."
Answer: a
Question (general): find the average of all the numbers between 6 and 34 which are divisible by 5 ?
Options: a ) 32 , b ) 20 , c ) 28 , d ) 11 , e ) 18
Rationale: "average = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = 20 . answer : b"
Answer: b
Question (general): set # 1 = { a , b , c , d , e } set # 2 = { k , l , m , n , o , p } there are these two sets of letters , and you are going to pick exactly one letter from each set . what is the probability of picking at least one vowel ?
Options: a ) 1 / 6 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 5 / 6
Rationale: so not a vowel in set - 1 : 3 / 5 and not a vowel in ser - 2 : 5 / 6 now , 3 / 5 ∗ 5 / 6 = 12 this is for not a vowel . then for at least one vowel will be = 1 − 1 / 2 = 1 / 2 answer will be c .
Answer: c
Question (other): in township k , 1 / 5 of the housing units are equiped with cable tv . if 1 / 15 of the housing units , including 1 / 3 of those that are equiped with cable tv , are equipped with videocassette recorders , what fraction of the housing units have neither cable tv nor videocassette recorders ?
Options: a ) 23 / 30 , b ) 11 / 15 , c ) 7 / 10 , d ) 4 / 5 , e ) 2 / 15
Rationale: "1 / 5 - - cable tv ( this includes some data from video cassette recorder ) 1 / 15 - - video cassette recorder including 1 / 3 ( equiped with cable tv ) i . e . 1 / 3 ( 1 / 5 ) = 1 / 15 therefore only video cassette recorder = 1 / 15 - 1 / 15 = 0 total = 1 / 5 + 0 + neither cable tv nor videocassette recorders 1 = 1 / 5 + neither cable tv nor videocassette recorders therefore neither cable tv nor videocassette recorders = 1 - 1 / 5 = 4 / 5 hence d ."
Answer: d
Question (physics): a man walking at the rate of 5 km / hr crosses a bridge in 15 minutes . the length of the bridge ( in metres ) is
Options: a ) 600 , b ) 750 , c ) 1000 , d ) 1250 , e ) none of these
Rationale: "explanation : speed = ( 5 × 5 / 18 ) m / sec = 25 / 18 m / sec . distance covered in 15 minutes = ( 25 / 18 × 15 × 60 ) m = 1250 m . answer : d"
Answer: d
Question (general): a student is ranked 17 th from right and 5 th from left . how many students are there in totality ?
Options: a ) 18 , b ) 19 , c ) 20 , d ) 21 , e ) 22
Rationale: "from right 17 , from left 5 total = 17 + 5 - 1 = 21 answer : d"
Answer: d
Question (gain): a reduction of 46 % in the price of bananas would enable a man to obtain 64 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 2.45 , b ) 8.45 , c ) 7.45 , d ) 3.45 , e ) 1.45
Rationale: "explanation : 40 * ( 46 / 100 ) = 18.4 - - - 64 ? - - - 12 = > rs . 3.45 answer : d"
Answer: d
Question (general): what should be the least number to be added to the 11002 number to make it divisible by 11 ?
Options: a ) 12 , b ) 9 , c ) 18 , d ) 77 , e ) 26
Rationale: "answer : 9 option : b"
Answer: b
Question (geometry): in right triangle abc , ac is the hypotenuse . if ac is 50 and ab + bc = 70 , what is the area of the triangle abc ?
Options: a ) 225
b ) 450
c ) 25 √ 2
d ) 200
e ) 600
Rationale: square ab + bc = 70 : ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 4900 . since ( ac ) ^ 2 = ( ab ) ^ 2 + ( bc ) ^ 2 = 50 ^ 2 = 2500 , then ( ab ) ^ 2 + 2 * ab * bc + ( bc ) ^ 2 = 2500 + 2 * ab * bc = 4900 . 2500 + 2 * ab * bc = 4900 . ab * bc = 1200 . the area = 1 / 2 * ab * bc = 600 . answer : e .
Answer: e
Question (general): the ratio between x and y is 8 / 5 ; x is increased by 10 and y is multiplied by 10 , what is the ratio between the new values of x and y ?
Options: a ) 8 / 5 , b ) 5 / 8 , c ) 1 , d ) 10 , e ) it can not be determined
Rationale: "ratio = 8 k / 5 k = 8 / 5 , 16 / 10 , etc . x and y are decreased by 5 - - > ( 8 k + 10 ) / ( 5 k * 10 ) new ratio can be 18 / 50 , 26 / 100 , etc . answer : e"
Answer: e
Question (general): the sum of three consecutive multiples of 3 is 72 . what is the largest number ?
Options: a ) 21 , b ) 24 , c ) 27 , d ) 36 , e ) 39
Rationale: "let the numbers be 3 x , 3 x + 3 and 3 x + 6 . then , 3 x + ( 3 x + 3 ) + ( 3 x + 6 ) = 72 9 x = 63 x = 7 largest number = 3 x + 6 = 27 . answer : c"
Answer: c
Question (geometry): cubes with each side one inch long are glued together to form a larger cube . the larger cube ' s face is painted with red color and the entire assembly is taken apart . 22 small cubes are found with no paints on them . how many of unit cubes have at least one face that is painted red ?
Options: a ) 64 , b ) 72 , c ) 86 , d ) 98 , e ) 103
Rationale: "use the options . the options which after getting added to 27 shows a cube of a number could be right . here 64 + 22 = 86 72 + 22 = 94 86 + 22 = 108 98 + 22 = 120 103 + 22 = 125 - - - ( 5 * 5 * 5 ) so we have 103 as the answer ! e"
Answer: e
Question (general): the average age of an adult class is 40 years . 12 new students with an avg age of 34 years join the class . therefore decreasing the average by 4 years . find what was the original average age of the class ?
Options: a ) 6 , b ) 12 , c ) 16 , d ) 20 , e ) 22
Rationale: "let original strength = y then , 40 y + 12 x 34 = ( y + 12 ) x 36 â ‡ ’ 40 y + 408 = 36 y + 432 â ‡ ’ 4 y = 48 â ˆ ´ y = 6 a"
Answer: a
Question (geometry): the ratio of the volumes of two cubes is 2197 : 1331 . what is the ratio of their total surface areas ?
Options: a ) 169 : 121 , b ) 169 : 127 , c ) 169 : 191 , d ) 121 : 169 , e ) 121 : 182
Rationale: "explanation : ratio of the sides = ³ √ 2197 : ³ √ 1331 = 13 : 11 ratio of surface areas = 13 ^ 2 : 11 ^ 2 = 169 : 121 answer : option a"
Answer: a
Question (physics): a train 150 m long crosses a platform 120 m long in 10 sec ; find the speed of the train ?
Options: a ) 87 kmph , b ) 65 kmph , c ) 97 kmph , d ) 16 kmph , e ) 18 kmph
Rationale: "d = 150 + 120 = 270 t = 10 s = 270 / 10 * 18 / 5 = 97 kmph answer : c"
Answer: c
Question (general): there were totally 100 men . 85 are married . 75 have t . v , 85 have radio , 70 have a . c . how many men have t . v , radio , a . c and also married ?
Options: a ) 11 , b ) 12 , c ) 13 , d ) 14 , e ) 15
Rationale: "100 - ( 100 - 85 ) - ( 100 - 75 ) - ( 100 - 85 ) - ( 100 - 70 ) = 100 - 15 - 25 - 15 - 30 = 100 - 85 = 15 answer : e"
Answer: e
Question (physics): two interconnected , circular gears travel at the same circumferential rate . if gear a has a diameter of 10 centimeters and gear b has a diameter of 50 centimeters , what is the ratio of the number of revolutions that gear a makes per minute to the number of revolutions that gear b makes per minute ?
Options: a ) 1 : 5 , b ) 9 : 25 , c ) 5 : 1 , d ) 25 : 9 , e ) can not be determined from the information provided
Rationale: "same circumferential rate means that a point on both the gears would take same time to come back to the same position again . hence in other words , time taken by the point to cover the circumference of gear a = time take by point to cover the circumference of gear b time a = 2 * pi * 25 / speed a time b = 2 * pi * 5 / speed b since the times are same , 50 pi / speed a = 10 pi / speed b speeda / speed b = 50 pi / 30 pi = 5 / 1 correct option : c"
Answer: c
Question (physics): a trader sells 45 meters of cloth for rs . 4500 at the profit of rs . 14 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) rs . 80 , b ) rs . 86 , c ) rs . 90 , d ) rs . 95 , e ) none of these
Rationale: "sp of 1 m of cloth = 4500 / 45 = rs . 100 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 105 - rs . 14 = rs . 86 . answer : 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 20 km , if the person completes half of the distance by walking and the other half by running ?
Options: a ) 2.75 , b ) 3.25 , c ) 3.75 , d ) 4.25 , e ) 4.75
Rationale: "time = 10 / 4 + 10 / 8 = 30 / 8 = 3.75 hours the answer is c ."
Answer: c
Question (general): 12 times a number gives 156 . the number is
Options: a ) 11 , b ) 12 , c ) 13 , d ) none , e ) can not be determined
Rationale: "explanation : let the number be ' n ' 12 × n = 156 ⇒ n = 13 correct option : c"
Answer: c
Question (geometry): if the sides of a triangle are 30 cm , 28 cm and 10 cm , what is its area ?
Options: a ) 120 , b ) 110 , c ) 130 , d ) 140 , e ) 150
Rationale: "the triangle with sides 30 cm , 28 cm and 10 cm is right angled , where the hypotenuse is 30 cm . area of the triangle = 1 / 2 * 28 * 10 = 140 cm 2 answer : option d"
Answer: d
Question (geometry): if the side length of square b is sqrt ( 3 ) times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 9
b ) 6
c ) 4
d ) 3
e ) 2
Rationale: let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 3 ) x ) ^ 2 = 3 x ^ 2 . the answer is d .
Answer: d
Question (gain): the price of an item is discounted 10 percent on day 1 of a sale . on day 2 , the item is discounted another 15 percent , and on day 3 , it is discounted an additional 20 percent . the price of the item on day 3 is what percentage of the sale price on day 1 ?
Options: a ) 28 % , b ) 40 % , c ) 68 % , d ) 70 % , e ) 72 %
Rationale: "let initial price be 1000 price in day 1 after 10 % discount = 900 price in day 2 after 15 % discount = 765 price in day 3 after 20 % discount = 612 so , price in day 3 as percentage of the sale price on day 1 will be = 612 / 900 * 100 = > 68 % answer will definitely be ( c )"
Answer: c
Question (general): an author received $ 0.80 in royalties for each of the first 100000 copies of her book sold , and $ 0.30 in royalties for each additional copy sold . if she received a total of $ 260000 in royalties , how many copies of her book were sold ?
Options: a ) 700,000 , b ) 300,000 , c ) 380,000 , d ) 400,000 , e ) 420,000
Rationale: total royalties for first 100.000 books = . 8 * 100,000 = 80,000 total royalties for the rest of the books = 260,000 - 80,000 = 180,000 remaining books = 180,000 / 0.3 = 600,000 total books = 600,000 + 100,000 = 700,000 answer a
Answer: a
Question (probability): in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 6 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 7 , e ) 7 / 8
Rationale: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 6 of the garden is green , so , since all the flowers must be either green or yellow , we know that 5 / 6 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 5 / 6 * 1 / 2 = 3 / 7 , or d ."
Answer: d
Question (general): virginia , adrienne , and dennis have taught history for a combined total of 102 years . if virginia has taught for 9 more years than adrienne and for 9 fewer years than dennis , for how many years has dennis taught ?
Options: a ) 23 , b ) 32 , c ) 35 , d ) 43 , e ) 44
Rationale: "let number of years taught by virginia = v number of years taught by adrienne = a number of years taught by dennis = d v + a + d = 96 v = a + 9 = > a = v - 9 v = d - 9 = > a = ( d - 9 ) - 9 = d - 18 d - 9 + d - 18 + d = 102 = > 3 d = 102 + 27 = 129 = > d = 43 answer d"
Answer: d
Question (general): the age of father 10 years ago was thirce the age of his son . 10 years hence , father ’ s age will be twice that of his son . the ration of their present ages is :
Options: a ) 5 : 2 , b ) 7 : 3 , c ) 9 : 2 , d ) 13 : 4 , e ) none of these
Rationale: solution let the ages of father and son 10 year ago be 3 x and x years respectively . then , ( 3 x + 10 ) + 10 = 2 [ ( x + 10 ) + 10 ⇔ 3 x + 20 = 2 x + 40 ⇔ x = 20 . ∴ required ratio = ( 3 x + 10 ) : ( x + 10 ) = 70 : 30 : 7 : 3 . answer b
Answer: b
Question (general): a one - foot stick is marked in 1 / 2 and 1 / 4 portion . how many total markings will there be , including the end points ?
Options: a ) 8 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "lcm of 8 = 4 1 / 2 marking are ( table of 2 ) 0 . . . . . . 2 . . . . . . . . . . . 4 ( total = 3 ) 1 / 4 marking are ( table of 1 ) 0 . . . . . . . 1 . . . . . . 2 . . . . . . 3 . . . . . . . . 4 ( total = 5 ) overlapping markings are 0 . . . . . . . . 2 . . . . . . . . . 4 ( total = 3 ) total markings = 3 + 5 - 3 = 5 answer = c"
Answer: c
Question (general): if integer k is equal to the sum of all even multiples of 25 between 200 and 600 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 11 , d ) 13 , e ) 17
Rationale: "if we break down what the stem is asking what is the sum of all mult of 50 between 200 and 600 . using arithmetic progression to find n : 600 = 200 + ( n - 1 ) 50 400 + 50 = 50 n 450 = 50 n = > n = 9 the sum would be : 9 * mean mean = [ 600 + 200 ] / 2 = 400 9 * 400 = 3600 d"
Answer: d
Question (general): how many integers between 324,700 and 448,600 have tens digit 1 and units digit 3 ?
Options: a ) 10,300 , b ) 8,030 , c ) 1,253 , d ) 1,252 , e ) 1,239
Rationale: "the integers are : 324,713 324,813 etc . . . 448,513 the number of integers is 4486 - 3247 = 1239 the answer is e ."
Answer: e
Question (general): g ( x ) is defined as the product of all even integers k such that 0 < k ≤ x . for example , g ( 14 ) = 2 × 4 × 6 × 8 × 10 × 12 × 14 . if g ( r ) is divisible by 4 ^ 11 , what is the smallest possible value for r ?
Options: a ) 22 , b ) 24 , c ) 28 , d ) 32 , e ) 44
Rationale: "g ( r ) = 4 ^ 11 = 2 ^ 22 . so we have to find a product with atleast 22 2 ' s in it . in option 1 22 the total no of 2 ' s = [ 22 / 2 ] + [ 22 / 4 ] + [ 22 / 8 ] + [ 22 / 16 ] = 11 + 5 + 2 + 1 = 19 in option 2 24 the total no of 2 ' s = [ 24 / 2 ] + [ 24 / 4 ] + [ 24 / 8 ] + [ 24 / 16 ] = 12 + 6 + 3 + 1 = 22 . hence b"
Answer: b
Question (general): if 1 / 12 of the passengers on a ship are from north america , 1 / 8 are europeans , 1 / 3 are from africa , 1 / 6 are from asia and the remaining 35 people are citizens of other continents , then how many passengers are on board the ship ?
Options: a ) 110 , b ) 115 , c ) 120 , d ) 125 , e ) 130
Rationale: 1 / 12 + 1 / 8 + 1 / 3 + 1 / 6 = ( 2 + 3 + 8 + 4 ) / 24 = 17 / 24 let x be the number of passengers on the ship . 35 = ( 7 / 24 ) x x = 120 the answer is c .
Answer: c
Question (general): 54671 - 14456 - 33466 = ?
Options: a ) 2449 , b ) 5449 , c ) 6749 , d ) 6449 , e ) 6468
Rationale: "c if we calculate we will get 6749"
Answer: c
Question (geometry): one side of a rectangular field is 15 m and one of its diagonal is 17 m . find the area of the field .
Options: a ) 100
b ) 120
c ) 150
d ) 180
e ) none
Rationale: solution other side = √ ( 17 ) 2 - ( 15 ) 2 = √ 289 - 225 = √ 64 = 8 m . ∴ area = ( 15 x 8 ) m 2 = 120 m 2 . answer b
Answer: b
Question (general): a gambler bought $ 3,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 13 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 3 more or 3 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 2,040 , b ) $ 2,120 , c ) $ 2,240 , d ) $ 1,920 , e ) $ 1,400
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 13 : x + x - 3 = 13 - - > x = 8 : 8 $ 20 chips were lost and 8 - 2 = 6 $ 100 chips were lost . total worth of chips lost is 8 * 20 + 6 * 100 = $ 760 , so the gambler kept $ 3,000 - $ 760 = $ 2,240 . answer : c ."
Answer: c
Question (general): the ages of two person differ by 20 years . if 7 years ago , the elder one be 5 times as old as the younger one , their present ages ( in years ) are respectively
Options: a ) 30 , 10 , b ) 32 , 12 , c ) 29 , 9 , d ) 50 , 30 , e ) 20,10
Rationale: "let their ages be x and ( x + 20 ) years . then , 5 ( x - 7 ) = ( x + 20 - 7 ) = > 4 x = 48 = > x = 12 their present ages are 32 years and 12 year . answer : b"
Answer: b
Question (general): how many integers between 1 and 10 ^ 18 are such that the sum of their digits is 2 ?
Options: a ) 161 , b ) 171 , c ) 181 , d ) 191 , e ) 201
Rationale: "the integers with a sum of 2 are : 2 , 20 , 200 , . . . , 2 * 10 ^ 17 and there are 18 integers in this list . also , these integers have a sum of 2 : 11 101 , 110 1001 , 1010 , 1100 etc . . . the number of integers in this list is 1 + 2 + . . . + 17 thus , the total number of integers is 1 + 2 + . . . + 17 + 18 = 18 * 19 / 2 = 171 the answer is b ."
Answer: b
Question (general): how many positive integers less than 27 are prime numbers , odd multiples of 5 , or the sum of a positive multiple of 2 and a positive multiple of 4 ?
Options: a ) 27 , b ) 25 , c ) 24 , d ) 20 , e ) 22
Rationale: "9 prime numbers less than 28 : { 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 } 3 odd multiples of 5 : { 5 , 15 , 25 } 11 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4 : { 6 , 8 , 10 , 12 , 14 , 16 , 18 , 20 , 22 , 24 , 26 } notice , that 5 is in two sets , thus total # of integers satisfying the given conditions is 9 + 3 + 11 - 1 = 22 . answer : e ."
Answer: e
Question (other): in a corporation , 50 percent of the male employees and 40 percent of the female employees are at least 35 years old . if 42 percent of all the employees are at least 35 years old , what fraction of the employees in the corporation are females ?
Options: a ) 3 / 5 , b ) 2 / 3 , c ) 3 / 4 , d ) 4 / 5 , e ) 5 / 6
Rationale: you can use the weighted averages formula for a 10 sec solution . no of females / no of males = ( 50 - 42 ) / ( 42 - 40 ) = 4 / 1 no of females as a fraction of total employees = 4 / ( 4 + 1 ) = 4 / 5 ; answer : d
Answer: d
Question (physics): if 4 men working 10 hours a day earn rs . 1400 per week , then 9 men working 6 hours a day will earn how much per week ?
Options: a ) rs 840 , b ) rs 1320 , c ) rs 1620 , d ) rs 1890 , e ) none of these
Rationale: "explanation : ( men 4 : 9 ) : ( hrs / day 10 : 6 ) : : 1400 : x hence 4 * 10 * x = 9 * 6 * 1400 or x = 9 * 6 * 1400 / 4 * 10 = 1890 answer : d"
Answer: d
Question (geometry): if a rectangular billboard has an area of 120 square feet and a perimeter of 46 feet , what is the length of each of the shorter sides ?
Options: a ) 4 , b ) 7 , c ) 8 , d ) 13 , e ) 26
Rationale: "this question can be solved algebraically or by testing the answers . we ' re told that a rectangle has an area of 120 and a perimeter of 46 . we ' re asked for the length of one of the shorter sides of the rectangle . since the answers are all integers , and the area is 120 , the shorter side will almost certainly be less than 10 ( since 10 x 10 = 100 , but we ' re not dealing with a square ) . answer b ( 7 ) does not divide evenly into 120 , let ' s test answer c : 8 if . . . the shorter side = 8 . . . the area = 120 . . . . 120 / 8 = 15 = the longer side perimeter = 8 + 8 + 15 + 15 = 46 c"
Answer: c
Question (physics): a car gets 33 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 16 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
Options: a ) 168 , b ) 172 , c ) 176 , d ) 180 , e ) 184
Rationale: "originally , the distance the car could go on a full tank was 16 * 33 = 528 miles . after it has been modified , the car can go 33 / 0.75 = 44 miles per gallon . on a full tank , the car can go 16 * 44 = 704 miles , thus 176 miles more . the answer is c ."
Answer: c
Question (general): for each 6 - month period during a light bulb ' s life span , the odds of it not burning out from over - use are half what they were in the previous 6 - month period . if the odds of a light bulb burning out during the first 6 - month period following its purchase are 2 / 7 , what are the odds of it burning out during the period from 6 months to 1 year following its purchase ?
Options: a ) 5 / 27 , b ) 2 / 9 , c ) 1 / 2 , d ) 4 / 9 , e ) 2 / 3
Rationale: "p ( of not burning out in a six mnth period ) = 1 / 2 of p ( of not burning out in prev 6 mnth period ) p ( of burning out in 1 st 6 mnth ) = 2 / 7 - - - > p ( of not burning out in 1 st 6 mnth ) = 1 - 2 / 7 = 5 / 7 - - - - > p ( of not burning out in a six mnth period ) = 1 / 2 * 5 / 7 = 1 / 3 - - - > p ( of burning out in a six mnth period ) = 1 - 1 / 3 = 2 / 3 now p ( of burning out in 2 nd six mnth period ) = p ( of not burning out in 1 st six mnth ) * p ( of burning out in a six mnth ) = 5 / 7 * 2 / 3 = 1 / 2 ans c"
Answer: c
Question (general): shekar scored 76 , 65 , 82 , 67 and 55 marks in mathematics , science , social studies , english and biology respectively . what are his average marks ?
Options: a ) 65 , b ) 69 , c ) 75 , d ) 85 , e ) 90
Rationale: "explanation : average = ( 76 + 65 + 82 + 67 + 55 ) / 5 = 375 / 5 = 69 hence average = 69 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 2500 resolutions ?
Options: a ) 1187 m , b ) 1704 m , c ) 2179 m , d ) 3520 m , e ) 4297 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 2500 resolutions . = 2500 * 2 * 22 / 7 * 22.4 = 352000 cm = 3520 m answer : d"
Answer: d
Question (general): the average of 10 numbers is 23 . if each number is increased by 4 , what will the new average be ?
Options: a ) 20 , b ) 27 , c ) 72 , d ) 28 , e ) 82
Rationale: "sum of the 10 numbers = 230 if each number is increased by 4 , the total increase = 4 * 10 = 40 the new sum = 230 + 40 = 270 the new average = 270 / 10 = 27 . answer : b"
Answer: b