Cheukting/mathqa huggingface dataset:
Question (general): ( 12345679 x 72 ) = ?
Options: a ) 88888888 , b ) 888888888 , c ) 898989898 , d ) 9999999998 , e ) none
Rationale: "explanation : 12345679 x 72 = 12345679 x ( 70 + 2 ) = 12345679 x 70 + 12345679 x 2 = 864197530 + 24691358 = 888888888 answer : option b"
Answer: b
Question (probability): a jar contains only red , yellow , and orange marbles . if there are 3 red , 5 yellow , and 4 orange marbles , and 3 marbles are chosen from the jar at random without replacing any of them , what is the probability that 2 yellow , 1 red , and no orange marbles will be chosen ?
Options: a ) 1 / 60 , b ) 1 / 45 , c ) 2 / 45 , d ) 3 / 22 , e ) 5 / 22
Rationale: 5 c 2 * 3 c 1 = 10 * 3 = 30 12 c 3 = 220 3 / 22 answer : d
Answer: d
Question (general): if 10 ! - 2 * ( 5 ! ) ^ 2 is divisible by 10 ^ n , what is the greatest value of n ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: = 10 ∗ 9 ∗ 8 ∗ 7 ∗ 6 ∗ 5 ! − 2 ∗ 5 ! ∗ 5 ∗ 4 ∗ 3 ∗ 2 ∗ 1 = 5 ! ∗ 10 ∗ 3 ∗ 8 ( 125 ) = 5 ∗ ( 2 ∗ 2 ) ∗ 3 ∗ 2 ∗ ( 5 ∗ 2 ) ∗ 24 ∗ 5 ∗ 5 ∗ 5 = 5 ∗ 2 ∗ 5 ∗ 2 ∗ 5 ∗ 2 ∗ 5 ∗ 2 ∗ 24 ∗ 5 ∗ 3 = 10 ^ 4 ∗ 2 ^ 4 ∗ 5 ∗ 3 = 10 ^ 4 ∗ 5 ∗ 2 ∗ 12 ∗ 3 = 10 ^ 5 ∗ 36 answer : e
Answer: e
Question (general): in a 3 digit number , the 100 digit is 2 more than the tens digit and the units digit is 2 less than the tens digit . if the sum of the digits is 27 , find the number ?
Options: a ) 867 , b ) 1179 , c ) 1196 , d ) 1098 , e ) 1197
Rationale: e 1197 let the three digit numbers be 100 a + 10 b + c a = b + 2 c = b - 2 a + b + c = 3 b = 27 = > b = 9 so a = 11 and b = 7 hence the three digit number is : 1197
Answer: e
Question (gain): a man sold 20 articles for $ 60 and gained 20 % . how many articles should he sell for $ 90 to incur a loss 10 % ?
Options: a ) 45 , b ) 41.2 , c ) 40 , d ) 50 , e ) 48
Rationale: "production cost per article : $ 60 * ( 100 % - 20 % ) / 20 = $ 2.40 required production costs for a loss of 20 % : $ 90 * ( 100 % + 10 % ) = $ 99 number of articles to be sold for $ 108 to incur a 20 % loss : $ 99 / $ 2.40 = 41.2 thus , solution b is correct ."
Answer: b
Question (gain): at what rate percent on simple interest will rs . 750 amount to rs . 900 in 2 years ?
Options: a ) 10 % , b ) 2 % , c ) 4 % , d ) 5 % , e ) 3 %
Rationale: "150 = ( 750 * 2 * r ) / 100 r = 10 % answer : a"
Answer: a
Question (general): what least number must be added to 686 , so that the sum is completely divisible by 5 ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 4 , e ) 6
Rationale: "if we divide 686 by 5 remainder is 1 5 - 1 = 4 answer : d"
Answer: d
Question (physics): 45 men took a dip in a water tank 40 m long and 20 m broad on a religious day . if the average displacement of water by a man is 4 m 3 , then the rise in the water level in the tank will be :
Options: a ) 20 cm , b ) 25 cm , c ) 35 cm , d ) 50 cm , e ) none of these
Rationale: explanation : total volume of water displaced = ( 4 x 45 ) m 3 = 180 m 3 rise in water level = 180 / 40 ã — 20 = 0.225 m = 22.5 cm answer : e
Answer: e
Question (geometry): square of 99 = ?
Options: a ) 9001
b ) 9621
c ) 9431
d ) 9801
e ) 9601
Rationale: square of ( 100 - 1 ) = 10000 + 1 - 200 9801 answer d
Answer: d
Question (physics): if 36 men can do a piece of work in 25 hours , in how many hours will 15 men do it ?
Options: a ) 10 hours , b ) 40 hours , c ) 20 hours , d ) 60 hours , e ) none of them
Rationale: "let the required number of hours be x . then , less men , more hours ( indirect proportion ) 15 : 36 : : 25 : x = ( 15 x x ) = ( 36 x 25 ) = ( 36 x 25 ) / 15 = 60 hence , 15 men can do it in 60 hours . answer is d ."
Answer: d
Question (physics): a train 420 m long is running at a speed of 48 km / hr . in what time will it pass a bridge 60 m long ?
Options: a ) 40 sec , b ) 36 sec , c ) 60 sec , d ) 48 sec , e ) 18 sec
Rationale: "total length = 420 + 60 = 480 speed = 48 km / h = ( 48 * 5 ) / 18 = 40 / 3 m / s time = ( 480 * 3 ) / 40 = 36 sec . answer : b"
Answer: b
Question (general): nina has exactly enough money to purchase 6 widgets . if the cost of each widget were reduced by $ 1 , then nina would have exactly enough money to purchase 8 widgets . how much money does nina have ?
Options: a ) $ 22 , b ) $ 24 , c ) $ 30 , d ) $ 36 , e ) $ 40
Rationale: "b its is . let price = x ( x - 1 ) 8 = 6 x x = 4 hence total money = 6 * 4 = 24"
Answer: b
Question (probability): a bag contains 10 black and 20 white balls . one ball is drawn at random . what is the probability that the ball drawn is white ?
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 2 / 3 , d ) 1 / 5 , e ) 3 / 7
Rationale: "total number of balls = 10 + 20 = 30 number of white balls = 20 probability of drawing a white ball = 20 / 30 = 2 / 3 answer is c"
Answer: c
Question (gain): a man invests rs . 7,000 at the rate of 5 % per annum . how much more should he invest at the rate of 8 % , so that he can earn a total of 6 % per annum ?
Options: a ) rs . 1200 , b ) rs . 1300 , c ) rs . 3500 , d ) rs . 2000 , e ) none of these
Rationale: "explanation : interest on rs . 7000 at 5 % per annum = ( 7000 × 5 × 1 ) / 100 = rs . 350 let his additional investment at 8 % = x interest on rs . x at 8 % per annum = ( x × 8 × 1 ) / 100 = 2 x / 25 . to earn 6 % per annum for the total , interest = ( 7000 + x ) × 6 × 1 / 100 . = > 350 + 2 x / 25 = ( 7000 + x ) × 6 × 1 / 100 . = > 35000 + 8 x = ( 7000 + x ) × 6 . = > 35000 + 8 x = 42000 + 6 x . = > 2 x = 7000 . = > x = 3500 . answer : c"
Answer: c
Question (general): if 16 ^ 5 * 15 ^ 4 * 14 ^ 3 * 13 ^ 2 = x , what is the units digit of x ?
Options: a ) 2 , b ) 3 , c ) 6 , d ) 5 , e ) 0
Rationale: 16 ^ 5 * 15 ^ 4 * 14 ^ 3 * 13 ^ 2 = x units digit of x will be 6 ^ 5 * 5 ^ 4 * 4 ^ 3 * 3 ^ 2 = 6 * 5 * 4 * 9 = 1080 therefore , units digit of x = 0 answer e
Answer: e
Question (gain): a fruit seller had some apples . he sells 80 % and still has 500 apples . originally , he had ?
Options: a ) 1588 apples , b ) 2500 apples , c ) 500 apples , d ) 2000 apples , e ) none
Rationale: "answer â ˆ µ 20 % of n = 500 â ˆ ´ n = ( 500 x 100 ) / 20 = 2500 correct option : b"
Answer: b
Question (general): a , b and c rent a pasture . if a puts 10 oxen for 7 months , b puts 12 oxen for 5 months and c puts 15 oxen for 3 months for grazing and the rent of the pasture is rs . 210 , then how much amount should c pay as his share of rent ?
Options: a ) 54 , b ) 45 , c ) 25 , d ) 15 , e ) 55
Rationale: "a : b : c = 10 × 7 : 12 × 5 : 15 × 3 = 2 × 7 : 12 × 1 : 3 × 3 = 14 : 12 : 9 amount that c should pay = 210 × 9 / 35 = 6 × 9 = 54 answer is a"
Answer: a
Question (physics): if 50 honey bees make 50 grams of honey in 50 days , then 1 honey bee will make 1 gram of honey in how many days ?
Options: a ) 1 , b ) 3.5 , c ) 20 , d ) 49 , e ) 50
Rationale: "explanation : let the required number days be x . less honey bees , more days ( indirect proportion ) less honey , less days ( direct proportion ) honey bees 1 : 50 : : 50 : x honey 50 : 1 = > 1 x 50 x x = 50 x 1 x 50 = > x = 50 . answer : e"
Answer: e
Question (gain): the charge for a single room at hotel p is 55 percent less than the charge for a single room at hotel r and 10 percent less than the charge for a single room at hotel g . the charge for a single room at hotel r is what percent greater than the charge for a single room at hotel g ?
Options: a ) 50 % , b ) 60 % , c ) 75 % , d ) 80 % , e ) 100 %
Rationale: "p = 0.45 r = 0.9 g r = 0.9 g / 0.45 = 2 g thus r is 100 % greater than g . the answer is e ."
Answer: e
Question (physics): 69 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 ) 20 , b ) 23 , c ) 24 , d ) 25 , e ) 26
Rationale: "according to the chain rule , m 1 x t 1 = m 2 x t 2 therefore , 69 x 12 x 5 = 30 x 6 x x x = 23 hence , the number of days = 23 . answer : b"
Answer: b
Question (geometry): how much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 11 inches than that of a rectangular sheet of paper measuring 5.5 inches by 11 inches ?
Options: a ) 50 % , b ) 87 % , c ) 100 % , d ) 187 % , e ) 200 %
Rationale: "let ' s just look at the dimensions ( no calculation needed ) . with dimension 11 the same , the other dimension 11 is twice 5.5 then the area will be double which means 100 % greater . the answer is c ."
Answer: c
Question (gain): a certain college ' s enrollment at the beginning of 1992 was 40 percent greater than it was at the beginning of 1991 , and its enrollment at the beginning of 1993 was 15 percent greater than it was at the beginning of 1992 . the college ' s enrollment at the beginning of 1993 was what percent greater than its enrollment at the beginning of 1991 ?
Options: a ) 63 % , b ) 24 % , c ) 50 % , d ) 55 % , e ) 61 %
Rationale: "suppose enrollment in 1991 was 100 then enrollment in 1992 will be 140 and enrollment in 1993 will be 140 * 1.15 = 161 increase in 1993 from 1991 = 161 - 100 = 61 answer : e"
Answer: e
Question (gain): if the cost price is 75 % of the selling price , then what is the profit percent ?
Options: a ) 5 % , b ) 11 % , c ) 13 % , d ) 21 % , e ) 33 %
Rationale: "let s . p . = $ 100 c . p . = $ 75 profit = $ 25 profit % = 25 / 75 * 100 = 25 / 6 = 33 % approximately answer is e"
Answer: e
Question (gain): double of quarter of 3 percent written as a decimal is :
Options: a ) 0.003 , b ) 0.015 , c ) 0.25 , d ) 0.005 , e ) none of these
Rationale: "explanation : solution : ( 2 ) * ( 1 / 4 ) * 3 % = 2 * ( 1 / 4 * 3 / 100 ) = 0.015 . answer : b"
Answer: b
Question (general): two brothers ram and ravi appeared for an exam . the probability of selection of ram is 5 / 7 and that of ravi is 1 / 5 . find the probability that both of them are selected .
Options: a ) 2 / 35 , b ) 2 / 3 , c ) 7 / 35 , d ) 1 / 7 , e ) 7 / 5
Rationale: "let a be the event that ram is selected and b is the event that ravi is selected . p ( a ) = 5 / 7 p ( b ) = 1 / 5 let c be the event that both are selected . p ( c ) = p ( a ) x p ( b ) as a and b are independent events : = 5 / 7 x 1 / 5 = 1 / 7 answer : d"
Answer: d
Question (general): find the least number must be subtracted from 11070 so that remaining number is divisible by 22 .
Options: a ) 2 , b ) 3 , c ) 4 , d ) 7 , e ) 8
Rationale: on dividing 11070 by 22 we get the remainder 4 , so 4 should be subtracted . answer is a .
Answer: a
Question (gain): rs . 2500 is divided into two parts such that if one part be put out at 5 % simple interest and the other at 6 % , the yearly annual income may be rs . 145 . how much was lent at 5 % ?
Options: a ) 2333 , b ) 2777 , c ) 2688 , d ) 500 , e ) 2871
Rationale: "( x * 5 * 1 ) / 100 + [ ( 2500 - x ) * 6 * 1 ] / 100 = 145 x = 500 answer : d"
Answer: d
Question (general): find the mean proportional between 49 & 64 ?
Options: a ) a ) 59 , b ) b ) 61 , c ) c ) 56 , d ) d ) 65 , e ) e ) 67
Rationale: "formula = √ a × b a = 49 and b = 64 √ 49 × 64 = 7 × 8 = 56 c"
Answer: c
Question (physics): one robot builds a robot in 1 hour , another one builds a robot in 2 hours . the 2 robots work together and when a new robot is complete , it joins the others , working at a constant rate of one robot in 2 hours . how much time will it take until there are 4 robots altogether , if the robots build only one robot at a time ?
Options: a ) 70 min , b ) 94 min , c ) 110 min , d ) 112 min , e ) 120 min
Rationale: first the 2 robots work at the rate of 1 + 1 / 2 = 3 / 2 so they complete one robot in 2 / 3 rd of an hour = 40 minutes - ( 1 ) now the 3 robots work together at the rate of 1 + 1 / 2 + 1 / 2 = 4 / 2 = 2 / 1 so they complete one robot in 1 / 2 an hour , i . e 30 minutes - ( 2 ) and now we have 4 robots so total = ( 1 ) + ( 2 ) = 70 minutes answer - a
Answer: a
Question (general): 50 % of a number is 10 less than 3 / 5 th of that number . what is the number ?
Options: a ) 100 , b ) 50 , c ) 150 , d ) 200 , e ) 75
Rationale: "let the number be x then , 3 x / 5 - ( 50 % of x ) = 10 3 x / 5 - 50 x / 100 = 10 x = 100 answer is a"
Answer: a
Question (general): 17 + 18 = 35 . how many such 2 consecutive numbers are there less than 200 when added gives a sum which is divisible by 5 ?
Options: a ) 80 , b ) 40 , c ) 50 , d ) 60 , e ) 20
Rationale: since 2 + 3 = 5 & 7 + 8 = 15 any combination with these no be will give u desirable result . . . so total no in 100 will be 20 & that ' s why in 200 , it will be 40 answer : b
Answer: b
Question (gain): the profit earned by selling an article for 872 is equal to the loss incurred when the same article is sold for 448 . what should be the sale price of the article for making 50 per cent profit ?
Options: a ) 960 , b ) 990 , c ) 1,200 , d ) 920 , e ) none of these
Rationale: "let the profit or loss be x and 872 – x = 448 + x or , x = 424 ⁄ 2 = 212 \ cost price of the article = 872 – x = 448 + x = 660 \ sp of the article = 660 × 150 ⁄ 100 = 990 answer b"
Answer: b
Question (gain): a candidate got 40 % of the votes polled and he lost to his rival by 2000 votes . how many votes were cast ?
Options: a ) 10000 , b ) 2028 , c ) 2775 , d ) 5496 , e ) 6851
Rationale: "40 % - - - - - - - - - - - l 60 % - - - - - - - - - - - w - - - - - - - - - - - - - - - - - - 20 % - - - - - - - - - - 2000 100 % - - - - - - - - - ? = > 10000 answer : a"
Answer: a
Question (gain): one night 17 percent of the female officers on a police force were on duty . if 170 police officers were on duty that night and half of these were female officers , how many female officers were on the police force ?
Options: a ) 400 , b ) 420 , c ) 450 , d ) 480 , e ) 500
Rationale: let x be the number of female police officers on the police force . the number of female police officers on duty was 85 . 0.17 x = 85 x = 500 the answer is e .
Answer: e
Question (geometry): the circumferences of two circles are 396 meters and 704 meters . find the difference between the areas of the larger and the smaller circles ?
Options: a ) 29960 sq m , b ) 26950 sq m , c ) 43120 sq m , d ) 27680 sq m , e ) 27786 sq m
Rationale: "let the radii of the smaller and the larger circles be s m and l m respectively . 2 ∏ s = 396 and 2 ∏ l = 704 s = 396 / 2 ∏ and l = 704 / 2 ∏ difference between the areas = ∏ l ^ 2 - ∏ s ^ 2 = ∏ { 198 ^ 2 / ∏ ^ 2 - 352 ^ 2 / ∏ ^ 2 } = 198 ^ 2 / ∏ - 352 ^ 2 / ∏ = ( 198 - 352 ) ( 198 + 352 ) / ∏ = ( 154 ) ( 550 ) / ( 22 / 7 ) = 26950 sq m answer : b"
Answer: b
Question (physics): a train 495 m long is running at a speed of 63 km / hr . in what time will it pass a bridge 240 m long ?
Options: a ) 39 , b ) 40 , c ) 41 , d ) 42 , e ) 43
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec total distance covered = 495 + 240 = 735 m required time = 700 * 2 / 35 = 42 sec answer : d"
Answer: d
Question (general): if a - b = 3 and a ^ 2 + b ^ 2 = 27 , find the value of ab .
Options: a ) 12 , b ) 15 , c ) 10 , d ) 18 , e ) 9
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 27 - 9 = 18 ab = 9 . answer is e ."
Answer: e
Question (general): in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 2 to the thrice of the remainder . the dividend is ?
Options: a ) 75 , b ) 78 , c ) 80 , d ) 82 , e ) 86
Rationale: "divisor = ( 6 * 3 ) + 2 = 20 5 * quotient = 20 quotient = 4 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 4 ) + 6 = 86 e )"
Answer: e
Question (general): the value of a scooter depreciates in such a way that its value of the end of each year is 3 / 4 of its value of the beginning of the same year . if the initial value of the scooter is rs . 40,000 , what is the value at the end of 6 years ?
Options: a ) 3277 , b ) 2977 , c ) 7119 , d ) 6077 , e ) 17112
Rationale: "explanation : 40,000 * ( 3 / 4 ) ^ 6 answer : c"
Answer: c
Question (general): there are 50 employees in the office of abc company . of these , 22 have taken an accounting course , 14 have taken a course in finance and 15 have taken a marketing course . 10 of the employees have taken exactly two of the courses and 1 employee has taken all 3 of the courses . how many of the 50 employees have taken none of the courses ?
Options: a ) 11 , b ) 5 , c ) 9 , d ) 8 , e ) 10
Rationale: 50 employees . counting every different attendand to the courses we have : accounting : 22 finance : 14 marketing : 15 which would add up to 51 different attendands , which is not possible . now 10 have taken exactly 2 courses , which means that there are 10 less different attendands . say that 10 of the finance attentands also attended accounting . 51 - 10 = 41 1 person has taken all three courses . as above , we subtract him from the number of different attendands . since this time the person took all three courses , we have to substract him two times . 41 - 2 = 39 . answer : a
Answer: a
Question (physics): if an object travels 80 feet in 2 seconds , what is the object ’ s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 21.21 , b ) 24.24 , c ) 27.27 , d ) 30.35 , e ) 33.33
Rationale: "80 feet / 2 seconds = 40 feet / second ( 40 feet / second ) * ( 3600 seconds / hour ) * ( 1 mile / 5280 feet ) = 27.27 miles / hour ( approximately ) the answer is c ."
Answer: c
Question (general): what is the sum of all possible 3 - digit numbers that can be constructed using the digits 1 , 2 , and 4 if each digit can be used only once in each number ?
Options: a ) 1210 , b ) 1221 , c ) 1332 , d ) 1443 , e ) 1554
Rationale: there are 6 possible arrangements of the three numbers . then each number will be in the hundreds , tens , and ones place two times each . the sum is 2 ( 111 ) + 2 ( 222 ) + 2 ( 444 ) = 1554 the answer is e .
Answer: e
Question (general): if x is real , find the maximum value of the expression - 2 x ^ 2 + 11 x + 13 .
Options: a ) 16.125 , b ) 20.125 , c ) 24.125 , d ) 28.125 , e ) 32.125
Rationale: "this is an equation of a downward facing parabola . the maximum value is the top point of the parabola . - 2 x ^ 2 + 11 x + 13 = ( - 2 x + 13 ) ( x + 1 ) the roots are 13 / 2 and - 1 . the maximum value must be when x is halfway between these two points . x = 2.75 the maximum value is - 2 ( 2.75 ) ^ 2 + 11 ( 2.75 ) + 13 = 28.125 the answer is d ."
Answer: d
Question (general): a number when divided by 5 gives a number which is 8 more than the remainder obtained on dividing the same number by 34 . such a least possible number x is
Options: a ) 74 , b ) x = 75 , c ) x = 175 , d ) x = 680 , e ) 690
Rationale: "i solved this question by plugging in numbers from the answer choices . a . ) 74 starting with answer choice a , i immediately eliminated it because 74 is not even divisible by 5 . b . ) 75 i divide 75 / 5 and get 15 as an answer . i divide 75 / 34 and get a remainder of 7 . 15 - 7 = 8 so i know the correct answer isb"
Answer: b
Question (general): if 1 = x . 2 = 2 x 3 = 4 x . . . . what is 2 x * 6 x + 5 x / 4 x - 56 x
Options: a ) 1 , b ) 22 , c ) 23 , d ) 10 , e ) 25
Rationale: let 1 = x 2 = 2 x 3 = 4 x 4 = 8 x 5 = 16 x 6 = 32 x 7 = 64 x now given 2 x * 6 x + 5 x / 4 x - 56 x i can write it as = 2 x * ( 2 x + 4 x ) + ( x + 4 x ) / 4 x - ( 64 x - 8 x ) now by putting the values i get = 2 * ( 2 + 3 ) + ( 8 + 1 ) / 3 - ( 7 - 4 ) = 2 * 5 + 9 / 3 - 3 = 10 + 9 / 3 - 3 = 10 + 3 - 3 = 10 answer : d
Answer: d
Question (general): the closest approximation of a ( 69.28 × 0.004 ) / 0.03 is
Options: a ) 0.092 , b ) 0.92 , c ) 9.2 , d ) 92 , e ) 920
Rationale: "a ( 69.28 × 0.004 ) / 0.03 1 . 0.004 = 4 × 10 ^ ( - 3 ) 2 . 0.03 = 3 × 10 ^ ( - 2 ) 3 . ( a × b ) / c = a × ( b / c ) 4 . 0.004 / 0.03 = 4 × 10 ^ ( - 3 ) / ( 3 × 10 ^ ( - 2 ) ) = 4 × 10 ^ ( - 3 - ( - 2 ) ) / 3 = 4 × 10 ^ ( - 1 ) / 3 = ( 4 / 3 ) × 10 ^ ( - 1 ) = 1.333 × 10 ^ ( - 1 ) therefore , ( 69.28 × 0.004 ) / 0.03 = 69.28 × ( 0.004 / 0.03 ) = 69.28 × 1.33 × 10 ^ ( - 1 ) = 69.28 × 1.33 / 10 = 6.928 * 1.33 now , 7 × 2 = 14 7 × 1 = 7 or better : 6.9 × 1 = 6.9 6.9 × 2 = 13.8 hence , 6.9 < 6.928 × 1.33 < 13.8 9.2 is the only answer that satisfies this condition . c"
Answer: c
Question (gain): a number exceeds 20 % of itself by 40 . the number is ?
Options: a ) 50 , b ) 60 , c ) 80 , d ) 320 , e ) none
Rationale: answer ∵ a - 20 % of a = 40 ⇒ a - a / 5 = 40 ⇒ 4 a / 5 = 40 ∴ a = ( 5 x 40 ) / 4 = 50 . correct option : a
Answer: a
Question (general): 9.009 / 5.005 =
Options: a ) 1.08 , b ) 1.4 , c ) 1.8018 , d ) 1.4014 , e ) 1.8
Rationale: "9.009 / 5.005 = 9009 / 5005 = 9 ( 1001 ) / 5 ( 1001 ) = 9 / 5 = 1.8 the answer is e ."
Answer: e
Question (geometry): the ratio between the perimeter and the width of a rectangle is 5 : 1 . if the area of the rectangle is 294 square centimeters , what is the length of the rectangle in centimeters ?
Options: a ) 19 , b ) 20 , c ) 21 , d ) 22 , e ) 23
Rationale: "perimeter = 2 ( w + l ) = 5 w 3 w = 2 l w = 2 l / 3 wl = 294 2 l ^ 2 / 3 = 294 l ^ 2 = 441 l = 21 cm the answer is c ."
Answer: c
Question (general): if each digit in the set a = { 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 } is used exactly once , in how many ways can the digits be arranged ?
Options: a ) 36,100 , b ) 38,210 , c ) 40,320 , d ) 42,430 , e ) 44,540
Rationale: "8 ! = 40,320 the answer is c ."
Answer: c
Question (general): mark and ann together were allocated n boxes of cookies to sell for a club project . mark sold 8 boxes less than n and ann sold 2 boxes less than n . if mark and ann have each sold at least one box of cookies , but together they have sold less than n boxes , what is the value of n ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "if n = 9 mark sold 1 box and ann sold 7 boxes total 8 < 9 answer : e"
Answer: e
Question (gain): a store reduced the price of all items in the store by 9 % on the first day and by another 10 % on the second day . the price of items on the second day was what percent of the price before the first reduction took place ?
Options: a ) 80.0 , b ) 80.9 , c ) 81.0 , d ) 81.1 , e ) 81.9
Rationale: "consider price of the all items as $ 100 after a initial reduction of 9 % price becomes = 0.91 * 100 = $ 91 after the final reduction of 10 % price becomes = 0.9 * 91 = $ 81.9 price of all items on second day is 81.9 % of price on first day correct answer option e"
Answer: e
Question (general): the maximum number of students among them 890 pens and 630 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 10 , b ) 910 , c ) 1001 , d ) 1911 , e ) none of these
Rationale: "explanation : required number of students = h . c . f of 890 and 630 = 10 . answer : a"
Answer: a
Question (physics): a certain bacteria colony doubles in size every day for 22 days , at which point it reaches the limit of its habitat and can no longer grow . if two bacteria colonies start growing simultaneously , how many days will it take them to reach the habitat ’ s limit ?
Options: a ) 6.33 , b ) 7.5 , c ) 21 , d ) 15 , e ) 19
Rationale: "if there is one bacteria colony , then it will reach the limit of its habitat in 20 days . if there are two bacteria colonies , then in order to reach the limit of habitat they would need to double one time less than in case with one colony . thus colonies need to double 21 times . answer : c . similar questions to practice : hope it helps ."
Answer: c
Question (gain): on a purchase of $ 110 , a store offered a payment plan consisting of a $ 10 down payment and 12 monthly payments of $ 10 each . what percent of the purchase price , to the nearest tenth of a percent , did the customer pay in interest by using this plan ?
Options: a ) 9.5 % , b ) 10.5 % , c ) 11.5 % , d ) 9.1 % , e ) 12.5 %
Rationale: "12 * 10 + 10 = 130 ( 10 / 110 ) * 100 = 9.1 answer : d"
Answer: d
Question (general): laura took out a charge account at the general store and agreed to pay 9 % simple annual interest . if she charges $ 35 on her account in january , how much will she owe a year later , assuming she does not make any additional charges or payments ?
Options: a ) $ 2.10 , b ) $ 37.10 , c ) $ 37.16 , d ) $ 38.10 , e ) $ 38.15
Rationale: principal that is amount taken by laura at year beginning = 35 $ rate of interest = 9 % interest = ( 9 / 100 ) * 35 = 3.15 $ total amount that laura owes a year later = 35 + 3.15 = 38.15 $ answer e
Answer: e