Cheukting/mathqa huggingface dataset:
Question (physics): the sum of the squares of three consecutive natural number is 2030 . what is the middle number ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: "let the numbers be x , x + 1 and x + 2 x 2 + ( x + 1 ) 2 + ( x + 2 ) 2 = 2030 3 x 2 + 6 x - 2025 = 0 ( x + 27 ) ( x - 25 ) = 0 x = 25 the middle number is 26 answer b 26"
Answer: b
Question (physics): in what time will two trains cross each other completely , which are running on the same parallel lines in opposite directions , each train running with a speed of 60 kmph being 130 m and 120 m in length respectively ?
Options: a ) 6.9 sec , b ) 7.1 sec , c ) 7.2 sec , d ) 7.4 sec , e ) 7.5 sec
Rationale: "d = 130 m + 120 m = 250 m * 1 / 1000 = 0.25 kms rs = 60 + 60 = 120 kmph t = ( 0.25 / 120 ) * 3600 = 7.5 sec answer : e"
Answer: e
Question (general): the population of a town increased from 1 , 75,000 to 2 , 62,500 in a decade . what is the average percent increase of population per year ?
Options: a ) 4 % , b ) 6 % , c ) 5 % , d ) 50 % , e ) none of these
Rationale: "explanation : increase in the population in 10 years = 2 , 62,500 - 1 , 75,000 = 87500 % ncrease in the population in 10 years = ( 87500 / 175000 ) × 100 = 8750 / 175 = 50 % average % increase of population per year = 50 % / 10 = 5 % answer : option c"
Answer: c
Question (general): the average age of 15 students of a class is 15 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 11 years , b ) 17 years , c ) 67 years , d ) 14 years , e ) 12 years
Rationale: "age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer : a"
Answer: a
Question (physics): rob also compared the empire state building and the petronas towers . what is the height difference between the two if the empire state building is 435 m tall and the petronas towers is 458 m tall ?
Options: a ) 9 , b ) 17 , c ) 23 , d ) 45 , e ) 12
Rationale: 458 - 435 = 23 . answer is c .
Answer: c
Question (physics): a and b together can do a work in 4 days . if a alone can do it in 20 days . in how many days can b alone do it ?
Options: a ) 11 , b ) 5 , c ) 6 , d ) 8 , e ) 25
Rationale: "b 5 1 / 4 â € “ 1 / 20 = 1 / 5 = > 5"
Answer: b
Question (general): when a merchant imported a certain item , she paid a 7 percent import tax on the portion of the total value of the item in excess of $ 1000 . if the amount of the import tax that the merchant paid was $ 109.90 , what was the total value of the item ?
Options: a ) $ 1940 , b ) $ 2150 , c ) $ 2360 , d ) $ 2570 , e ) $ 2780
Rationale: let x be the value of the item . 0.07 * ( x - 1000 ) = 109.90 x = 2570 the answer is d .
Answer: d
Question (physics): a train passes a station platform in 34 sec and a man standing on the platform in 20 sec . if the speed of the train is 54 km / hr . what is the length of the platform ?
Options: a ) 228 , b ) 240 , c ) 887 , d ) 166 , e ) 210
Rationale: "speed = 54 * 5 / 18 = 15 m / sec . length of the train = 15 * 20 = 300 m . let the length of the platform be x m . then , ( x + 300 ) / 34 = 15 = > x = 210 m . answer : e"
Answer: e
Question (physics): find the area , diameter = 11 m .
Options: a ) 113.00 square meter
b ) 95.07 square meter
c ) 93.08 square meter
d ) 93.24 square meter
e ) 113.43 square meter
Rationale: diameter = 11 meter . radius = diameter / 2 . = 11 / 2 . = 5.5 meter . area of a circle = ï € r 2 . here , pi ( ï € ) = 3.14 meter , radius ( r ) = 5.5 . area of a circle = 3.14 ã — 5.5 ã — 5.5 . . = 3.14 ã — 30.25 . = 95.07 square meter answer : b
Answer: b
Question (general): when positive integer n is divided by 3 , the remainder is 1 . when n is divided by 5 , the remainder is 4 . what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 ?
Options: a ) 1 , b ) 2 , c ) 5 , d ) 7 , e ) 20
Rationale: when positive integer n is divided by 3 , the remainder is 1 i . e . , n = 3 x + 1 values of n can be one of { 1 , 4 , 7 , 10 , 13 , 16 , 19 , 22 . . . . . . . . . . . . . . 49 , 52 , 59 . . . . . . . . . . . . . . . . . . } similarly , when n is divided by 5 , the remainder is 5 . . i . e . , n = 5 y + 4 values of n can be one of { 4 , 9 , 14 , 19 , . . . } combining both the sets we get n = { 4,19 , 52 , . . . . . . . . . . . } what is the smallest positive integer p , such that ( n + p ) is a multiple of 11 or 11 x in case of n = 4 p = 7 so for min value of p , we take min value of n . d is the answer .
Answer: d
Question (gain): a , b and c invested rs . 6300 , rs . 4200 and rs . 10500 respectively , in a partnership business . find the share of a in profit of rs . 12400 after a year ?
Options: a ) 3630 , b ) 2881 , c ) 3720 , d ) 9977 , e ) 2212
Rationale: "6300 : 4200 : 10500 3 : 2 : 5 3 / 10 * 12400 = 3720 . answer : c"
Answer: c
Question (physics): two tains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post . if the length of each train be 100 metres , in what time ( in seconds ) will they cross each other travelling in opposite direction ?
Options: a ) 12 , b ) 11.9 , c ) 16 , d ) 20 , e ) 18
Rationale: sol . speed of the first train = [ 100 / 10 ] m / sec = 10 m / sec . speed of the second train = [ 100 / 15 ] m / sec = 6.7 m / sec . relative speed = ( 10 + 6.7 ) = m / sec = 16.7 m / sec . ∴ required time = ( 100 + 100 ) / 16.7 secc = 11.9 sec . answer b
Answer: b
Question (general): if 40 % of ( x - y ) = 20 % of ( x + y ) , then what percent of x is y ?
Options: a ) 50.5 % , b ) 44.4 % , c ) 22.2 % , d ) 33.3 % , e ) 25 %
Rationale: "40 % of ( x - y ) = 20 % of ( x + y ) 40 / 100 ( x - y ) = 20 / 100 ( x + y ) x = 3 y required percentage = y / x * 100 = y / 3 y * 100 = 33.3 % answer is d"
Answer: d
Question (physics): in a 500 m race , the ratio of the speeds of two contestants a and b is 3 : 4 . a has a start of 170 m . then , a wins by :
Options: a ) 60 m , b ) 20 m , c ) 43 m , d ) 20 m , e ) 23 m
Rationale: "to reach the winning post a will have to cover a distance of ( 500 - 170 ) m , i . e . , 330 m . while a covers 3 m , b covers 4 m . while a covers 330 m , b covers 4 x 330 / 3 m = 440 m . thus , when a reaches the winning post , b covers 440 m and therefore remains 60 m behind . a wins by 60 m . answer : a"
Answer: a
Question (probability): from a pack of cards , two cards are drawn one after the other , with replacement . what is the probability that the first card is a club and the second card is a red king ?
Options: a ) 1 / 13 , b ) 1 / 15 , c ) 1 / 26 , d ) 1 / 52 , e ) 1 / 104
Rationale: p ( club ) = 1 / 4 p ( red king ) = 1 / 26 p ( club then a red king ) = 1 / 4 * 1 / 26 = 1 / 104 the answer is e .
Answer: e
Question (geometry): a cube is painted red on all faces . it is then cut into 27 equal smaller cubes . how many cubes are painted on only 2 faces ?
Options: a ) 12
b ) 8
c ) 6
d ) 10
e ) 16
Rationale: the mini - cubes with 2 painted sides are all on the edge of the cube , in the ` ` middle ' ' of the edge . there are 4 in front , 4 in back and 4 more on the ` ` strip ' ' that runs around the left / top / right / bottom of the cube . 4 + 4 + 4 = 12 . answer a
Answer: a
Question (gain): in a certain pond , 40 fish were caught , tagged , and returned to the pond . a few days later , 40 fish were caught again , of which 2 were found to have been tagged . if the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond , what is the approximate number of fish in the pond ?
Options: a ) 1000 , b ) 625 , c ) 1,250 , d ) 2,500 , e ) 10,000
Rationale: "total fish = x percentage of second catch = ( 2 / 40 ) * 100 = 5 % so , x * 5 % = 50 x = 1000 ans . a"
Answer: a
Question (physics): a man can do a piece of work in 6 days , but with the help of his son he can do it in 3 days . in what time can the son do it alone ?
Options: a ) 7 days , b ) 6 days , c ) 5 days , d ) 4 days , e ) none of these
Rationale: "explanation : in this type of question , where we have one person work and together work done . then we can easily get the other person work just by subtracting them . as son ' s one day work = ( 1 / 3 − 1 / 6 ) = ( 6 − 3 ) / 18 = 1 / 6 so son will do whole work in 6 days answer : b"
Answer: b
Question (general): meena wrote all the numbers from 1 to 59,999 inclusive . how many digits did she write in total ?
Options: a ) 248,889 , b ) 268,889 , c ) 288,889 , d ) 308,889 , e ) 328,889
Rationale: "1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 59999 = > 5 * 50,000 = 250,000 the answer is 288,889 the answer is c ."
Answer: c
Question (general): if 3 < x < 6 < y < 9 , then what is the greatest possible positive integer difference of x and y ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 < x < 6 < y < 9 ; 3 < x y < 9 3 + y < x + 9 y - x < 6 . positive integer difference is 5 ( for example y = 8.5 and x = 3.5 ) answer : c ."
Answer: c
Question (gain): if 125 % of j is equal to 25 % of k , 150 % of k is equal to 50 % of l , and 175 % of l is equal to 75 % of m , then 20 % of m is equal to what percent of 150 % of j ?
Options: a ) 0.35 , b ) 466 , c ) 35 , d ) 350 , e ) 3500
Rationale: "imo answer should be 350 . . . consider j = 10 , then k = 50 , l = 150 and m = 350 . . . . 20 % of 350 , comes out to be 70 . . . . 150 % of 10 is 15 . . . . ( 70 * 100 ) / 15 = 466.66 . . . . ans : b"
Answer: b
Question (gain): a producer of tea blends two varieties of tea from two tea gardens one costing rs 18 per kg and another rs 20 per kg in the ratio 5 : 3 . if he sells the blended variety at rs 22 per kg , then his gain percent is
Options: a ) 12 % , b ) 13 % , c ) 14 % , d ) 15 % , e ) 17 %
Rationale: "explanation : suppose he bought 5 kg and 3 kg of tea . cost price = rs . ( 5 x 18 + 3 x 20 ) = rs . 150 . selling price = rs . ( 8 x 22 ) = rs . 176 . profit = 176 - 150 = 26 so , profit % = ( 26 / 150 ) * 100 = 17 % option e"
Answer: e
Question (gain): the cost price of 20 articles is the same as the selling price of x articles . if the profit is 25 % , find out the value of x
Options: a ) 13 , b ) 14 , c ) 15 , d ) 16 , e ) 17
Rationale: "explanation : let the cost price of one article = rs . 1 cp of x articles = rs . x cp of 20 articles = 20 selling price of x articles = 20 profit = 25 % [ given ] ⇒ ( sp − cp / cp ) = 25 / 100 = 1 / 4 ⇒ ( 20 − x ) / x = 1 / 4 ⇒ 80 − 4 x = x ⇒ 5 x = 80 option d ⇒ x = 805 = 16"
Answer: d
Question (physics): convert the 19 / 36 m / s into kilometers per hour ?
Options: a ) 1.7 , b ) 1.5 , c ) 1.3 , d ) 1.1 , e ) 1.9
Rationale: "19 / 36 m / s = 19 / 36 * 18 / 5 = 19 / 10 = 1.9 kmph . answer : e"
Answer: e
Question (gain): an error 5 % in excess is made while measuring the side of a square . what is the percentage of error in the calculated area of the square ?
Options: a ) 4.05 % , b ) 4.02 % , c ) 4 % , d ) 10.28 % , e ) 2 %
Rationale: "percentage error in calculated area = ( 5 + 5 + ( 5 ã — 5 ) / 100 ) % = 10.25 % answer : d"
Answer: d
Question (general): for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 6 minutes from 9 : 00 in the morning to 6 : 00 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 2 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 23400 , b ) $ 25920 , c ) $ 28080 , d ) $ 28500 , e ) $ 29160
Rationale: "from 9 : 00 in the morning to 6 : 00 in the afternoon , inclusive there are 9 * 10 = 90 five - minute intervals , thus total of 54 * 30 tickets were sold . say x student and 2 x regular tickets were sold , then x + 2 x = 90 * 30 - - > x = 30 * 30 and 2 x = 2 * ( 30 * 30 ) = 30 * 60 . therefore , the total revenue from ticket sales that day was 30 * 30 * 6 + 30 * 60 * 10 = $ 23,400 . answer : a ."
Answer: a
Question (physics): a can give b 100 meters start and c 170 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 11.77 meters , b ) 55.77 meters , c ) 77.77 meters , d ) 113.77 meters , e ) none of these
Rationale: "explanation : a runs 1000 meters while b runs 900 meters and c runs 830 meters . therefore , b runs 900 meters while c runs 830 meters . so , the number of meters that c runs when b runs 1000 meters = ( 1000 x 830 ) / 900 = 922.22 meters thus , b can give c ( 1000 - 922.22 ) = 77.77 meters start answer : c"
Answer: c
Question (general): company t produces two kinds of stereos : basic and deluxe . of the stereos produced by company t last month , 2 / 3 were basic and the rest were deluxe . if it takes 7 / 5 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 5 / 17 , b ) 7 / 17 , c ) 4 / 17 , d ) 3 / 17 , e ) 5
Rationale: # of basic stereos was 2 / 3 of total and # of deluxe stereos was 1 / 3 of total , let ' s assume total = 15 , then basic = 10 and deluxe = 5 . now , if time needed to produce one deluxe stereo is 1 unit than time needed to produce one basic stereo would be 7 / 5 units . total time for basic would be 10 * 1 = 10 and total time for deluxe would be 5 * 7 / 5 = 7 - - > total time for both of them would be 10 + 7 = 17 - - > deluxe / total = 7 / 17 . b
Answer: b
Question (geometry): a rectangular block 10 cm by 20 cm by 30 cm is cut into an exact number of equal cubes . find the least possible number of cubes ?
Options: a ) 6 , b ) 10 , c ) 15 , d ) 40 , e ) 22
Rationale: "volume of the block = 10 * 20 * 30 = 6000 cm ^ 3 side of the largest cube = h . c . f of 10 , 20,30 = 10 cm volume of the cube = 10 * 10 * 10 = 1000 cm ^ 3 number of cubes = 6000 / 1000 = 6 answer is a"
Answer: a
Question (general): at a certain company , each employee has a salary grade s that is at least 1 and at most 5 . each employee receives an hourly wage p , in dollars , determined by the formula p = 11.50 + 0.25 ( s – 1 ) . an employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 1 ?
Options: a ) $ 0.50 , b ) $ 1.00 , c ) $ 1.25 , d ) $ 1.50 , e ) $ 1.75
Rationale: oa is definitely wrong . the answer should be e .
Answer: e
Question (gain): by selling an article at rs . 800 , a shopkeeper makes a profit of 25 % . at what price should he sell the article so as to make a loss of 45 % ?
Options: a ) s . 429 , b ) s . 352 , c ) s . 429 , d ) s . 128 , e ) s . 419
Rationale: "sp = 800 profit = 25 % cp = ( sp ) * [ 100 / ( 100 + p ) ] = 800 * [ 100 / 125 ] = 640 loss = 45 % = 45 % of 640 = rs . 288 sp = cp - loss = 640 - 288 = rs . 352 answer : b"
Answer: b
Question (physics): at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 5 for each visit after that in the same calendar month . in the last calendar month , 100 customers visited the salon , of which 30 made a second visit , and 10 made a third visit . all other customers made only one visit . if those visits were the only source of revenue for the salon , what was the revenue for the last calendar month at the salon ?
Options: a ) $ 1220 , b ) $ 1200 , c ) $ 1300 , d ) $ 1340 , e ) $ 1880
Rationale: "i get b . this question seems too straightforward for 600 + . am i missing something ? 100 first - time visits - - > 100 ( 10 ) = $ 1000 30 + 10 = 40 subsequent visits - - > 40 ( 5 ) = $ 200 total revenue : 1000 + 200 = $ 1200 the answer is b ."
Answer: b
Question (general): pat , kate , and mark charged a total of 126 hours to a certain project . if pat charged twice as much time to the project as kate and 1 / 3 as much time as mark , how many more hours did mark charge to the project than kate ?
Options: a ) 18 , b ) 36 , c ) 72 , d ) 70 , e ) 108
Rationale: "70 all u do is do 2 : 1 : 6 = > 2 x + x + 6 x = 126 = > x = 14 28 : 14 : 84 84 - 14 = 70 answer d"
Answer: d
Question (geometry): calculate the area of a triangle , if the sides of are 52 cm , 48 cm and 20 cm , what is its area ?
Options: a ) 480 cm 2 , b ) 580 cm 2 , c ) 380 cm 2 , d ) 180 cm 2 , e ) 280 cm 2
Rationale: "the triangle with sides 52 cm , 48 cm and 20 cm is right angled , where the hypotenuse is 52 cm . area of the triangle = 1 / 2 * 48 * 20 = 480 cm 2 answer : a"
Answer: a
Question (general): employees of a certain company are each to receive a unique 9 - digit identification code consisting of the digits 0 , 1 , 2 , 3 , 4 , 5 , 6 , 7 , and 8 such that no digit is used more than once in any given code . in valid codes , the second digit in the code is exactly twice the first digit . how many valid codes are there ?
Options: a ) 14,720 , b ) 16,240 , c ) 18,320 , d ) 20,160 , e ) 22,480
Rationale: "there are 7 ! ways to make codes starting with 12 . there are 7 ! ways to make codes starting with 24 . there are 7 ! ways to make codes starting with 36 . there are 7 ! ways to make codes starting with 48 . the number of codes is 4 * 7 ! = 20,160 . the answer is d ."
Answer: d
Question (physics): the amount of time that three people worked on a special project was in the ratio of 2 to 4 to 6 . if the project took 144 hours , how many more hours did the hardest working person work than the person who worked the least ?
Options: a ) 47 hours , b ) 45 hours , c ) 48 hours , d ) 49 hours , e ) 50 hours
Rationale: let the persons be a , b , c . hours worked : a = 2 * 144 / 12 = 24 hours b = 4 * 144 / 12 = 48 hours c = 6 * 144 / 12 = 72 hours c is the hardest worker and a worked for the least number of hours . so the difference is 72 - 24 = 48 hours . answer : c
Answer: c
Question (general): how many positive integers less than 50 have a reminder 5 when divided by 7 ?
Options: a ) 3 , b ) 7 , c ) 4 , d ) 5 , e ) 6
Rationale: "take the multiples of 7 and add 5 0 x 7 + 5 = 5 . . . . 6 x 7 + 5 = 47 there are 7 numbers answer b"
Answer: b
Question (gain): a car is purchased on hire - purchase . the cash price is $ 24 000 and the terms are a deposit of 10 % of the price , then the balance to be paid off over 60 equal monthly installments . interest is charged at 12 % p . a . what is the monthly installment ?
Options: a ) $ 503 , b ) $ 504 , c ) $ 555 , d ) $ 576 , e ) $ 587
Rationale: "explanation : cash price = $ 24 000 deposit = 10 % ã — $ 24 000 = $ 2400 loan amount = $ 24000 â ˆ ’ $ 2400 number of payments = 60 = $ 21600 i = p * r * t / 100 i = 12960 total amount = 21600 + 12960 = $ 34560 regular payment = total amount / number of payments = 576 answer : d"
Answer: d
Question (physics): a truck covers a distance of 550 metres in 1 minute whereas a train covers a distance of 33 kms in 45 minutes . what is the ratio of their speed ?
Options: a ) 3 : 7 , b ) 4 : 7 , c ) 1 : 4 , d ) 3 : 4 , e ) 2 : 5
Rationale: "explanation : speed of the truck = distance / time = 550 / 1 = 550 meters / minute speed of the train = distance / time = 33 / 45 km / minute = 33000 / 45 meters / minut speed of the truck / speed of the train = 550 / ( 33000 / 45 ) = ( 550 × 45 ) / 33000 = ( 55 × 45 ) / 3300 = ( 11 × 45 ) / 660 = ( 11 × 9 ) / 132 = 9 / 12 = 34 hence , speed of the truck : speed of the train = 3 : 4 answer : option d"
Answer: d
Question (general): a sum of money is distributed among a , b , c , d in the proportion of 6 : 4 : 8 : 5 . if c gets $ 3000 more than d , what is the b ' s share ?
Options: a ) $ 2000 , b ) $ 6000 , c ) $ 1000 , d ) $ 4000 , e ) $ 5000
Rationale: "let the shares of a , b , c , d are 6 x , 4 x , 8 x , 5 x 8 x - 5 x = 3000 3 x = 3000 , x = 1000 b ' s share = 4 x = $ 4000 answer is d"
Answer: d
Question (general): on the independence day , bananas were be equally distributed among the children in a school so that each child would get two bananas . on the particular day 380 children were absent and as a result each child got two extra bananas . find the actual number of children in the school ?
Options: a ) 237 , b ) 287 , c ) 760 , d ) 287 , e ) 720
Rationale: "explanation : let the number of children in the school be x . since each child gets 2 bananas , total number of bananas = 2 x . 2 x / ( x - 380 ) = 2 + 2 ( extra ) = > 2 x - 760 = x = > x = 760 . answer : c"
Answer: c
Question (gain): in town p , 70 percent of the population are employed , and 42 percent of the population are employed males . what percent of the employed people in town p are females ?
Options: a ) 25 % , b ) 30 % , c ) 35 % , d ) 40 % , e ) 45 %
Rationale: "the percent of the population who are employed females is 70 - 42 = 28 % the percent of employed people who are female is 28 % / 70 % = 40 % . the answer is d ."
Answer: d
Question (physics): at 15 : 00 there were 20 students in the computer lab . at 15 : 03 and every three minutes after that , 3 students entered the lab . if at 15 : 10 and every ten minutes after that 9 students left the lab , how many students were in the computer lab at 15 : 44 ?
Options: a ) 7 , b ) 14 , c ) 25 , d ) 27 , e ) 30
Rationale: "initial no of students + 3 * ( 1 + no of possible 3 minute intervals between 15 : 03 and 15 : 44 ) - 8 * ( 1 + no of possible 10 minute intervals between 15 : 10 and 15 : 44 ) 20 + 3 * 14 - 8 * 4 = 25 c"
Answer: c
Question (general): the toll for crossing a certain bridge is $ 0.65 each crossing . drivers who frequently use the bridge may instead purchase a sticker each month for $ 13.00 and then pay only $ 0.30 each crossing during that month . if a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day , what is the least value of x for which this driver can save money by using the sticker ?
Options: a ) 14 , b ) 15 , c ) 16 , d ) 28 , e ) 29
Rationale: "option # 1 : $ 0.75 / crossing . . . . cross twice a day = $ 1.5 / day option # 2 : $ 0.30 / crossing . . . . cross twice a day = $ 0.6 / day + $ 13 one time charge . if we go down the list of possible answers , you can quickly see that 14 days will not be worth purchasing the sticker . 1.5 x 14 ( 21 ) is cheaper than 0.6 x 14 + 13 ( 21.4 ) . . . it ' s pretty close so let ' s see if one more day will make it worth it . . . if we raise the number of days to 15 , the sticker option looks like a better deal . . . 1.5 x 15 ( 22.5 ) vs 0.6 x 15 + 13 ( 22 ) . answer : c"
Answer: c
Question (physics): a cubical tank is filled with water to a level of 3 feet . if the water in the tank occupies 75 cubic feet , to what fraction of its capacity is the tank filled with water ?
Options: a ) 1 / 2 , b ) 2 / 3 , c ) 3 / 4 , d ) 2 / 5 , e ) 3 / 5
Rationale: "the volume of water in the tank is h * l * b = 75 cubic feet . since h = 3 , then l * b = 25 and l = b = 5 . since the tank is cubical , the capacity of the tank is 5 * 5 * 5 = 125 . the ratio of the water in the tank to the capacity is 75 / 125 = 3 / 5 the answer is e ."
Answer: e
Question (general): andy solves problems 74 to 135 inclusive in a math exercise . how many problems does he solve ?
Options: a ) 53 , b ) 62 , c ) 51 , d ) 50 , e ) 49
Rationale: "135 - 74 + 1 = 62 ' b ' is the answer"
Answer: b
Question (general): 9.009 / 1.001
Options: a ) 0.009 , b ) 0.09 , c ) 0.9 , d ) 9 , e ) 90
Rationale: "answer is 9 , move the decimal forward three places for both numerator and denominator or just multiply both by a thousand . the result is 9009 / 1001 = 9 answer d"
Answer: d
Question (gain): a number increased by 25 % gives 520 . the number is ?
Options: a ) 216 , b ) 316 , c ) 616 , d ) 516 , e ) 416
Rationale: "formula = total = 100 % , increase = ` ` + ' ' decrease = ` ` - ' ' a number means = 100 % that same number increased by 25 % = 125 % 125 % - - - - - - - > 520 ( 120 ã — 4.16 = 520 ) 100 % - - - - - - - > 416 ( 100 ã — 4.16 = 416 ) option ' e '"
Answer: e
Question (physics): a , b and c can do a piece of work in 14 , 30 and 40 days respectively . they start the work together but c leaves 4 days before the completion of the work . in how many days is the work done ?
Options: a ) 7.6 days , b ) 7.7 days , c ) 6.7 days , d ) 5.7 days , e ) 8.7 days
Rationale: "x / 14 + x / 30 + x / 40 = 1 x = 7.7 days answer : b"
Answer: b