Cheukting/mathqa huggingface dataset:
Question (general): what is the sum of all even numbers from 1 to 601 ?
Options: a ) 122821 , b ) 281228 , c ) 90300 , d ) 122850 , e ) 128111
Rationale: "explanation : 600 / 2 = 300 300 * 301 = 90300 answer : c"
Answer: c
Question (general): 60 percent of movie theatres in town x have 3 screens or less . 20 % of those theatres sell an average of more than $ 200 worth of popcorn per showing . 56 percent of all the movie theatres in town x sell $ 300 or less of popcorn per showing . what percent of all the stores on the street have 4 or more screens and sell an average of more than $ 300 worth of popcorn per day ?
Options: a ) 12 , b ) 18 , c ) 32 , d ) 40 , e ) 44
Rationale: "lets take numbers here . assume that the total number of movie theaters in the town = 100 then number of movie theaters with 3 screens or less = 60 = > number of movie theaters with 4 screens or more = 40 movie theaters with 3 screens or less selling popcorn at more than $ 200 = 20 % of 60 = 12 number of movie theaters selling popcorn at $ 300 or less = 56 = > number of movie theaters selling popcorn at more than $ 300 = 100 - 56 = 44 of these 44 theaters , 12 are those with 3 screens or less therefore 18 ( 44 - 12 ) must be those with four screens or more b is the answer"
Answer: b
Question (gain): in a certain pond , 70 fish were caught , tagged , and returned to the pond . a few days later , 50 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 ) 400 , b ) 625 , c ) 1,750 , d ) 2,500 , e ) 10,000
Rationale: "this is a rather straight forward ratio problem . 1 . 70 fish tagged 2 . 2 out of the 50 fish caught were tagged thus 2 / 50 2 / 50 = 70 / x thus , x = 1750 think of the analogy : 2 fish is to 50 fish as 50 fish is to . . . ? you ' ve tagged 50 fish and you need to find what that comprises as a percentage of the total fish population - we have that information with the ratio of the second catch . c"
Answer: c
Question (general): there are 990 male and female participants in a meeting . half the female participants and one - quarter of the male participants are democrats . one - third of all the participants are democrats . how many of the democrats are female ?
Options: a ) 75 , b ) 100 , c ) 125 , d ) 175 , e ) 165
Rationale: "female = x male = 990 - x x / 2 + 990 - x / 4 = 1 / 3 * ( 990 ) = 330 x = 330 x / 2 = 165 is supposed to be the answer m is missing something correct option e"
Answer: e
Question (general): 5 years ago amith was 3 times as old as his daughter and 10 years hence , he will be two times as old as his daughter . then amith ’ s current age is ,
Options: a ) 10 , b ) 50 , c ) 40 , d ) 20 , e ) 60
Rationale: d 20 amith ’ s age = a and daughter ’ s age = b then , a – 5 = 3 ( b – 5 ) = > a – 3 b + 10 = 0 … … ( 1 ) and , a + 10 = 2 ( a + 10 ) = > a – 2 b – 10 = 0 … … ( 2 ) solving the 2 eqns , we will get a = 50 , b = 20 . therefore , amith ’ s age is 50 and his daughter ’ s age is 20
Answer: d
Question (physics): at a tanning salon , customers are charged $ 10 for their first visit in a calendar month and $ 7 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 ) $ 1280 , 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 ( 7 ) = $ 280 total revenue : 1000 + 280 = $ 1280 the answer is b ."
Answer: b
Question (gain): a retailer buys a radio for rs 232 . his overhead expenses are rs 15 . he sellis the radio for rs 300 . the profit percent of the retailer is
Options: a ) 10 % , b ) 50 % , c ) 21.4 % , d ) 52 % , e ) none of these
Rationale: explanation : cost price = ( 232 + 15 ) = 247 sell price = 300 gain = ( 53 / 247 ) * 100 = 21.4 % . answer : c
Answer: c
Question (general): a batch of cookies was divided among 3 tins : 2 / 3 of all the cookies were placed in either the blue tin or the green tin , and the rest were placed in the red tin . if 1 / 4 of all the cookies were placed in the blue tin , what fraction q of the cookies that were placed in the other tins were placed in the green tin ?
Options: a ) 15 / 2 , b ) 9 / 4 , c ) 5 / 9 , d ) 7 / 5 , e ) 9 / 7
Rationale: blue tin or red tin : 2 / 3 ( n ) red tin : ( 1 / 3 ) n blue tin : ( 1 / 4 ) n what the last statment meant , is it wants this fraction : ( # of cookies in green tin ) / ( # of cookies in red and green tin ) # of cookies in green tin = 2 n / 3 - n / 4 = 8 n - 3 n / 12 = 5 n / 12 # of cookies in red and green tin = n / 3 + 5 n / 12 = 9 n / 12 fraction q = 5 n / 12 * 12 / 9 n = 5 / 9 ( c )
Answer: c
Question (physics): aaron will jog from home at 3 miles per hour and then walk back home by the same route at 6 miles per hour . how many miles from home can aaron jog so that he spends a total of 3 hours jogging and walking ?
Options: a ) 3 , b ) 6 , c ) 2 , d ) 5 , e ) 8
Rationale: "xyt / ( x + y ) x = 3 , y = 6 , t = 3 3 * 6 * 3 / 3 + 6 = 54 / 9 = 6 answer : b"
Answer: b
Question (general): a man engaged a servant on the condition that he would pay him rs . 710 and a uniform after a year service . he served only for 8 months and got rs . 460 and a uniform . find the price of the uniform ?
Options: a ) rs . 40 , b ) rs . 30 , c ) rs . 25 , d ) rs . 20 , e ) rs . 45
Rationale: "8 / 12 = 2 / 3 * 710 = 473.33 460.00 - - - - - - - - - - - - - - - 13.33 1 / 3 uniform 13.33 1 - - - - - - - - - - - - - - - ? = > rs . 40 answer : a"
Answer: a
Question (general): the cricket team of 11 members is 26 yrs old & the wicket keeper is 3 yrs older . if the ages ofthese 2 are excluded , the average age of theremaining players is 1 year less than the average age of the whole team . what is the average age of the team ?
Options: a ) 19 , b ) 21 , c ) 23 , d ) 25 , e ) 27
Rationale: "let the average age of the whole team be x years . 11 x - ( 26 + 29 ) = 9 ( x - 1 ) = > 11 x - 9 x = 46 = > 2 x = 46 = > x = 23 . so , average age of the team is 23 years . c"
Answer: c
Question (general): a student has to obtain 33 % of the total marks to pass . he got 125 marks and failed by 73 marks . the maximum marks are ?
Options: a ) 450 , b ) 300 , c ) 500 , d ) 600 , e ) 175
Rationale: "let the maximum marks be x then , 33 % of x = 125 + 73 33 x / 100 = 198 x = 600 answer is d"
Answer: d
Question (other): a ratio between two numbers is 3 : 4 and their l . c . m . is 180 . the first number is
Options: a ) 60 , b ) 45 , c ) 20 , d ) 15 , e ) none
Rationale: "sol . let the required numbers be 3 x and 4 x . then , their l . c . m . is 12 x . ∴ 12 x = 180 ⇔ x = 15 . hence , the first number is 45 . answer b"
Answer: b
Question (physics): mike , jim and bob are all professional fisherman . mike can catch 30 fish in one hour , jim can catch twice as much and bob can catch 50 % more than jim . if the 3 started to fish together and after 40 minutes mike and bob left , how many fish did the 3 fishermen catch in one hour ?
Options: a ) 110 , b ) 120 , c ) 140 , d ) 130 , e ) 112
Rationale: all of them catch fishes in relation to number 30 . . . . 2 / 3 * 30 + 2 * 30 + 2 * 1.5 * 30 * 2 / 3 = 140 answer is c
Answer: c
Question (general): in a certain game of dice , the player ’ s score is determined as a sum of two throws of a single die . the player with the highest score wins the round . if more than one player has the highest score , the winnings of the round are divided equally among these players . if john plays this game against 22 other players , what is the probability of the minimum score that will guarantee john some monetary payoff ?
Options: a ) 41 / 50 , b ) 1 / 221 , c ) 1 / 216 , d ) 1 / 36 , e ) 1 / 42
Rationale: "to guarantee that john will get some monetary payoff he must score the maximum score of 6 + 6 = 12 , because if he gets even one less than that so 11 , someone can get 12 and john will get nothing . p ( 12 ) = 1 / 6 ^ 2 = 1 / 36 . answer : d ."
Answer: d
Question (physics): it was calculated that 75 men could complete a piece of work in 10 days . when work was scheduled to commence , it was found necessary to send 25 men to another project . how much longer will it take to complete the work ?
Options: a ) 10 days . , b ) 20 days . , c ) 25 days . , d ) 12.5 days . , e ) 15 days .
Rationale: "one day work = 1 / 10 one man ’ s one day work = 1 / ( 10 * 75 ) now : no . of workers = 50 one day work = 50 * 1 / ( 10 * 75 ) the total no . of days required to complete the work = ( 75 * 10 ) / 50 = 15 answer : e"
Answer: e
Question (general): two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs , x and y . now , jug x is 1 / 7 full , while jug y is 2 / 3 full . if water is poured from jug x into jug y until jug y is filled , what fraction of jug x then contains water ?
Options: a ) 0 , b ) 1 / 14 , c ) 2 / 15 , d ) 1 / 10 , e ) 2 / 10
Rationale: suppose the water in each jug is l liters cx x ( 1 / 7 ) = l cx = 7 l liters cx is capacity of x cy x ( 2 / 3 ) = l cy = 3 l / 2 liters cy is capacity of y now , y is 3 l / 2 - l empty = l / 2 empty so , we can put only l / 2 water in jug y from jug x jug x ' s remaining water = l - l / 2 = l / 2 fraction of x which contains water = water / cx = ( l / 2 ) / 7 l = 1 / 14 answer will be b
Answer: b
Question (other): a grocery store bought some mangoes at a rate of 4 for a dollar . they were separated into two stacks , one of which was sold at a rate of 3 for a dollar and the other at a rate of 6 for a dollar . what was the ratio of the number of mangoes in the two stacks if the store broke even after having sold all of its mangoes ?
Options: a ) 1 : 4 , b ) 1 : 5 , c ) 2 : 3 , d ) 1 : 2 , e ) 1 : 2
Rationale: "the cost price of a mango = 1 / 4 dollars . the selling price of a mango from the first stack = 1 / 3 dollars - - > the profit from one mango = 1 / 3 - 1 / 4 = 1 / 12 dollars . the selling price of a mango from the second stack = 1 / 6 dollars - - > the loss from one mango = 1 / 3 - 1 / 6 = 1 / 6 dollars . the profit from one mango from the first stack is 4 times the loss from one mango from the second stack . the ratio is 1 / 12 * 6 / 1 = 1 / 2 = 1 : 2 e"
Answer: e
Question (physics): if the weight of 13 meters long rod is 13.4 kg . what is the weight of 6 meters long rod ?
Options: a ) 7.2 kg . , b ) 10.8 kg . , c ) 12.4 kg . , d ) 6.18 kg , e ) none
Rationale: answer ∵ weight of 13 m long rod = 13.4 kg ∴ weight of 1 m long rod = 13.4 / 13 kg ∴ weight of 6 m long rod = 13.4 x 6 / 13 = 6.18 kg option : d
Answer: d
Question (geometry): if each side of a rectangle is increased by 50 % with the length being double the width , find the percentage change in its area ?
Options: a ) 284 % , b ) 276 % , c ) 265.25 % , d ) 284.5 % , e ) 275 %
Rationale: "area = 2 a x a new length = 250 a / 100 = 5 a / 2 new width = 150 a / 100 = 3 a / 2 new area = ( 5 a x 3 a ) / ( 2 x 2 ) = ( 15 a ² / 4 ) increased area = = ( 15 a ² / 4 ) - a ² increase % = [ ( 11 a ² / 4 ) x ( 1 / a ² ) x 100 ] % = 275 % answer : e"
Answer: e
Question (physics): the length of a room is 5.5 m and width is 3.75 m . find the cost of paying the floor by slabs at the rate of rs . 800 per sq . metre
Options: a ) 22488 , b ) 16500 , c ) 27889 , d ) 23778 , e ) 29982
Rationale: "explanation : area = 5.5 × 3.75 sq . metre . cost for 1 sq . metre . = rs . 800 hence total cost = 5.5 × 3.75 × 800 = 5.5 × 3000 = rs . 16500 answer : b ) rs . 16500"
Answer: b
Question (geometry): if the area of a circle decreases by 25 % , then the radius of a circle decreases by
Options: a ) 13 % , b ) 18 % , c ) 36 % , d ) 64 % , e ) none of these
Rationale: "if area of a circle decreased by x % then the radius of a circle decreases by ( 100 − 10 √ 100 − x ) % = ( 100 − 10 √ 100 − 25 ) % = ( 100 − 10 √ 75 ) % = 100 - 87 = 13 % answer a"
Answer: a
Question (gain): alfred buys an old scooter for $ 4700 and spends $ 1000 on its repairs . if he sells the scooter for $ 5800 , his gain percent is ?
Options: a ) 5.45 % , b ) 6.23 % , c ) 1.75 % , d ) 8.12 % , e ) 10 %
Rationale: "c . p . = 4700 + 1000 = $ 5700 s . p . = $ 5800 gain = 5800 - 5700 = $ 100 gain % = 100 / 5700 * 100 = 1.75 % answer is c"
Answer: c
Question (general): find the average of all the numbers between 11 and 36 which are divisible by 5 .
Options: a ) 25 , b ) 77 , c ) 20 , d ) 28 , e ) 10
Rationale: "explanation : average = ( 15 + 20 + 25 + 30 + 35 ) / 5 = 125 / 5 = 25 answer : a"
Answer: a
Question (general): how many e ways can jason sit with his 5 friends in a row of 6 seats with an aisle on either side of the row , if jason insists on sitting next to one of the aisles ?
Options: a ) 120 , b ) 240 , c ) 360 , d ) 540 , e ) 720
Rationale: jason can select his seat in 2 ways ( two aisles ) his 1 st of 4 friends have 5 seats to select = > his 2 nd of remaining 3 friends will have 4 seat to chose from . . . and so on total ways e = > 2 * 5 * 4 * 3 * 2 * 1 = 240 . b
Answer: b
Question (general): 56 : 65 : : 68 : ?
Options: a ) 49 , b ) 84 , c ) 86 , d ) 64 , e ) 56
Rationale: "ans 86 reverse of 68 answer : c"
Answer: c
Question (general): in the biology lab of ` ` jefferson ' ' high school there are 0.037 * 10 ^ 5 germs , equally divided among 148000 * 10 ^ ( - 3 ) petri dishes . how many germs live happily in a single dish ?
Options: a ) 10 , b ) 25 , c ) 35 , d ) 40 , e ) 55
Rationale: "0.037 * 10 ^ 5 can be written as 3700 148000 * 10 ^ ( - 3 ) can be written as 148 required = 3700 / 148 = 25 answer : b"
Answer: b
Question (general): the sum of ages of 5 children born 1.5 years different each is 50 years . what is the age of the elder child ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 16 , e ) 13
Rationale: "let the ages of children be x , ( x + 1.5 ) , ( x + 3 ) , ( x + 4.5 ) and ( x + 6 ) years . then , x + ( x + 1.5 ) + ( x + 3 ) + ( x + 4.5 ) + ( x + 6 ) = 50 5 x = 35 x = 7 . x + 6 = 7 + 6 = 13 answer : e"
Answer: e
Question (general): what is the average ( arithmetic mean ) of all multiples of 10 from 10 to 100 inclusive ?
Options: a ) 190 , b ) 195 , c ) 200 , d ) 205 , e ) 55
Rationale: "this question can be solved with the average formula and ' bunching . ' we ' re asked for the average of all of the multiples of 10 from 10 to 100 , inclusive . to start , we can figure out the total number of terms rather easily : 1 ( 10 ) = 10 2 ( 10 ) = 20 . . . 10 ( 10 ) = 100 so we know that there are 10 total numbers . we can now figure out the sum of those numbers with ' bunching ' : 10 + 100 = 110 20 + 90 = 110 30 + 80 = 110 etc . since there are 10 total terms , this pattern will create 5 ' pairs ' of 110 . thus , since the average = ( sum of terms ) / ( number of terms ) , we have . . . ( 5 ) ( 110 ) / ( 10 ) = 55 answer : e"
Answer: e
Question (physics): a cistern can be filled by a tap in 4 hours while it can be emptied by another tap in 5 hours . if both the taps are opened simultaneously , then after how much time will the cistern get filled ?
Options: a ) 7.5 , b ) 20 , c ) 30 , d ) 32 , e ) 40
Rationale: "net part filled in 1 hour = ( 1 / 4 - 1 / 5 ) = 1 / 20 the cistern will be filled in 20 / 1 hrs i . e . , 20 hrs . answer : b"
Answer: b
Question (general): what is the sum of all 3 digit numbers that leave a remainder of ' 2 ' when divided by 4 ?
Options: a ) 123,750 , b ) 164,850 , c ) 164,749 , d ) 149,700 , e ) 156,720
Rationale: "find the number , upon sum of 3 digits of a number gives a reminder 2 when it is divided by 4 seeing the options after dividing and finding the reminder of 2 my answer was a"
Answer: a
Question (gain): in an election a candidate who gets 60 % of the votes is elected by a majority of 1200 votes . what is the total number of votes polled ?
Options: a ) 4500 , b ) 5200 , c ) 6900 , d ) 7520 , e ) 6000
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1200 20 x / 100 = 1200 x = 1200 * 100 / 20 = 6000 answer is e"
Answer: e
Question (general): if money is invested at r percent interest , compounded annually , the amount of investment will double in approximately 70 / r years . if pat ' s parents invested $ 5000 in a long term bond that pays 8 percent interest , compounded annually , what will be the approximate total amount of investment 18 years later , when pat is ready for college ?
Options: a ) $ 20000 , b ) $ 15000 , c ) $ 12000 , d ) $ 10000 , e ) $ 9000
Rationale: "since investment doubles in 70 / r years then for r = 8 it ' ll double in 70 / 8 = ~ 9 years ( we are not asked about the exact amount so such an approximation will do ) . thus in 18 years investment will double twice and become ( $ 5,000 * 2 ) * 2 = $ 20,000 ( after 9 years investment will become $ 5,000 * 2 = $ 10,000 and in another 9 years it ' ll become $ 10,000 * 2 = $ 20,000 ) . answer : a ."
Answer: a
Question (probability): tomeka is playing a dice game . if she rolls the same number on her second roll as she rolls on her first , she wins . each roll is with two , fair , 6 - sided dice . if tomeka rolled a 7 on her first roll , what is the probability that she will win on her second roll ?
Options: a ) 1 / 4 , b ) 1 / 5 , c ) 1 / 6 , d ) 1 / 9 , e ) 1 / 12
Rationale: there are 6 ways to roll a seven : 1 and 6 , 6 and 1 , 2 and 5 , 5 and 2 , 3 and 4 , 4 and 3 . there are 6 * 6 = 36 ways to roll two six - sided dice . thus the probability of winning by rolling a seven on the second roll given a seven on the first roll is 6 / 36 = 1 / 6 c
Answer: c
Question (general): a company has 15 managers and 75 associates . the 15 managers have an average salary of $ 90000 . the 75 associates have an average salary of $ 30000 . what is the average salary for the company ?
Options: a ) $ 35,000 , b ) $ 40,000 , c ) $ 55,000 , d ) $ 65,000 , e ) $ 75,000
Rationale: another method is to get ratios say 30000 = a and we know the # of people are in 1 : 5 ratio average = ( 3 a * 1 + a * 5 ) / 6 = 8 a / 6 = 40000 answer is b . $ 40,000
Answer: b
Question (physics): a man can row upstream at 37 kmph and downstream at 53 kmph , and then find the speed of the man in still water ?
Options: a ) 29 , b ) 92 , c ) 30 , d ) 32 , e ) 45
Rationale: "us = 37 ds = 53 m = ( 53 + 37 ) / 2 = 45 answer : e"
Answer: e
Question (other): a certain car dealership sells economy cars , luxury cars , and sport utility vehicles . the ratio of economy to luxury cars is 3 : 2 . the ratio of economy cars to sport utility vehicles is 5 : 4 . what is the ratio of luxury cars to sport utility vehicles ?
Options: a ) 9 : 8 , b ) 8 : 9 , c ) 3 : 2 , d ) 10 : 12 , e ) 1 : 2
Rationale: "the ratio of economy to luxury cars is 3 : 2 - - > e : l = 3 : 2 = 15 : 10 . the ratio of economy cars to sport utility vehicles is 5 : 4 - - > e : s = 5 : 4 = 15 : 12 . thus , l : s = 10 : 12 . answer : d ."
Answer: d
Question (general): in a certain apartment building , there are one - bedroom and two - bedroom apartments . the rental prices of the apartment depend on a number of factors , but on average , two - bedroom apartments have higher rental prices than do one - bedroom apartments . let m be the average rental price for all apartments in the building . if m is $ 1,500 higher than the average rental price for all one - bedroom apartments , and if the average rental price for all two - bedroom apartments is $ 6,000 higher that m , then what percentage of apartments in the building are two - bedroom apartments ?
Options: a ) 40 % , b ) 35 % , c ) 30 % , d ) 20 % , e ) 28 %
Rationale: "ratio of 2 bedroom apartment : 1 bedroom apartment = 1500 : 6000 - - - - - > 1 : 4 let total number of apartments be x no . of 2 bedroom apartment = ( 1 / 5 ) * x percentage of apartments in the building are two - bedroom apartments - - - - > ( 1 / 5 ) * 100 - - - > 20 % answer : d"
Answer: d
Question (general): solve below question 2 x - 1 = 17
Options: a ) - 8 , b ) - 9 , c ) - 5 , d ) - 4 , e ) 9
Rationale: 1 . add 1 to both sides : 2 x - 1 + 1 = 17 + 1 2 . simplify both sides : 2 x = 18 3 . divide both sides by 2 : 4 . simplify both sides : x = 9 e
Answer: e
Question (gain): john and jane went out for a dinner and they ordered the same dish . both used a 10 % discount coupon . john paid a 15 % tip over the original price of the dish , while jane paid the tip over the discounted price for the coupon . if john paid $ 0.54 more than jane , what was the original price of the dish ?
Options: a ) 24 , b ) 34.8 , c ) 36 , d ) 42 , e ) 84
Rationale: "the difference between the amounts john paid and jane paid is the deference between 15 % of p and 15 % of 0.9 p : 0.15 p - 0.15 * 0.9 p = 0.54 - - > 15 p - 13.5 p = 54 - - > p = 36 . answer : c ."
Answer: c
Question (general): 80 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0
Rationale: "should be simple . 0.8 * 5 / 8 = 4 / 8 = 1 / 2 = 0.5 correct option : b"
Answer: b
Question (general): if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is ?
Options: a ) 6 , b ) 12 , c ) 24 , d ) 36 , e ) 48
Rationale: "q : if n is a positive integer and n ^ 2 is divisible by 72 , then the largest positive integer t that must divide n is : a 6 , b 12 , c 24 , d 36 , e 48 n ^ 2 is divisible by 72 , but it must also be greater than 72 . if n is an integer , then n ^ 2 must be a perfect square . the factorization of 72 is ( 8 ) ( 9 ) , so if it is multiplied by 2 , it will be ( 2 ) ( 8 ) ( 9 ) = ( 16 ) ( 9 ) = 144 , a perfect square . so n ^ 2 must be at least 144 or a multiple of 144 , which means that n must be 12 or a multiple of 12 . b"
Answer: b
Question (physics): angelina walked 720 meters from her home to the grocery at a constant speed . she then walked 480 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 6 , e ) 24
Rationale: "let the speed be x . . . so time taken from home to grocery = 720 / x . . the speed to gym = 2 x . . so time taken = 480 / 2 x = 240 / x . . its given 720 / x - 240 / x = 40 . . 480 / x = 40 . . x = 12 m / secs . . so grocery to gym = 2 * 12 = 24 m / s . . . e"
Answer: e
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 , b ) 14 , c ) 15 , d ) 13 , e ) 18
Rationale: "age of the 15 th student = [ 15 * 15 - ( 14 * 5 + 16 * 9 ) ] = ( 225 - 214 ) = 11 years . answer a"
Answer: a
Question (probability): john and peter are among the 9 players a volleyball coach can choose from to field a 6 - player team . if all 6 players are chosen at random , what is the probability of choosing a team that includes john and peter ?
Options: a ) 3 / 10 , b ) 4 / 11 , c ) 5 / 12 , d ) 6 / 13 , e ) 7 / 15
Rationale: the total possible ways of selecting a 6 - member team is 9 c 6 = 84 the possible ways which include john and peter is 7 c 4 = 35 the probability of choosing both john and peter is 35 / 84 = 5 / 12 the answer is c .
Answer: c
Question (general): a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.6 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 1,200 , e ) e . 360
Rationale: "volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.6 = 360 answer : e"
Answer: e