Cheukting/mathqa huggingface dataset:
Question (general): if two positive numbers are in the ratio 1 / 7 : 1 / 4 , then by what percent is the second number more than the first ?
Options: a ) 67 % . , b ) 70 % . , c ) 75 % . , d ) 68 % . , e ) 80 % .
Rationale: "given ratio = 1 / 7 : 1 / 4 = 4 : 7 let first number be 4 x and the second number be 7 x . the second number is more than first number by 3 x . required percentage = 3 x / 4 x * 100 = 75 % . answer : c"
Answer: c
Question (general): a certain library assesses fines for overdue books as follows . on the first day that a book is overdue , the total fine is $ 0.09 . for each additional day that the book is overdue , the total fine is either increased by $ 0.30 or doubled , whichever results in the lesser amount . what is the total for a book on the fourth day it is overdue ?
Options: a ) $ 0.66 , b ) $ 0.70 , c ) $ 0.80 , d ) $ 0.90 , e ) $ 1.00
Rationale: "1 st day fine - 0.09 2 nd day fine - 0.09 * 2 = 0.18 ( as doubling gives lower value ) 3 rd day fine - 0.18 * 2 = 0.36 ( as doubling gives lower value ) 4 th day fine - 0.36 + 0.3 = 0.66 ( as doubling gives higher value we add 0.3 this time ) answer : a ."
Answer: a
Question (general): what is the sum of the numbers between 1 and 14 , inclusive ?
Options: a ) 105 , b ) 110 , c ) 125 , d ) 150 , e ) 160
Rationale: "sol . add up the numbers between 1 and 14 . answer is a , 105"
Answer: a
Question (general): how many prime numbers are between 25 / 3 and 84 / 6 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "25 / 3 = 8 . xxx 84 / 6 = 14 . xxx so we need to find prime numbers between 8 ( exclusive ) - 13 ( inclusive ) there are 2 prime numbers 1113 hence answer will be ( b ) 2 b"
Answer: b
Question (general): a company wants to spend equal amounts of money for the purchase of two types of computer printers costing $ 400 and $ 350 per unit , respectively . what is the fewest number of computer printers that the company can purchase ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "the smallest amount that the company can spend is the lcm of 400 and 350 , which is 2800 for each , which is total 5600 . the number of 1 st type of computers which costing $ 400 = 2800 / 400 = 7 . the number of 2 nd type of computers which costing $ 350 = 2800 / 350 = 8 . total = 7 + 8 = 15 answer is c ."
Answer: c
Question (general): if 13 = 13 w / ( 1 - w ) , then ( 6 w ) 2 =
Options: a ) 1 / 4 , b ) 1 / 2 , c ) 1 , d ) 2 , e ) 6
Rationale: "13 - 13 w = 13 w 26 w = 13 w = 1 / 2 6 w = 3 6 w * 2 = 3 * 2 = 6 answer : e"
Answer: e
Question (physics): a man can row upstream at 25 kmph and downstream at 55 kmph , and then find the speed of the man in still water ?
Options: a ) 65 , b ) 40 , c ) 30 , d ) 78 , e ) 38
Rationale: "us = 25 ds = 55 m = ( 55 + 25 ) / 2 = 40 answer : b"
Answer: b
Question (general): in a room filled with 6 people , all 6 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 3 / 5 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 6 , e ) 7 / 12
Rationale: "the 6 people consist of two sets of 3 siblings . the number of ways to choose 2 people is 6 c 2 = 15 . the number of ways to choose 2 from the first group of siblings is 3 c 2 = 3 . the number of ways to choose 2 from the second group of siblings is 3 c 2 = 3 . the number of ways to choose 2 people who are siblings is 3 + 3 = 6 . the number of ways to choose 2 people who are not siblings is 15 - 6 = 9 . p ( the two people are not siblings ) = 9 / 15 = 3 / 5 the answer is a ."
Answer: a
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 60 ?
Options: a ) s . 3944 , b ) s . 3948 , c ) s . 4080 , d ) s . 3965 , e ) s . 3929
Rationale: "let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 60 = rs . 4080 . answer : c"
Answer: c
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 32 hours and 16 hours respectively . the ratio of their speeds is
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 12 , d ) 1 : 2 , e ) 4 : 5
Rationale: let us name the trains as a and b . then , ( a ' s speed ) : ( b ' s speed ) = b : a = 16 : 32 = 1 : 2 . answer : d
Answer: d
Question (general): an electrical appliances store sold this month 400 % more than the average of all the other months in the year . the sales total for this month was approximately what percent of total sales for this year ?
Options: a ) 14 % , b ) 21 % . , c ) 31 % . , d ) 37 % . , e ) 43 % .
Rationale: the average sales for all the other months ( 11 months ) of the year is x . so , the total sales of those 11 months will be = 11 x now , this month ' s sales , which is 400 % more than the average of other months ' sales , is 5 x , ( x + 400 % of x ) . thus , this month ' s ' sales are ( 5 x / 16 x ) * 100 = 31.25 % of the total yearly sales . [ total sales = 11 x + 5 x = 16 x ] answer is b
Answer: b
Question (other): a bag contains 10 green and 8 white balls . if two balls are drawn simultaneously , the probability that both are of the same colour is
Options: a ) 8 / 15 , b ) 21 / 44 , c ) 3 / 5 , d ) 11 / 15 , e ) 7 / 15
Rationale: drawing two balls of same color from ten green balls can be done in 10 c ₂ ways . similarly from eight white balls two can be drawn in ⁸ c ₂ ways . p = 10 c ₂ / ¹ ⁵ c ₂ + ⁸ c ₂ / ¹ ⁵ c ₂ = 21 / 44 answer : b
Answer: b
Question (physics): two bike riders ride in opposite directions around a circular track , starting at the same time from the same point . biker a rides at a speed of 16 kmph and biker b rides at a speed of 14 kmph . if the track has a diameter of 40 km , after how much time ( in hours ) will the two bikers meet ?
Options: a ) 8.18 hrs . , b ) 6.18 hrs . , c ) 4.18 hrs . , d ) 1.18 hrs . , e ) 7.18 hrs .
Rationale: explanation : distance to be covered = = 40 km relative speed of bikers = 16 + 14 = 30 kmph . now , = = 4.18 hrs . answer : c
Answer: c
Question (physics): a cistern 12 m long and 14 m wide contains water up to a depth of 1 m 25 cm . the total area of the wet surface is :
Options: a ) 224 m 2 , b ) 250 m 2 , c ) 220 m 2 , d ) 230 m 2 , e ) 233 m 2
Rationale: "area of the wet surface = [ 2 ( lb + bh + lh ) - lb ] = 2 ( bh + lh ) + lb = [ 2 ( 14 x 1.25 + 12 x 1.25 ) + 12 x 14 ] m 2 = 233 m 2 . answer : e"
Answer: e
Question (general): if a / b = 1 / 3 , b / c = 2 , c / d = 1 / 2 , d / e = 3 and e / f = 1 / 10 , then what is the value of abc / def ?
Options: a ) 27 / 4 , b ) 27 / 8 , c ) 3 / 4 , d ) 3 / 20 , e ) 1 / 4
Rationale: say a = 2 . then : a / b = 1 / 3 - - > b = 6 ; b / c = 2 - - > c = 3 ; c / d = 1 / 2 - - > d = 6 ; d / e = 3 - - > e = 2 ; e / f = 1 / 10 - - > f = 20 . abc / def = ( 2 * 6 * 3 ) / ( 6 * 2 * 20 ) = 3 / 20 . answer : d .
Answer: d
Question (gain): john and david can finish a job together in 2 hours . if john can do the job by himself in 3 hours , what percent of the job does david do ?
Options: a ) 36.33 % , b ) 33.33 % , c ) 39.33 % , d ) 40.33 % , e ) 33 %
Rationale: "you can also plug in numbers . for example , bob and alice work at a donut factory and make 18 donuts which is the job ( i picked this as a smart number ) . john on his own works 18 / 3 = 6 donuts per hour . john and david work 18 / 2 = 9 donuts per hour so david works 3 donuts / hour to find out the percentage , david works 3 donuts / hr x 2 hours = 6 donuts per hour . therefore 6 donuts / 18 donuts = 1 / 3 = 33.33 % answer : b"
Answer: b
Question (gain): find the compound interest on $ 10000 in 2 years at 4 % per annum , the interest being compounded half - yearly ?
Options: a ) $ 645.56 , b ) $ 824.32 , c ) $ 954.26 , d ) $ 745.69 , e ) $ 1020.45
Rationale: "principle = $ 10000 rate = 2 % half yearly = 4 half years amount = 10000 * ( 1 + 2 / 100 ) ^ 4 = 10000 * 51 / 50 * 51 / 50 * 51 / 50 * 51 / 50 = $ 10824.32 c . i . = 10824.32 - 10000 = $ 824.32 answer is b"
Answer: b
Question (general): if a = 105 and a ^ 3 = 21 × 25 × 45 × z , what is the value of z ?
Options: a ) 35 , b ) 42 , c ) 45 , d ) 49 , e ) 54
Rationale: "a = 105 = 3 * 5 * 7 a ^ 3 = 21 × 25 × 45 × z = > a ^ 3 = ( 7 * 3 ) x ( 5 * 5 ) x ( 3 ^ 2 * 5 ) x z = > a ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x z = > ( 3 * 5 * 7 ) ^ 3 = 3 ^ 3 * 5 ^ 3 * 7 x z z = 7 ^ 2 = 49 answer d"
Answer: d
Question (gain): if the cost price of 50 articles is equal to the selling price of 45 articles , then the gain or loss percent is ?
Options: a ) 11.11 , b ) 65 , c ) 78 , d ) 33 , e ) 25
Rationale: "given that , cost price of 50 article is equal to selling price of 45 articles . let cost price of one article = rs . 1 selling price of 45 articles = rs . 50 but cost price of 45 articles = rs . 45 therefore , the trader made profit . \ percentage of profit = 5 / 45 * 100 = 11.11 % answer : a"
Answer: a
Question (general): the area of one square is x ^ 2 + 6 x + 9 and the area of another square is 4 x ^ 2 − 28 x + 49 . if the sum of the perimeters of both squares is 56 , what is the value of x ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "the areas are ( x + 3 ) ^ 2 and ( 2 x - 7 ) ^ 2 . the lengths of the sides are x + 3 and 2 x - 7 . if we add the two perimeters : 4 ( x + 3 ) + 4 ( 2 x - 7 ) = 56 12 x = 72 x = 6 the answer is d ."
Answer: d
Question (physics): a train moves with a speed of 162 kmph . its speed in metres per second is
Options: a ) 10.8 , b ) 18 , c ) 30 , d ) 38.8 , e ) 45
Rationale: "solution speed = 108 kmph = ( 162 x 5 / 18 ) m / sec = 45 m / sec . answer e"
Answer: e
Question (general): which number should replace both the asterisks in ( * / 20 ) x ( * / 80 ) = 1 ?
Options: a ) 20 , b ) 40 , c ) 60 , d ) 80 , e ) 120
Rationale: "let ( y / 20 ) x ( y / 80 ) = 1 y ^ 2 = 20 x 80 = 20 x 20 x 4 y = ( 20 x 2 ) = 40 the answer is b ."
Answer: b
Question (physics): two trains of equal length , running with the speeds of 60 and 90 kmph , take 50 seconds to cross each other while they are running in the same direction . what time will they take to cross each other if they are running in opposite directions ?
Options: a ) 3.2 , b ) 2.6 , c ) 6.6 , d ) 32.2 , e ) 42.2
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 90 = 150 * 5 / 18 t = 2500 / 9 * 18 / 750 = 6.6 sec . answer : c"
Answer: c
Question (general): a couple spent $ 211.20 in total while dining out and paid this amount using a credit card . the $ 211.20 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 120 , b ) $ 140 , c ) $ 150 , d ) $ 160 , e ) $ 180
Rationale: "let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = $ 211.20 x = $ 160 the correct answer is d ."
Answer: d
Question (general): at a school , 3 - fifths of the male students and two - thirds of the female students speak a foreign language . if the number of males is equal to the number of females , what fraction of the students speak a foreign language ?
Options: a ) 17 / 30 , b ) 19 / 30 , c ) 11 / 15 , d ) 7 / 15 , e ) 2 / 5
Rationale: let x be the number of students in the school . the number of males who speak a foreign language is ( 3 / 5 ) ( 1 / 2 ) x = ( 3 / 10 ) x the number of females who speak a foreign language is ( 2 / 3 ) ( 1 / 2 ) x = ( 1 / 3 ) x the total number of students who speak a foreign language is ( 3 / 10 ) x + ( 1 / 3 ) x = ( 19 / 30 ) x the answer is b .
Answer: b
Question (general): 11 + 12 + 13 + . . . 51 + 52 = ?
Options: a ) 1361 , b ) 1362 , c ) 1323 , d ) 1364 , e ) 1365
Rationale: "sum = 11 + 12 + 13 + . . . 50 + 51 + 52 sum of n consecutive positive integers starting from 1 is given as n ( n + 1 ) / 2 sum of first 52 positive integers = 52 * 53 / 2 sum of first 10 positive integers = 10 * 11 / 2 sum = 11 + 12 + 13 + 14 + . . . 51 + 52 = 52 * 53 / 2 - 10 * 11 / 2 = 1323 answer : c"
Answer: c
Question (physics): it is currently 7 : 05 pm . what time was it in the morning exactly 51,132 minutes ago ?
Options: a ) 6 : 53 , b ) 6 : 55 , c ) 6 : 59 , d ) 7 : 03 , e ) 7 : 09
Rationale: convert 51,132 minutes to hours by dividing by 60 : 51,132 / 60 = 852 r 12 . that is 852 hours , 12 minutes . convert 852 hours to days by dividing by 24 : 852 / 24 = 35 r 12 . that is 35 days , 12 hours . thus 852 hours before 7 : 05 pm is 12 hours before 7 : 05 pm which is 7 : 05 am . 12 minutes before that is 6 : 53 am . a
Answer: a
Question (physics): the time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream . if the speed of the boat in still water is 60 kmph , find the speed of the stream ?
Options: a ) 18 kmph , b ) 19 kmph , c ) 21 kmph , d ) 22 kmph , e ) 20 kmph
Rationale: "the ratio of the times taken is 2 : 1 . the ratio of the speed of the boat in still water to the speed of the stream = ( 2 + 1 ) / ( 2 - 1 ) = 3 / 1 = 3 : 1 speed of the stream = 60 / 3 = 20 kmph . answer : e"
Answer: e
Question (physics): a contractor undertook to do a piece of work in 18 days . he employed certain number of laboures but 9 of them were absent from the very first day and the rest could finish the work in only 6 days . find the number of men originally employed ?
Options: a ) 3.5 , b ) 4 , c ) 4.5 , d ) 4.2 , e ) 4.3
Rationale: "let the number of men originally employed be x . 18 x = 6 ( x â € “ 9 ) or x = 4.5 answer c"
Answer: c
Question (geometry): the length of a rectangular plot is thrice its width . if the area of the rectangular plot is 432 sq meters , then what is the width ( in meters ) of the rectangular plot ?
Options: a ) 10
b ) 11
c ) 12
d ) 13
e ) 14
Rationale: area = l * w = 3 w ^ 2 = 432 w ^ 2 = 144 w = 12 the answer is c .
Answer: c
Question (physics): a certain car uses 12 gallons of gasoline in traveling 120 miles . in order for the car to travel the same distance using 10 gallons of gasoline , by how many miles per gallon must the car ’ s gas mileage be increased ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 8 , e ) 10
Rationale: 120 / 10 = 12 . the difference is 12 - 10 = 2 . answer a
Answer: a
Question (general): the captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older . if the ages of these two are excluded , the average age of the remaining players is one year less than the average age of the whole team . find out the average age of the team .
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 25
Rationale: "number of members in the team = 11 let the average age of of the team = x = > ( sum of ages of all 11 members ) / 11 = x = > sum of the ages of all 11 members = 11 x age of the captain = 26 age of the wicket keeper = 26 + 3 = 29 sum of the ages of 9 members of the team excluding captain and wicket keeper = 11 x − 26 − 29 = 11 x − 55 average age of 9 members of the team excluding captain and wicket keeper = ( 11 x − 55 ) / 9 given that ( 11 x − 55 ) / 9 = ( x − 1 ) ⇒ 11 x − 55 = 9 ( x − 1 ) ⇒ 11 x − 55 = 9 x − 9 ⇒ 2 x = 46 ⇒ x = 46 / 2 = 23 years answer is d ."
Answer: d
Question (general): a box contains 7 pairs of shoes ( 14 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 13 , e ) 1 / 9
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 14 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 13 ( as after taking one at random there are 13 shoes left and only one is the pair of the first one ) = 1 / 13 answer : d ."
Answer: d
Question (physics): a man can row at 5 kmph in still water . if the velocity of current is 1 kmph and it takes him 2 hour to row to a place and come back , how far is the place ?
Options: a ) 2.4 km , b ) 4.8 km , c ) 3.4 km , d ) 4.4 km , e ) 5.6 km
Rationale: "explanation : speed in still water = 5 kmph speed of the current = 1 kmph speed downstream = ( 5 + 1 ) = 6 kmph speed upstream = ( 5 - 1 ) = 4 kmph let the required distance be x km total time taken = 2 hour â ‡ ’ x / 6 + x / 4 = 2 â ‡ ’ 2 x + 3 x = 24 â ‡ ’ 5 x = 24 â ‡ ’ x = 4.8 km answer : option b"
Answer: b
Question (general): when positive integer x is divided by positive integer y , the remainder is 3 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 48 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 3 - - > x = qy + 3 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 3 - - > y = 25 . answer : d ."
Answer: d
Question (physics): twelve machines , each working at the same constant rate , together can complete a certain job in 6 days . how many additional machines , each working at the same constant rate , will be needed to complete the job in 3 days ?
Options: a ) 14 , b ) 12 , c ) 15 , d ) 16 , e ) 18
Rationale: "rate of one machine = 1 job / ( 12 * 6 ) days let x = number of machines needed to complete the job in 3 days 1 / ( 12 * 6 ) * 3 * x = 1 job x = 24 24 - 12 = 12 answer : b"
Answer: b
Question (general): if 2 + 3 = 13 ; 3 + 5 = 31 ; 5 + 7 = 59 , then 7 + 9 = ?
Options: a ) 95 , b ) 86 , c ) 67 , d ) 98 , e ) 89
Rationale: "2 x 2 + 3 ^ 2 = 4 + 9 = 13 3 x 2 + 5 ^ 2 = 6 + 25 = 31 5 x 2 + 7 ^ 2 = 10 + 49 = 59 and 7 x 2 + 9 ^ 2 = 14 + 81 = 95 answer : a"
Answer: a
Question (general): if john makes a contribution to a charity fund at school , the average contribution size will increase by 50 % reaching $ 75 per person . if there were 1 other contributions made before john ' s , what is the size of his donation ?
Options: a ) $ 100 , b ) $ 150 , c ) $ 200 , d ) $ 250 , e ) $ 450
Rationale: "cavg = average contribution before john cavg * 1.5 = 75 , therefore the average cont is $ 50 before john . if he needs to increase the average contribution by $ 25 , he must put in $ 25 for each of the 1 people . so $ 25 . but , he also has to put in the average for himself ( the twoth person ) , so add $ 75 . so $ 100 is your answer . answer a"
Answer: a
Question (physics): 15 men can complete a work in 10 days while 20 boys can complete the same work in 15 days . how many days will 10 men and 10 boys together take to complete the same work
Options: a ) 9 days , b ) 10 days , c ) 11 days , d ) 12 days , e ) 13 days
Rationale: solution : work done by one man in one day = 1 / ( 15 * 10 ) work done by one boy in one day = 1 / ( 20 * 15 ) work done by 10 men and 10 boys in one day = 10 [ 1 / ( 15 * 10 ) + 1 / ( 20 * 15 ) ] days taken = 1 / work done by 10 men and 10 boys in one day answer b
Answer: b
Question (geometry): a rectangular tiled patio is composed of 96 square tiles . the rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles . after the change in layout , the patio will still have 96 tiles , and it will still be rectangular . how many rows are in the tile patio before the change in layout ?
Options: a ) 5 , b ) 6 , c ) 8 , d ) 13 , e ) 28
Rationale: "suppose there are c columns and there are r rows original situation so , number of tiles = c * r = 96 also . reach column has r tiles and each row has c tiles new situation number of tiles in each column is r - 2 and number of tiles in each row is c + 4 so , number of rows = r - 2 and number of columns is c + 4 so , number of tiles = ( r - 2 ) * ( c + 4 ) = 96 comparing both of them we get c * r = ( r - 2 ) * ( c + 4 ) = > 4 r - 2 c = 8 c = 2 r - 4 putting it in c * r = 96 ( 2 r - 4 ) * r = 96 2 r ^ 2 - 4 r - 96 = 0 r can not be negative so r = 8 and c = 12 so , answer will be c"
Answer: c
Question (gain): what is 78 % of 4 / 5 ?
Options: a ) 6.9 , b ) 69.0 , c ) 0.6845 , d ) 0.624 , e ) 0.69
Rationale: "78 % * ( 4 / 5 ) = 0.78 * 0.8 = 0.624 answer : d"
Answer: d
Question (geometry): find the area of a parallelogram with base 12 cm and height 48 cm ?
Options: a ) 122 cm 2 , b ) 576 cm 2 , c ) 246 cm 2 , d ) 42 cm 2 , e ) 39 cm 2
Rationale: "area of a parallelogram = base * height = 12 * 48 = 576 cm 2 answer : b"
Answer: b
Question (other): of the diplomats attending a summit conference , 25 speak french , 32 do not speak russian , and 20 % of the diplomats speak neither french nor russian . if 10 % of the diplomats speak both languages , then how many diplomats attended the conference ?
Options: a ) 72 , b ) 70 , c ) 108 , d ) 120 , e ) 150
Rationale: "{ total } = { french } + { russian } - { both } + { neither } { total } = 25 + ( { total } - 32 ) - ( 0.1 * { total } ) + 0.2 * { total } solving gives { total } = 70 . answer : b ."
Answer: b
Question (general): a vendor buys 10 t - shirts at an average price of $ 14 per t - shirt . he then buys 15 more t - shirts at an average price of $ 11 per t - shirt . what is the average price q per t - shirt that the vendor paid for these purchases ?
Options: a ) $ 12.20 , b ) $ 12.50 , c ) $ 12.55 , d ) $ 12.70 , e ) $ 13.00
Rationale: "correct answer : a explanation : the relevant formula for this problem is average q = ( sum ) / ( number of terms ) . another way to look at the formula is sum = average x number of terms . for the first purchase , the vendor ' s sum ( total cost ) was $ 140 , since 14 x 10 = 140 . for the second purchase , the vendor ' s cost was $ 165 , since 11 x 15 = 165 . the grand sum is then $ 140 + $ 165 , which equals $ 305 . the total number of shirts purchased was 25 , so to get the average price per shirt , we divide 305 by 25 , which equals $ 12.20 . as a result , the correct answer is a . note : a relative understanding of weighted average offers a shortcut to this problem . because the true average of 11 and 14 is 12.5 , but the vendor sells more shirts at the lower price than at the higher price , the weighted average must be less than $ 12.50 ; only answer choice a is a possibility ."
Answer: a
Question (physics): excluding the stoppages , the speed of a bus is 48 km / hr and including the stoppages the speed of the bus is 12 km / hr . for how many minutes does the bus stop per hour ?
Options: a ) 45 min , b ) 10 min , c ) 12 min , d ) 20 min , e ) 18 min
Rationale: "speed of the bus without stoppage = 48 km / hr speed of the bus with stoppage = 12 km / hr difference in speed = 36 km / hr so , the time taken in the stoppages = time taken to cover 36 km = ( 36 / 48 ) hr = 3 / 4 hr = 45 min answer : a"
Answer: a
Question (gain): a furniture dealer purchased a desk for $ 120 and then set the selling price equal to the purchase price plus a markup that was 40 % of the selling price . if the dealer sold the desk at the selling price , what was the amount of the dealer ' s gross profit from the purchase and the sale of the desk ?
Options: a ) $ 40 , b ) $ 60 , c ) $ 80 , d ) $ 90 , e ) $ 100
Rationale: "purchase price = 120 selling price = x 120 + 0.4 * x = x 0.6 * x = 120 x = 200 profit = 200 - 150 = 50 answer : a"
Answer: a
Question (probability): there are 15 boys and 10 girls in a class . if three students are selected at random , in how many ways that 1 girl or 2 boys are selected ?
Options: a ) 100 , b ) 105 , c ) 115 , d ) 120 , e ) 125
Rationale: "n ( s ) = sample space = 25 c 3 = 2300 e = event that 1 girl and 2 boys are selected n ( e ) = we have to select 2 boys from 15 or 1 girl from 10 = 15 c 2 + 10 c 1 = 115 ans - c"
Answer: c