Cheukting/mathqa huggingface dataset:
Question (geometry): the surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 10 cm each . the radius of the sphere is
Options: a ) 3 cm , b ) 5 cm , c ) 6 cm , d ) 8 cm , e ) none
Rationale: "solution 4 î r 2 = 2 î 5 x 10 â ‡ ’ r 2 = ( 5 x 10 / 2 ) â ‡ ’ 25 â ‡ ’ r = 5 cm . answer b"
Answer: b
Question (general): find a number such that it exceeds 18 by 3 times the number by which it is less than 86 ?
Options: a ) 67 , b ) 68 , c ) 69 , d ) 70 , e ) 71
Rationale: x - 18 = 3 [ 86 - x ] x = 69 answer : c
Answer: c
Question (general): of the 3600 employees of company x , 12 / 25 are clerical . if the clerical staff were to be reduced by 1 / 4 , what percent of the total number of the remaining employees would then be clerical ?
Options: a ) 40 % , b ) 22.2 % , c ) 20 % , d ) 12.5 % , e ) 11.1 %
Rationale: let ' s see , the way i did it was 12 / 25 are clerical out of 3600 so 1728 are clerical 1728 reduced by 1 / 4 is 1728 * 1 / 4 so it reduced 432 people , so there is 1296 clerical people left but since 432 people left , it also reduced from the total of 3600 so there are 3168 people total since 1296 clerical left / 3168 people total you get ( a ) 40 %
Answer: a
Question (general): for an agricultural experiment , 300 seeds were planted in one plot and 200 were planted in a second plot . if exactly 25 percent of the seeds in the first plot germinated and exactly 40 percent of the seeds in the second plot germinated , what percent of the total number of seeds germinated ?
Options: a ) 12 % , b ) 26 % , c ) 29 % , d ) 31 % , e ) 60 %
Rationale: "in the first plot 25 % of 300 seeds germinated , so 0.25 x 300 = 75 seeds germinated . in the second plot , 40 % of 200 seeds germinated , so 0.4 x 200 = 80 seeds germinated . since 75 + 80 = 155 seeds germinated out of a total of 300 + 200 = 500 seeds , the percent of seeds that germinated is ( 155 / 500 ) x 100 % , or 31 % . answer : d ."
Answer: d
Question (geometry): an equilateral triangle t 2 is formed by joining the mid points of the sides of another equilateral triangle t 1 . a third equilateral triangle t 3 is formed by joining the mid - points of t 2 and this process is continued indefinitely . if each side of t 1 is 60 cm , find the sum of the perimeters of all the triangles .
Options: a ) 180 cm , b ) 220 cm , c ) 240 cm , d ) 270 cm , e ) 360 cm
Rationale: "we have 60 for first triangle , when we join mid - points of first triangle we get the second equilateral triangle then the length of second one is 30 and continues . so we have 60 , 30,15 , . . . we have ratio = 1 / 2 , and it is gp type . sum of infinite triangle is a / 1 - r = 60 / 1 - ( 1 / 2 ) = 120 equilateral triangle perimeter is 3 a = 3 * 120 = 360 . so option e ."
Answer: e
Question (general): in an election , candidate douglas won 66 percent of the total vote in counties x and y . he won 74 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 25 % , b ) 30 % , c ) 50 % , d ) 75 % , e ) 80 %
Rationale: given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 66 % voted means 74 * 200 = 148 votes combined for xy has 300 voters and voted 66 % so total votes = 198 balance votes = 198 - 148 = 50 as y has 100 voters so 50 votes means 50 % of votes required ans c
Answer: c
Question (general): amithab ' s average expenditure for the january to june is rs . 4200 and he spends rs . 1200 in january and rs . 1500 in july . the average expenditure for the months of febraury to july is
Options: a ) rs . 4250 , b ) rs . 4228 , c ) rs . 4128 , d ) rs . 4988 , e ) rs . 4192
Rationale: amithab ' s total expenditure for jan - june = 4200 x 6 = 25200 expenditure for feb - june = 25200 - 1200 = 24000 expenditure for the months of feb - july = 24000 + 1500 = 25500 the average expenditure = { 25500 } / { 6 } = 4250 answer : a
Answer: a
Question (general): one week , a certain truck rental lot had a total of 20 trucks , all of which were on the lot monday morning . if 50 % of the trucks that were rented out during the week were returned to the lot on or before saturday morning of that week , and if there were at least 16 trucks on the lot that saturday morning , what is the greatest number of different trucks that could have been rented out during the week ?
Options: a ) 18 , b ) 16 , c ) 12 , d ) 14 , e ) 8
Rationale: "n - not rented trucks ; r - rented trucks n + r = 20 n + r / 2 = 16 r = 8 e"
Answer: e
Question (physics): a person walks from one end to the other of a 80 - meter long moving walkway at a constant rate in 40 seconds , assisted by the walkway . when this person reaches the end , they reverse direction and continue walking with the same speed , but this time it takes 120 seconds because the person is traveling against the direction of the moving walkway . if the walkway were to stop moving , how many seconds would it take this person to walk from one end of the walkway to the other ?
Options: a ) 56 , b ) 60 , c ) 64 , d ) 68 , e ) 72
Rationale: "let v be the speed of the person and let x be the speed of the walkway . 40 ( v + x ) = 80 then 120 ( v + x ) = 240 120 ( v - x ) = 80 when we add the two equations : 240 v = 320 v = 4 / 3 time = 80 / ( 4 / 3 ) = 60 seconds the answer is b ."
Answer: b
Question (general): neha ' s mother was 4 times her age 12 years ago . she will be twice as old as neha 12 years from now . what is the present age of neha ' s mother ?
Options: a ) 60 years , b ) 33 , c ) 77 , d ) 66 , e ) 101
Rationale: explanation : let neha ' s present age be ' x ' years . her age 12 years ago = ( x – 12 ) years therefore , her mother ' s age 12 years ago = 4 ( x – 12 ) her mother ' s present age = 4 x – 48 + 12 = 4 x – 36 neha ' s age after 12 years = x + 12 her mother ' s age after 12 years = 4 x – 36 + 12 = 4 x – 24 4 x – 24 = 2 ( x + 12 ) 4 x – 2 x = 24 + 24 x = 24 therefore , neha ' s present age = 24 her mother ' s present age = 4 x – 36 = 4 ( 24 ) – 36 = 60 years answer : a
Answer: a
Question (geometry): what is the measure of the radius of the circle that circumscribes a triangle whose sides measure 3 , 4 , and 5 ?
Options: a ) 3.5 , b ) 3 , c ) 5 , d ) 4 , e ) 2.5
Rationale: "some of pyhtagron triplets we need to keep it in mind . like { ( 2 , 3,5 ) , ( 5 , 12,13 ) , ( 7 , 24,25 ) , ( 11 , 60,61 ) . so now we know the triangle is an right angle triangle . the circle circumscribes the triangle . the circum raduis of the circle that circumscribes the right angle triangle = hypotanse / 2 = 5 / 2 = 2.5 ans . e"
Answer: e
Question (general): what is the sum of the numbers between 1 and 5 , inclusive ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: "sol . add numbers between 1 and 5 . answer = c , 15 ."
Answer: c
Question (general): a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 46 instead of 96 then find the correct average marks up to two decimal places .
Options: a ) 73.41 , b ) 74.31 , c ) 73.42 , d ) 73.43 , e ) can not be determined
Rationale: "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 46 + 96 = 2570 correct average = 2570 / 35 = 73.42 answer : c"
Answer: c
Question (geometry): if the sides of a triangle are 36 cm , 34 cm and 20 cm , what is its area ?
Options: a ) 320 cm 2 , b ) 360 cm 2 , c ) 340 cm 2 , d ) 310 cm 2 , e ) 300 cm 2
Rationale: "the triangle with sides 36 cm , 34 cm and 20 cm is right angled , where the hypotenuse is 36 cm . area of the triangle = 1 / 2 * 34 * 20 = 340 cm 2 answer : c"
Answer: c
Question (physics): a group of hikers is planning a trip that will take them up a mountain using one route and back down using another route . they plan to travel down the mountain at a rate of one and a half times the rate they will use on the way up , but the time each route will take is the same . if they will go up the mountain at a rate of 3 miles per day and it will take them two days , how many miles long is the route down the mountain ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "on the way down , the rate is 1.5 * 3 = 4.5 miles per day . the distance of the route down the mountain is 2 * 4.5 = 9 miles . the answer is c ."
Answer: c
Question (gain): how many ounces of a 60 % salt solution must be added to 70 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 30 , c ) 50 , d ) 60.33 , e ) 70
Rationale: let x = ounces of 60 % salt solution to be added . 2 * 70 + . 6 x = . 4 ( 70 + x ) x = 70 answer e
Answer: e
Question (general): the average of 1 st 3 of 4 numbers is 16 and of the last 3 are 15 . if the sum of the first and the last number is 15 . what is the last numbers ?
Options: a ) 2 , b ) 4 , c ) 6 , d ) 5 , e ) 7
Rationale: "a + b + c = 48 b + c + d = 45 a + d = 13 a – d = 3 a + d = 15 2 d = 12 d = 6 answer c"
Answer: c
Question (physics): how many plants will be there in a circular bed whose outer edge measure 33 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 21 , d ) 120 , e ) none of these
Rationale: "circumference of circular bed = 33 cm area of circular bed = ( 33 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 33 ) 2 â  „ 4 ï € ã · 4 = 21.65 = 21 ( approx ) answer c"
Answer: c
Question (geometry): rectangle a has sides a and b , and rectangle b has sides c and d . if a / c = b / d = 4 / 5 , what is the ratio of rectangle a ’ s area to rectangle b ’ s area ?
Options: a ) 5 / 4 , b ) 25 / 16 , c ) 4 / 5 , d ) 16 / 25 , e ) 16 / 5
Rationale: "the area of rectangle a is ab . c = 5 a / 4 and d = 5 b / 4 . the area of rectangle b is cd = 25 ab / 16 . the ratio of rectangle a ' s area to rectangle b ' s area is ab / ( 25 ab / 16 ) = 16 / 25 . the answer is d ."
Answer: d
Question (physics): pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 5 : 00 am and pipe b at 6 : 00 am , at what time will the pool be full ?
Options: a ) 13 : 00 , b ) 14 : 00 , c ) 15 : 00 , d ) 17 : 00 , e ) 16 : 00
Rationale: "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 5 : 00 a . m and pipe b at 6 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 6 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 5 : 00 a . m , pool is full at 15 : 00 hrs answer : c"
Answer: c
Question (general): a student multiplied a number by 3 / 5 instead of 5 / 3 , what is the percentage error in the calculation ?
Options: a ) 22 , b ) 64 , c ) 365 , d ) 29 , e ) 36
Rationale: "let the number be x . then , ideally he should have multiplied by x by 5 / 3 . hence correct result was . by mistake he multiplied x by 3 / 5 . hence the result with error = then , error = error % = = 64 % answer : b"
Answer: b
Question (general): a team of 6 entered for a shooting competition . the best marks man scored 85 points . if he had scored 92 points , the average scores for . the team would have been 84 . how many points altogether did the team score ?
Options: a ) 288 , b ) 497 , c ) 168 , d ) 127 , e ) 664
Rationale: explanation : 6 * 84 = 504 - 7 = 497 answer : b
Answer: b
Question (general): if 60 percent of 500 is 50 percent of x , then x = ?
Options: a ) 600 , b ) 620 , c ) 650 , d ) 700 , e ) 720
Rationale: "0.6 * 500 = 0.5 * x x = 6 / 5 * 500 = 600"
Answer: a
Question (physics): a car gets 40 kilometers per gallon of gasoline . how many gallons of gasoline would the car need to travel 220 kilometers ?
Options: a ) 4.5 , b ) 5.5 , c ) 6.5 , d ) 7.5 , e ) 8.5
Rationale: "each 40 kilometers , 1 gallon is needed . we need to know how many 40 kilometers are there in 220 kilometers ? 220 ÷ 40 = 5.5 × 1 gallon = 5.5 gallons correct answer b"
Answer: b
Question (other): the sum of 3 numbers is 98 . if the ratio between first and second be 2 : 3 and that between second and third be 5 : 8 , then the second number is ?
Options: a ) 30 , b ) 20 , c ) 58 , d ) 48 , e ) 68
Rationale: let the numbers be x , y and z . then , x + y + z = 98 , x / y = 2 / 3 and y / z = 5 / 8 therefore , x = 2 y / 3 and z = 8 y / 5 . so , 2 y / 3 + y + 8 y / 5 = 98 . 49 y / 15 = 98 y = 30 . answer : a
Answer: a
Question (physics): a courtyard is 25 meter long and 18 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 20000 , d ) 22500 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2500 × 1800 / 20 × 10 ) = 22500 answer : d"
Answer: d
Question (geometry): the perimeter of one square is 24 m & that of another is 32 m . perimeter of a square whose area is equal to the sum of the areas of the 2 squares will be
Options: a ) 20 m
b ) 24 m
c ) 28 m
d ) 40 m
e ) 43 m
Rationale: perimeter of square = 4 * side perimeter of first square = 24 m . side of first square = ∴ area of first square = perimeter of second square = 32 m . side of second square = ∴ area of second square = sum of the areas of two squares = 36 + 64 = 100 m 2 ∴ side of square = ∴ perimeter of square = 4 * 10 = 40 m . d
Answer: d
Question (physics): the speeds of three asteroids were compared . asteroids x - 13 and y - 14 were observed for identical durations , while asteroid z - 15 was observed for 2 seconds longer . during its period of observation , asteroid y - 14 traveled three times the distance x - 13 traveled , and therefore y - 14 was found to be faster than x - 13 by 2500 kilometers per second . asteroid z - 15 had an identical speed as that of x - 13 , but because z - 15 was observed for a longer period , it traveled five times the distance x - 13 traveled during x - 13 ' s inspection . asteroid x - 13 traveled how many kilometers during its observation ?
Options: a ) 500 , b ) 625 , c ) 1,000 , d ) 1,500 , e ) 2,500
Rationale: "x 13 : ( t , d , s ) y 14 : ( t , 3 d , s + 2500 mi / hour ) z 15 : ( t + 2 seconds , s , 5 d ) d = ? distance = speed * time x 13 : d = s * t x 14 : 3 d = ( s + 2500 ) * t = = = > 3 d = ts + 2500 t z 15 : 5 d = s * ( t + 2 t ) = = = > 5 d = st + 2 st = = = > 5 d - 2 st = st 3 d = 5 d - 2 st + 2500 t - 2 d = - 2 st + 2500 t 2 d = 2 st - 2500 t d = st - 1250 t x 13 : d = s * t st - 1250 t = s * t s - 1250 = s - 625 = s i got to this point and could n ' t go any further . this seems like a problem where i can set up individual d = r * t formulas and solve but it appears that ' s not the case . for future reference how would i know not to waste my time setting up this problem in the aforementioned way ? thanks ! ! ! the distance of z 15 is equal to five times the distance of x 13 ( we established that x 13 is the baseline and thus , it ' s measurements are d , s , t ) s ( t + 2 ) = 5 ( s * t ) what clues would i have to know to set up the equation in this fashion ? is it because i am better off setting two identical distances together ? st + 2 s = 5 st t + 2 = 5 t 2 = 4 t t = 1 / 2 we are looking for distance ( d = s * t ) so we need to solve for speed now that we have time . speed y 14 - speed x 13 speed = d / t 3 d / t - d / t = 2500 ( remember , t is the same because both asteroids were observed for the same amount of time ) 2 d = 2500 2 = 1250 d = s * t d = 1250 * ( 1 / 2 ) d = 625 answer : b"
Answer: b
Question (general): what is the value of 3 x ^ 2 − 2.4 x + 0.3 for x = 0.6 ?
Options: a ) − 0.3 , b ) 0 , c ) 0.06 , d ) 1.08 , e ) 2.46
Rationale: "3 x ^ 2 - 2.4 x + 0.3 for x = 0.6 = 3 ( 0.6 * 0.6 ) - 4 * 0.6 * ( 0.6 ) + 0.3 = - 0.6 * 0.6 + 0.3 = 0.06 correct option : c"
Answer: c
Question (general): if x = 1 - 3 t and y = 2 t - 3 , then for what value of t does x = y ?
Options: a ) 5 / 2 , b ) 3 / 2 , c ) 4 / 5 , d ) 2 / 5 , e ) 0
Rationale: "we are given x = 1 – 3 t and y = 2 t – 3 , and we need to determine the value for t when x = y . we should notice that both x and y are already in terms of t . thus , we can substitute 1 – 3 t for x and 2 t – 3 for y in the equation x = y . this gives us : 1 – 3 t = 2 t – 3 4 = 5 t 4 / 5 = t the answer is c ."
Answer: c
Question (gain): find the simple interest on the rs . 2000 at 25 / 4 % per annum for the period from 4 th feb 2005 to 18 th april 2005
Options: a ) rs 25 , b ) rs 30 , c ) rs 35 , d ) rs 40 , e ) none of these
Rationale: explanation : one thing which is tricky in this question is to calculate the number of days . always remember that the day on which money is deposited is not counted while the day on which money is withdrawn is counted . so lets calculate the number of days now , time = ( 24 + 31 + 18 ) days = 73 / 365 years = 1 / 5 years p = 2000 r = 25 / 4 % s . i . = = 2000 × 254 × 5 × 100 = 25 answer : a
Answer: a
Question (geometry): volume of a right circular cylinder is 6 o l . if radius of cylinder is doubled , then what will be the increase in volume ?
Options: a ) 120 l
b ) 180 l
c ) 240 l
d ) 300 l
e ) 360 l
Rationale: pi ∗ r ^ 2 ∗ h = 60 double the radius . . . . . pi ∗ ( 2 r ) ^ 2 ∗ h = pi ∗ 4 ∗ r ^ 2 ∗ h = 4 ∗ 60 = 240 important . . we are looking at the increase so 240 - 60 = 180 answer : b
Answer: b
Question (gain): you enter a weight loss challenge game and manage to lose 10 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 8.2 % , c ) 9 % , d ) 14 % , e ) 12 %
Rationale: "( 100 % - 10 % ) * ( 100 % + 2 % ) = 0.90 * 1.02 = 8.2 % the weigh in records your weight loss at 8.2 % ! the answer is b"
Answer: b
Question (general): a person was asked to state his age in years . his reply was , ` ` take my age 5 years hence , multiply it by 3 and subtract 3 times my age 5 years ago and you will know how old i am . ' ' what was the age of the person ?
Options: a ) 18 , b ) 92 , c ) 27 , d ) 26 , e ) 30
Rationale: "explanation : let the present age of person be x years . then , 3 ( x + 5 ) - 3 ( x - 5 ) = x < = > ( 3 x + 15 ) - ( 3 x - 15 ) = x < = > x = 30 . . answer : e"
Answer: e
Question (physics): the radius of a semi circle is 6.3 cm then its perimeter is ?
Options: a ) 32.9 , b ) 32.4 , c ) 32.2 , d ) 32.1 , e ) 32.7
Rationale: "36 / 7 r = 6.3 = 32.4 answer : b"
Answer: b
Question (physics): a train is 300 meter long is running at a speed of 54 km / hour . in what time will it pass a tunnel of 1200 meter length ?
Options: a ) 90 seconds , b ) 85 seconds , c ) 40 seconds , d ) 100 seconds , e ) 120 seconds
Rationale: speed = 54 km / hr = 54 * ( 5 / 18 ) m / sec = 15 m / sec total distance = 300 + 1200 = 1500 meter time = distance / speed = 1500 * ( 15 ) = 100 seconds answer : d
Answer: d
Question (probability): in a single throw of a die , what is probability of getting a number greater than 4 ?
Options: a ) 2 / 3 , b ) 3 / 5 , c ) 4 / 7 , d ) 8 / 9 , e ) 1 / 3
Rationale: "e = { 5,6 } n ( e ) = 2 p ( s ) = n ( e ) / n ( s ) = 2 / 6 = 1 / 3 ans : e"
Answer: e
Question (other): a certain bag contains 60 balls — 22 white , 18 green , 8 yellow , 5 red , and 7 purple . if a ball is to be chosen at random , what is the probability that the ball will be neither red nor purple ?
Options: a ) 0.09 , b ) 0.15 , c ) 0.54 , d ) 0.8 , e ) 0.91
Rationale: "according to the stem the ball can be white , green or yellow , so the probability is ( white + green + yellow ) / ( total ) = ( 22 + 18 + 8 ) / 60 = 48 / 60 = 0.8 . answer : d ."
Answer: d
Question (geometry): a 10 meter long wire is cut into two pieces . if the longer piece is then used to form a perimeter of a square , what is the probability that the area of the square will be more than 4 if the original wire was cut at an arbitrary point ?
Options: a ) 1 / 6
b ) 1 / 5
c ) 3 / 10
d ) 1 / 3
e ) 4 / 10
Rationale: a square with an area of 4 has a perimeter of 8 . for the area to be > 4 , the longer piece must be > 8 . the wire must be cut within 2 meters from either end . the probability of this is 4 / 10 = 2 / 5 . the answer is e .
Answer: e
Question (general): the mean of 50 observations was 40 . it was found later that an observation 45 was wrongly taken as 15 the corrected new mean is
Options: a ) 40 , b ) 36.5 , c ) 46.5 , d ) 20.5 , e ) 40.6
Rationale: "explanation : correct sum = ( 40 * 50 + 45 - 15 ) = 2030 correct mean = = 2030 / 50 = 40.6 answer : e"
Answer: e
Question (physics): the current of a stream runs at the rate of 4 kmph . a boat goes 6 km and back to the starting point in 4 hours , then find the speed of the boat in still water ?
Options: a ) a ) 7 , b ) b ) 2 , c ) c ) 8.73 , d ) d ) 5.77 , e ) e ) 3
Rationale: "s = 4 m = x ds = x + 4 us = x - 4 6 / ( x + 4 ) + 6 / ( x - 4 ) = 4 x = 5.77 answer : d"
Answer: d
Question (gain): by selling 14 pencils for a rupee a man loses 20 % . how many for a rupee should he sell in order to gain 20 % ?
Options: a ) 28 , b ) 26 , c ) 25 , d ) 23 , e ) 21
Rationale: "80 % - - - 14 120 % - - - ? 80 / 120 * 14 = 21 answer : e"
Answer: e
Question (gain): a money lender lent rs . 1000 at 3 % per year and rs . 1400 at 5 % per year . the amount should be returned to him when the total interest comes to rs . 350 . find the number of years .
Options: a ) 3.5 , b ) 3.75 , c ) 4 , d ) 4.25 , e ) 4.5
Rationale: ( 1000 xtx 3 / 100 ) + ( 1400 xtx 5 / 100 ) = 350 → t = 3.5 answer a
Answer: a
Question (general): caleb spends $ 70.50 on 50 hamburgers for the marching band . if single burgers cost $ 1.00 each and double burgers cost $ 1.50 each , how many double burgers did he buy ?
Options: a ) 5 , b ) 10 , c ) 20 , d ) 41 , e ) 45
Rationale: "solution - lets say , single hamburgersxand double hamburgersy given that , x + y = 50 and 1 x + 1.5 y = 70.50 . by solving the equations y = 41 . ans d ."
Answer: d
Question (physics): tom traveled the entire 100 miles trip . if he did the first 50 miles of at a constant rate 20 miles per hour and the remaining trip of at a constant rate 50 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 28.36 mph , b ) 26.55 mph , c ) 28.57 mph , d ) 25.56 mph , e ) 28.45 mph
Rationale: "avg speed = total distance / total time = ( d 1 + d 2 ) / ( t 1 + t 2 ) = ( 50 + 50 ) / ( ( 50 / 20 ) + ( 50 / 50 ) ) = 60 * 2 / 3 = 28.57 mph c"
Answer: c
Question (general): when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 6 , the quotient is 3 y and the remainder is 5 . what is the value of 7 y – x ?
Options: a ) 2 , b ) 1 , c ) 0 , d ) - 1 , e ) - 2
Rationale: "( 1 ) x = 11 y + 4 ( 2 ) 2 x = 18 y + 5 let ' s subtract equation ( 1 ) from equation ( 2 ) . 7 y + 1 = x 7 y - x = - 1 the answer is d ."
Answer: d
Question (general): a total of 30 percent of the geese included in a certain migration study were male . if some of the geese migrated during the study and 30 percent of the migrating geese were male , what was the ratio of the migration rate for the male geese to the migration rate for the female geese ? [ migration rate for geese of a certain sex = ( number of geese of that sex migrating ) / ( total number of geese of that sex ) ]
Options: a ) 1 / 4 , b ) 7 / 12 , c ) 2 / 3 , d ) 1 , e ) 8 / 7
Rationale: "let ' take the number of geese to be 100 . male = 30 . female = 70 . now the second part of the q , let ' s take the number migrated to be 20 . so we have 20 geese that migrated and out of that 20 % are male i . e 20 / 100 * 30 = 6 geese ( males ) and now we know out of the total 20 geese , 6 are male , then 14 have to be female . now the ratio part , male geese ratios = 6 / 30 = 1 / 5 . - a female geese ratios = 14 / 70 = 1 / 5 - b cross multiply equations a and b and you get = 1 . ans d"
Answer: d