Cheukting/mathqa huggingface dataset:
Question (general): according to the directions on a packet of smoothie mix , 1 3 - ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie . how many 3 - ounce packets of smoothie mix are required to prepare 120 12 - ounce smoothies ?
Options: a ) 120 , b ) 150 , c ) 180 , d ) 240 , e ) 600
Rationale: "this question was n ' t particularly grueling , but i think it ' s the first where i had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the gmat . it actually came to me by accident . basically , if we thought that the 3 packets of powder were included in the 12 ounces of water , that would mean we would need 150 packets of smoothie mix ( along with 12 ( 150 ) ounces of water for a total of 150 packets . however , we know , after a more careful reading of the stimulus , that the 3 ounces are not included in the 12 ounces . as such , the answer has to be less than 150 packets , since 150 would be too much powder considering you already have 150 ( 12 ) ounces of water and need less packets than water to make a smoothie . as such , the only answer less than 150 is 120 , a . does this make sense ? or am i way off base ? d"
Answer: d
Question (probability): there are 20 balls in a jar . you take out 2 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 5 . how many blue balls were there in the beginning ?
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Rationale: "12 = 3 blue balls + 18 / 2 answer : a"
Answer: a
Question (geometry): the volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is :
Options: a ) 3 / 4 ∏
b ) 4 / 3 ∏
c ) 5 ∏
d ) 5 / 9 ∏
e ) none
Rationale: sol . required volume = volume of a sphere of radius 1 cm = [ 4 / 3 ∏ * 1 * 1 * 1 ] cm ³ = 4 / 3 ∏ cm ³ answer b
Answer: b
Question (general): a = { 20 , 1 , - 3 , 6 , - 8 } b = { - 1 , 2 , - 4 , 7 , - 620 } if a is a number that is randomly selected from set a , and b is a number that is randomly selected from set b , what is the probability that ab > 0 ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 5 / 12 , d ) 4 / 9 , e ) 1 / 2
Rationale: for the product of 2 numbers to be positive either both of them must be positive or both of them must be negative : p ( positive , positive ) = 3 / 6 * 3 / 6 = 9 / 36 ; p ( negative , negative ) = 2 / 6 * 3 / 6 = 6 / 36 . p = 9 / 36 + 6 / 36 = 15 / 36 = 5 / 12 . answer : c .
Answer: c
Question (general): if x is 40 percent greater than 88 , then x =
Options: a ) 68 , b ) 70.4 , c ) 123.2 , d ) 105.6 , e ) 108
Rationale: "x = 88 * 1.4 = 123.2 so the answer is c ."
Answer: c
Question (geometry): the perimeter of an isosceles right triangle is 4 + 4 sq rt 2 . what is the length of the hypotenuse of the triangle ?
Options: a ) 2.82 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "side of triangle is a then perimeter = a + a + a . sqrt 2 ( right angle and pythagorus ) = 2 a + a . sqrt 2 = 4 + 4 sqrt 2 or , a . ( 2 + sqrt 2 ) = 4 ( 1 + sqrt 2 ) a = 4 . ( 1 + sqrt 2 ) / 2 + sqrt 2 = 4 * 2.414 / 3.414 = then hypotenuse = 2.82 a"
Answer: a
Question (geometry): an 11 - 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 ) 3 / 7
b ) 5 / 8
c ) 3 / 10
d ) 5 / 11
e ) 6 / 11
Rationale: the longer wire will form a square with an area more than 4 if the wire is cut at a point within three meters of either end . the probability of this is 6 / 11 . the answer is e .
Answer: e
Question (other): how many different positive integers are factors of 36 ?
Options: a ) 4 , b ) 6 , c ) 7 , d ) 9 , e ) 11
Rationale: "6 × 6 = 3 ^ 2 × 2 ^ 2 so total factors = ( 2 + 1 ) ( 2 + 1 ) = 9 answer : d"
Answer: d
Question (gain): the list price of an article is rs . 65 . a customer pays rs . 57.33 for it . he was given two successive discounts , one of them being 10 % . the other discount is ?
Options: a ) 8 % , b ) 7 % , c ) 10 % , d ) 12 % , e ) 2 %
Rationale: "option e explanation : 65 * ( 90 / 100 ) * ( ( 100 - x ) / 100 ) = 57.33 x = 2 %"
Answer: e
Question (geometry): the supplementary of an angle is thrice its complimentary . find the angle .
Options: a ) 60 , b ) 45 , c ) 90 , d ) 180 , e ) 120
Rationale: let angle = x ; by question - - 180 - x = 3 ( 90 - x ) x = 45 answer : b
Answer: b
Question (other): 9 log 9 ( 2 ) = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: exponential and log functions are inverse of each other . hence aloga ( x ) = x , for all x real and positive . and therefore 9 log 9 ( 2 ) = 2 correct answer b
Answer: b
Question (other): there are 2 vessels a & b containing 25 liters each of pure milk and pure water respectively . 5 liters of milk from a is taken and poured into b , then 6 liters of mixture from b is taken and poured in a . what is ratio of water a and b respectively .
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 1 : 5 , d ) 1 : 6 , e ) 1 : 7
Rationale: at first a cotain milk = 25 water = 0 b cotain milk = 00 water = 25 5 litres of milk taken from a and poured in b then a cotain milk = 20 water = 0 b cotain milk = 5 water = 25 6 litres ( 1 lit milk & 5 lit water ) of mixture from b and poured in a . so , finally a cotain milk = 21 water = 5 b cotain milk = 4 water = 20 ratio of water in a & b is 5 : 20 = 1 : 4 answer : b
Answer: b
Question (physics): tim and é lan are 150 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 30 miles . , b ) 35 miles . , c ) 45 miles . , d ) 90 miles . , e ) 100 miles .
Rationale: "tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice e meet the 2 : 1 ( tim : elan = 100 : 50 ) ratio of maintaining total distance traveled 150 miles socorrect answer e"
Answer: e
Question (physics): 16 boys or 24 girls can construct the wall in 6 days . the number of days that 8 boys and 4 girls will take to construct ?
Options: a ) 7 days , b ) 14 days , c ) 6 days , d ) 8 days , e ) 9 days
Rationale: "explanation : 16 boys = 24 girls , 1 boy = 24 / 16 girls 1 boy = 6 / 4 girls 8 boys + 4 girls = 8 ã — 6 / 4 + 12 = 12 + 4 = 16 girls 9 days to complete the work answer : option e"
Answer: e
Question (general): 30 pens and 75 pencils were purchased for 630 . if the average price of a pencil was 2.00 , find the average price of a pen .
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 16
Rationale: "since average price of a pencil = 2 ∴ price of 75 pencils = 150 ∴ price of 30 pens = ( 630 – 150 ) = 480 ∴ average price of a pen = 480 ⁄ 60 = 16 answer e"
Answer: e
Question (gain): a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 1,600 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 5.55 % , b ) 5.65 % , c ) 5.75 % , d ) 5.85 % , e ) 5.95 %
Rationale: "the amount of sodium chloride is 0.05 * 10,000 = 500 gallons 500 / 8400 = 5 / 84 which is about 5.95 % the answer is e ."
Answer: e
Question (physics): find the cost of fencing around a circular field of diameter 34 m at the rate of rs . 2 a meter ?
Options: a ) 215 , b ) 212 , c ) 278 , d ) 279 , e ) 222
Rationale: "2 * 22 / 7 * 17 = 106 106 * 2 = rs . 212 answer : b"
Answer: b
Question (physics): a man covered a certain distance at some speed . if he had moved 3 kmph faster , he would have taken 40 minutes less . if he had moved 2 kmph slower , he would have taken 40 minutes more . what is the the distance in km ?
Options: a ) 33 , b ) 37 , c ) 40 , d ) 38 , e ) 27
Rationale: "let the distance be x km , the speed in which he moved = v kmph time taken when moving at normal speed - time taken when moving 3 kmph faster = 40 minutes ⇒ xv − xv + 3 = 4060 ⇒ x [ 1 v − 1 v + 3 ] = 23 ⇒ x [ v + 3 − vv ( v + 3 ) ] = 23 ⇒ 2 v ( v + 3 ) = 9 x . . . . . . . . . . . . . . . . ( equation 1 ) time taken when moving 2 kmph slower - time taken when moving at normal speed = 40 minutes ⇒ xv − 2 − xv = 4060 ⇒ x [ 1 v − 2 − 1 v ] = 23 ⇒ x [ v − v + 2 v ( v − 2 ) ] = 23 ⇒ x [ 2 v ( v − 2 ) ] = 23 ⇒ x [ 1 v ( v − 2 ) ] = 13 ⇒ v ( v − 2 ) = 3 x . . . . . . . . . . . . . . . . ( equation 2 ) equation 1 equation 2 ⇒ 2 ( v + 3 ) ( v − 2 ) = 3 ⇒ 2 v + 6 = 3 v − 6 ⇒ v = 12 substituting this value of v in equation 1 ⇒ 2 × 12 × 15 = 9 x = > x = 2 × 12 × 159 = 2 × 4 × 153 = 2 × 4 × 5 = 40 hence distance = 40 km answer : c"
Answer: c
Question (general): if x + y = 280 , x - y = 200 , for integers of x and y , y = ?
Options: a ) 200 , b ) 240 , c ) 50 , d ) 115 , e ) 150
Rationale: "x + y = 280 x - y = 200 2 x = 80 x = 40 y = 240 answer is b"
Answer: b
Question (probability): there are 10 students named alphabetically from a to j . what is the probability that a and d do not sit together if all 10 sit around a circular table ?
Options: a ) 2 / 9 , b ) 2 / 5 , c ) 7 / 9 , d ) 4 / 5 , e ) 8 / 9
Rationale: number of students = 10 number of ways 10 students can sit around a circular table = ( 10 - 1 ) ! = 9 ! number of ways a and d sit together ( consider a and d as one entity ) = ( 9 - 1 ) ! = 8 ! * 2 number of ways a and d do not sit together = 9 ! - ( 8 ! * 2 ) probability = ( 9 ! - ( 8 ! * 2 ) ) / 9 ! = 1 - 2 / 9 = 7 / 9 answer : c
Answer: c
Question (physics): a pipe can empty 2 / 3 rd of a cistern in 10 mins . in 8 mins , what part of the cistern will be empty ?
Options: a ) 2 / 3 , b ) 3 / 7 , c ) 8 / 15 , d ) 3 / 8 , e ) 4 / 7
Rationale: "2 / 3 - - - - 10 ? - - - - - 8 = = > 8 / 15 c"
Answer: c
Question (general): if $ 10 be allowed as true discount on a bill of $ 110 due at the end of a certain time , then the discount allowed on the same sum due at the end of double the time is :
Options: a ) $ 18.33 , b ) $ 22.33 , c ) $ 28.33 , d ) $ 26.23 , e ) $ 16.23
Rationale: s . i . on $ ( 110 - 10 ) for a certain time = $ 10 . s . i . on $ 100 for double the time = $ 20 . t . d . on $ 120 = $ ( 120 - 100 ) = $ 20 . t . d . on $ 110 = $ ( 20 / 120 * 100 ) = $ 18.33 answer : a
Answer: a
Question (general): if you multiply two integers together and then add 4 , the result is 40 . which of the following could not be the sum of the two numbers ?
Options: a ) 12 , b ) 13 , c ) 15 , d ) 18 , e ) 20
Rationale: let the two integers equal x and y , and then create the following equation and simplify : xy + 4 = 40 xy = 36 so x and y are a pair of integers that equal 36 . try adding all possible combinations of two integers that multiply out to 36 : 1 × 36 = 36 1 + 36 = 37 2 × 18 = 36 2 + 18 = 20 3 × 12 = 36 3 + 12 = 15 4 × 9 = 36 4 + 9 = 13 6 × 6 = 36 6 + 6 = 12 this list of sums includes 12 , 13 , 15 , and 20 , but not 18 . thus , no pair of integers both satisfies the original equation and adds up to 18 correct answer d ) 18
Answer: d
Question (physics): a train 460 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 140 m long ?
Options: a ) 40 , b ) 87 , c ) 48 , d ) 21 , e ) 14
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 460 + 140 = 600 m required time = 600 * 2 / 25 = 48 sec answer : c"
Answer: c
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 45 kg . what might be the weight of the new person ?
Options: a ) 65 kg , b ) 90 kg , c ) 85 kg , d ) data inadequate , e ) none of these
Rationale: "a 65 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 64 + 20 ) kg = 65 kg ."
Answer: a
Question (gain): a shopkeeper loses 15 % , if an article is sold for rs . 187 . what should be the selling price of the article to gain 20 % ?
Options: a ) s . 247 , b ) s . 248 , c ) s . 264 , d ) s . 329 , e ) s . 412
Rationale: "given that sp = rs . 187 and loss = 15 % cp = [ 100 ( sp ) ] / ( 100 - l % ) = ( 100 * 187 ) / 85 = 20 * 6 = rs . 220 . to get 20 % profit , new sp = [ ( 100 + p % ) cp ] / 100 = ( 220 * 120 ) / 100 = rs . 264 answer : c"
Answer: c
Question (general): if 9 a - b = 10 b + 65 = - 12 b - 2 a , what is the value of 11 a + 11 b ?
Options: a ) - 11 , b ) - 5 , c ) 0 , d ) 5 , e ) 11
Rationale: "( i ) 9 a - 11 b = 65 ( ii ) 2 a + 22 b = - 65 adding ( i ) and ( ii ) : 11 a + 11 b = 0 the answer is c ."
Answer: c
Question (general): find the average of all numbers between 1 and 76 which are divisible by 5
Options: a ) 40 , b ) 20 , c ) 25 , d ) 30 , e ) 35
Rationale: "explanation : average = ( 5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50 + 55 + 60 + 65 + 70 + 75 ) / 15 = 600 / 15 = 40 answer : option a"
Answer: a
Question (general): a cricketer makes a score of 134 runs in the 22 nd inning and thus increases his average by 3.5 . find his average after 22 nd inning .
Options: a ) 40 , b ) 60.5 , c ) 52 , d ) 55 , e ) 36
Rationale: explanation : let the average after 22 nd innings = x then average after 21 th innings = ( x - 3.5 ) therefore 21 ( x - 3.5 ) + 134 = 22 x therefore x = 60.5 answer : b
Answer: b
Question (general): for each of her sales , a saleswoman receives a commission equal to 20 percent of the first $ 500 of the total amount of the sale , plus 30 percent of the total amount in excess of $ 500 . if the total amount of one of her sales was $ 800 , the saleswoman ’ s commission was approximately what percent of the total amount of the sale ?
Options: a ) 22 % , b ) 24 percent , c ) 25 % , d ) 28 % , e ) 27 %
Rationale: "total sales = 800 commission = ( 20 / 100 ) * 500 + ( 30 / 100 ) * 300 = 100 + 90 = 190 % commission = ( 190 / 800 ) * 100 = 23.7 ~ 24 % answer is b"
Answer: b
Question (general): in a certain brick wall , each row of bricks above the bottom row contains one less brick than the row just below it . if there are 6 rows in all and a total of 135 bricks in the wall , how many bricks does the bottom row contain ?
Options: a ) 21 , b ) 20 , c ) 22 , d ) 19 , e ) 24
Rationale: "the bottom row has x bricks x + x - 1 + x - 2 + x - 3 + x - 4 + x - 5 = 135 6 x - 15 = 135 6 x = 120 x = 20 answer : b"
Answer: b
Question (general): the average marks of a class of 25 students is 50 and that of another class of 40 students is 65 . find the average marks of all the students ?
Options: a ) 52.6 , b ) 52.4 , c ) 52.1 , d ) 59 , e ) 52.9
Rationale: "sum of the marks for the class of 25 students = 25 * 50 = 1250 sum of the marks for the class of 40 students = 40 * 65 = 2600 sum of the marks for the class of 65 students = 1250 + 2600 = 3850 average marks of all the students = 4850 / 65 = 59 . answer : d"
Answer: d
Question (physics): how many plants will be there in a circular bed whose outer edge measure 34 cms , allowing 4 cm 2 for each plant ?
Options: a ) 18 , b ) 750 , c ) 23 , d ) 120 , e ) none of these
Rationale: "circumference of circular bed = 34 cm area of circular bed = ( 34 ) 2 â  „ 4 ï € space for each plant = 4 cm 2 â ˆ ´ required number of plants = ( 34 ) 2 â  „ 4 ï € ã · 4 = 22.98 = 23 ( approx ) answer c"
Answer: c
Question (gain): a person buys an article at rs . 500 . at what price should he sell the article so as to make a profit of 10 % ?
Options: a ) 550 , b ) 882 , c ) 772 , d ) 652 , e ) 271
Rationale: "cost price = rs . 500 profit = 10 % of 500 = rs . 50 selling price = cost price + profit = 500 + 50 = 550 answer : a"
Answer: a
Question (physics): stacy and helon are 30 miles apart and walk towards each other along the same route . stacy walks at constant rate that is 1 mile per hour faster than helon ' s constant rate of 5 miles / hour . if helon starts her journey 24 minutes after stacy , how far from the original destination has helon walked when the two meet ?
Options: a ) 5 miles , b ) 8 miles , c ) 6 miles , d ) 13 miles , e ) 12 miles
Rationale: original distance between s and h = 30 miles . speed of s = 5 + 1 = 6 mph , speed of h = 5 mph . time traveled by h = t hours - - - > time traveled by s = t + 24 / 60 = t + 2 / 5 hours . now , the total distances traveled by s and h = 20 miles - - - > 6 * ( t + 2 / 5 ) + 5 * t = 30 - - - > t = 138 / 55 hours . thus h has traveled for 138 / 55 hours giving you a total distance for h = 5 * 138 / 55 = 13 miles . d is thus the correct answer . p . s . : based on the wording of the question , you should calculatehow far from theoriginal destination has heather walkedwhen the two meet . ' original destination ' for h does not make any sense . original destination for h was situated at a distance of 20 miles .
Answer: d
Question (other): if log 2 = 0.30103 and log 3 = 0.4771 , find the number of digits in ( 648 ) 5
Options: a ) 14.05 , b ) 14.02 , c ) 277 , d ) 288 , e ) 222
Rationale: "log ( 648 ) 5 = 5 log ( 648 ) = 5 log ( 81 × 8 ) = 5 [ log ( 81 ) + log ( 8 ) ] = 5 [ log ( 34 ) + log ( 23 ) ] = 5 [ 4 log ( 3 ) + 3 log ( 2 ) ] = 5 [ 4 × 0.4771 + 3 × 0.30103 ] = 5 ( 1.9084 + 0.90309 ) = 5 × 2.81149 ≈ 14.05 answer : a"
Answer: a
Question (geometry): if the ratio of the areas of two squares is 225 : 256 , then the ratio of their perimeters is :
Options: a ) 15 : 12
b ) 15 : 14
c ) 15 : 16
d ) 15 : 22
e ) none of these
Rationale: explanation : a 2 / b 2 = 225 / 256 = 15 / 16 < = > 4 a / 4 b = 4 ∗ 15 / 4 ∗ 16 = 15 / 16 = 15 : 16 option c
Answer: c
Question (general): what least number must be subtracted from 12702 to get number exactly 99 ?
Options: a ) 49 , b ) 30 , c ) 29 , d ) 31 , e ) 32
Rationale: "explanation : divide the given number by 99 and find the remainder . if you subtract the remainder from the given number then it is exactly divisible by 99 . 99 ) 12702 ( 128 99 280 198 822 792 30 required number is 30 . answer is b"
Answer: b
Question (general): if x is 20 percent greater than 40 , then x =
Options: a ) 48 , b ) 70.4 , c ) 86 , d ) 105.6 , e ) 108
Rationale: "x is 20 % greater than 40 means x is 1.2 times 40 ( in other words 40 + 20 / 100 * 40 = 1.2 * 40 ) therefore , x = 1.2 * 40 = 48 answer : a"
Answer: a
Question (general): in a theater , the first row has 14 seats and each row has 2 more seats than previous row . if the last row has 56 seats , what is the total number of seats in the theater ?
Options: a ) 770 , b ) 780 , c ) 790 , d ) 800 , e ) 810
Rationale: "the number of seats in the theater is 14 + ( 14 + 2 ) + . . . + ( 14 + 42 ) = 22 ( 14 ) + 2 ( 1 + 2 + . . . + 21 ) = 22 ( 14 ) + 2 ( 21 ) ( 22 ) / 2 = 22 ( 14 + 21 ) = 22 ( 35 ) = 770 the answer is a ."
Answer: a
Question (physics): a certain automobile company ’ s best - selling model is the speedster . the speedster , like all of their other models , comes in coupe and convertible styles . 2 / 3 of the current inventory is speedsters , of which 4 / 5 are convertibles . if there are 60 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 36 , b ) 96 , c ) 100 , d ) 76 , e ) 72
Rationale: "total vehicle = 2 / 3 of speedster + 1 / 3 of others . speedster convertibles = 2 / 3 total vehicle * 4 / 5 given : 1 / 3 constitutes 60 vehicles . hence 2 / 3 constitutes 120 speedster convertibls = 120 * 4 / 5 = 96 b"
Answer: b
Question (general): a bag of potatoes weighs 12 lbs divided by half of its weight . how much does the bag of potatoes weight ?
Options: a ) 20 lb , b ) 18 lb , c ) 12 lb , d ) 15 lb , e ) 5 lb
Rationale: "sol . 12 ÷ 1 = 12 . answer : c"
Answer: c
Question (general): the price of 80 apples is equal to that of 120 oranges . the price of 60 apples and 75 oranges together is rs . 1320 . the total price of 25 apples and 40 oranges is
Options: a ) 620 , b ) 610 , c ) 630 , d ) 625 , e ) 635
Rationale: "let the price of one apple = a and price of one orange = b the price of 80 apples is equal to that of 120 oranges 80 a = 120 b = > 2 a = 3 b ⇒ b = 2 a / 3 - - - - - ( equation 1 ) price of 60 apples and 75 oranges together is rs . 1320 = > 60 a + 75 b = 1320 = > 4 a + 5 b = 88 ⇒ 4 a + 5 ( 2 a ) / 3 = 88 ( ∵ substituted the value of b from equation 1 ) = > 12 a + 10 a = 88 × 3 = > 6 a + 5 a = 44 × 3 = > 11 a = 44 × 3 = > a = 4 × 3 = 12 b = 2 a / 3 = ( 2 × 12 ) / 3 = 8 total price of 25 apples and 40 oranges = 25 a + 40 b = ( 25 × 12 ) + ( 40 × 8 ) = 300 + 320 = 620 answer is a ."
Answer: a
Question (other): two vessels a and b contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively . find the ratio in which these mixture be mixed to obtain a new mixture in vessel c containing spirit and water in the ration 8 : 5 ?
Options: a ) 4 : 3 , b ) 3 : 4 , c ) 5 : 6 , d ) 7 : 9 , e ) none
Rationale: let the c . p . of spirit be re . 1 litre . spirit in 1 litre mix . of a = 5 / 7 litre , c . p . of 1 litre mix . in a = re . 5 / 7 spirit in 1 litre mix . of b = 7 / 13 litre , c . p . of 1 litre mix . in b = re . 7 / 13 spirit in 1 litre mix . of c = 8 / 13 litre , mean price = re . 8 / 13 . by the rule of alligation , we have : required ratio = 1 / 13 : 9 / 91 = 7 : 9 . answer d
Answer: d
Question (general): a scale 7 ft . 6 inches long is divided into 5 equal parts . find the length of each part .
Options: a ) 20 inches , b ) 77 inches , c ) 66 inches , d ) 18 inches , e ) 66 inches
Rationale: "explanation : total length of scale in inches = ( 7 * 12 ) + 6 = 90 inches length of each of the 5 parts = 90 / 5 = 18 inches answer : d"
Answer: d
Question (geometry): a cheese factory sells its cheese in rectangular blocks . a normal block has a volume of three cubic feet . if a large block has twice the width , twice the depth , and three times the length of a normal block , what is the volume of cheese in a large block in cubic feet ?
Options: a ) 18
b ) 6
c ) 27
d ) 48
e ) 36
Rationale: volume of cube = lbh = 3 new cube l , b , h are increases of 3 l , 2 b , 2 h new volume of cube = 3 l * 2 b * 2 h = 12 lbh = 12 * 3 = 36 answer : e
Answer: e
Question (general): having received his weekly allowance , a student spent 3 / 5 of his allowance at the arcade . the next day he spent one third of his remaining allowance at the toy store , and then spent his last $ 0.60 at the candy store . what is this student ’ s weekly allowance ?
Options: a ) $ 2.25 , b ) $ 2.75 , c ) $ 3.00 , d ) $ 3.50 , e ) $ 3.75
Rationale: "let x be the value of the weekly allowance . ( 2 / 3 ) ( 2 / 5 ) x = 60 cents ( 4 / 15 ) x = 60 x = $ 2.25 the answer is a ."
Answer: a
Question (general): there are 14 players in a chess group , and each player plays each of the others once . given that each game is played by two players , how many total games will be played ?
Options: a ) 91 , b ) 30 , c ) 45 , d ) 60 , e ) 90
Rationale: "10 players are there . two players play one game with one another . so 14 c 2 = 14 * 13 / 2 = 91 so option a is correct"
Answer: a
Question (gain): a team won 40 percent of its first 30 games in a particular season , and 80 percent of its remaining games . if the team won a total of 60 percent of its games that season , what was the total number of games that the team played ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "60 % is 20 % - points above 40 % and 20 % - points below 80 % . thus the ratio of ` ` the first 30 games ' ' to ` ` remaining games ' ' is 1 : 1 . so the team played a total of 30 + 30 = 60 games . the answer is b ."
Answer: b
Question (general): cereal a is 11 % sugar by weight , whereas healthier but less delicious cereal b is 2 % sugar by weight . to make a delicious and healthy mixture that is 4 % sugar , what should be the ratio of cereal a to cereal b , by weight ?
Options: a ) 2 : 5 , b ) 1 : 3 , c ) 2 : 7 , d ) 3 : 4 , e ) 1 : 5
Rationale: "2 % is 2 % - points below 4 % and 11 % is 7 % - points above 4 % . the ratio of a : b should be 2 : 7 . the answer is c ."
Answer: c
Question (general): 10 years ago a was half of b in age . if the ratio of their present ages is 3 : 4 , what will be the total of their present ages
Options: a ) 30 , b ) 35 , c ) 37 , d ) 41 , e ) 43
Rationale: explanation : let a ' s age 10 years ago = x years . then , b ' s age 10 years ago = 2 x years . ( x + 10 ) / ( 2 x + lo ) = 3 / 4 = > x = 5 . so , the total of their present ages = ( x + 10 + 2 x + 10 ) = ( 3 x + 20 ) = 35 years . answer : option b
Answer: b