Cheukting/mathqa huggingface dataset:
Question (gain): the sale price of an article including the sales tax is rs . 616 . the rate of sales tax is 10 % . if the shopkeeper has made a profit of 12 % , then the cost price of the article is :
Options: a ) 500 , b ) 277 , c ) 266 , d ) 288 , e ) 261
Rationale: "110 % of s . p . = 616 s . p . = ( 616 * 100 ) / 110 = rs . 560 c . p = ( 110 * 560 ) / 112 = rs . 500 . answer : a"
Answer: a
Question (general): if 2 log ( 4 * 5 ^ 2 ) = x , find x
Options: a ) 5 , b ) 6 , c ) 7 , d ) 4 , e ) 8
Rationale: "2 ( log 2 ^ 2 * 5 ^ 2 ) = x 2 log ( 5 * 2 ) ^ 2 = x 2 * 2 log ( 5 * 2 ) = x 4 log 10 = x log 10 base 10 = 1 so 4 * 1 = x x = 4 answer : d"
Answer: d
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 . 3 / 4 of the current inventory is speedsters , of which 3 / 5 are convertibles . if there are 30 vehicles that are not speedsters , how many speedster convertibles are there ?
Options: a ) 30 , b ) 54 , c ) 60 , d ) 70 , e ) 90
Rationale: "total vehicle = 3 / 4 of speedster + 1 / 4 of others . speedster convertibles = 3 / 4 total vehicle * 3 / 5 given : 1 / 4 constitutes 30 vehicles . hence 3 / 4 constitutes 90 speedster convertibls = 90 * 3 / 5 = 54 b"
Answer: b
Question (physics): a rower can row 6 km / h in still water . when the river is running at 1 km / h , it takes the rower 1 hour to row to big rock and back . how many kilometers is it to big rock ?
Options: a ) 2.66 , b ) 2.78 , c ) 2.8 , d ) 2.87 , e ) 2.92
Rationale: "let x be the distance to big rock . time = x / 5 + x / 7 = 1 x = 35 / 12 = 2.92 the answer is e ."
Answer: e
Question (gain): in a stockpile of products produced by 3 machines m 1 , m 2 and m 3 , 40 % and 30 % were manufactured by m 1 and m 2 respectively . 3 % of the products of m 1 are defective , 1 % of products of m 2 defective , while 93 % of the products of m 3 iii are not defective . what is the percentage of defective in the stockpile ?
Options: a ) 3 % , b ) 5 % , c ) 2.5 % , d ) 4 % , e ) 3.6 %
Rationale: explanation : let there be 100 products in the stockpile . 40 % and 30 % were manufactured by m 1 and m 2 respectively . so , 30 % are manufactured by m 3 . products from m 1 = 40 , from m 2 = 30 and from m 3 = 30 . number of defective products from m 1 = 0.03 x 40 = 1.2 , from m 2 = 0.01 x 30 = 0.3 and from m 3 = 0.07 x 30 = 2.1 therefore , total number of defective products = 3.6 answer : e
Answer: e
Question (geometry): the parameter of a square is equal to the perimeter of a rectangle of length 18 cm and breadth 10 cm . find the circumference of a semicircle whose diameter is equal to the side of the square .
Options: a ) 44.0 , b ) 23.59 , c ) 23.55 , d ) 23.53 , e ) 23.57
Rationale: "let the side of the square be a cm . parameter of the rectangle = 2 ( 18 + 10 ) = 56 cm parameter of the square = 56 cm i . e . 4 a = 56 a = 14 diameter of the semicircle = 14 cm circimference of the semicircle = 1 / 2 ( â ˆ  ) ( 14 ) = 22 / 7 * 14 = 44 cm answer : a"
Answer: a
Question (general): the average mark obtained by 22 candidates in an examination is 48 . the average of the first 10 is 55 while the last 11 is 40 . the marks obtained by the 11 th candidate is ?
Options: a ) 22 , b ) 0 , c ) 49 , d ) 58 , e ) 66
Rationale: it is clear that 22 x 48 = 10 x 55 + k + 11 x 40 ⇒ ⇒ k = 66 answer : e
Answer: e
Question (general): ' a ' and ' b ' are positive integers such that their lcm is 20 and their hcf is 1 . what is the difference between the minimum and maximum possible values of ' a + b ' ?
Options: a ) 0 , b ) - 24 , c ) - 32 , d ) - 20 , e ) - 12
Rationale: "possible values of a and b can be 5,4 ; 4,5 ( which are same for a + b ) and 1,20 ; 20,1 ( same result for a + b ) so 9 - 21 = - 12 . ans e ."
Answer: e
Question (gain): a certain company reported that the revenue on sales increased 50 % from 2000 to 2003 , and increased 80 % from 2000 to 2005 . what was the approximate percent increase in revenue for this store from 2003 to 2005 ?
Options: a ) 20 % , b ) 40 % , c ) 35 % , d ) 32 % , e ) 29 %
Rationale: "assume the revenue in 2000 to be 100 . then in 2003 it would be 150 and and in 2005 180 , so from 2003 to 2005 it increased by ( 180 - 150 ) / 150 = 30 / 150 = ~ 20 % . answer : a"
Answer: a
Question (physics): if 21 lines are drawn in a plane such that no two of them are parallel and no three are concurrent , then in how many points do they intersect ?
Options: a ) 150 , b ) 170 , c ) 190 , d ) 210 , e ) 230
Rationale: "if two lines are not parallel , then they will intersect in exactly one point . lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel . we are also given that no three lines are concurrent . this means that no three lines intersect at the same point . so every pair of two lines we select will have a unique point of intersection which they will not share with any third line . the number of ways to select 2 lines from 21 lines is 21 c 2 = 210 the answer is d ."
Answer: d
Question (geometry): three rugs have a combined area of 200 square meters . by overlapping the rugs to cover floor area of 140 square meters , the area that is covered by exactly two layers of rug is 22 square meters . what is the area that is covered with three layers of rug ?
Options: a ) 18 square meters
b ) 20 square meters
c ) 24 square meters
d ) 19 square meters
e ) 30 square meters
Rationale: total = rug 1 + rug 2 + rug 3 - { overlap of exactly 2 rugs } - 2 * { overlap of exactly 3 rugs } 140 = 200 - 22 - 2 * { overlap of exactly 2 rugs } - - > { overlap of exactly 3 rugs } = 19 . answer : d .
Answer: d
Question (gain): find the simple interest on $ 3200 for 3 years at 10 % per annum ?
Options: a ) $ 250 , b ) $ 300 , c ) $ 500 , d ) $ 600 , e ) $ 960
Rationale: "si = ptr / 100 = 3200 * 3 * 10 / 100 = $ 960 answer is e"
Answer: e
Question (general): if a person walks at 12 km / hr instead of 8 km / hr , he would have walked 20 km more . the actual distance traveled by him is ?
Options: a ) 50 km , b ) 58 km , c ) 60 km , d ) 40 km , e ) 65 km
Rationale: "let the actual distance traveled be x km . then , x / 8 = ( x + 20 ) / 12 3 x - 2 x = 40 = > x = 40 km . answer : d"
Answer: d
Question (physics): two different primes may be said torhymearound an integer if they are the same distance from the integer on the number line . for instance , 3 and 7 rhyme around 5 . what integer e between 1 and 20 , inclusive , has the greatest number of distinct rhyming primes around it ?
Options: a ) 12 , b ) 15 , c ) 17 , d ) e = 18 , e ) 20
Rationale: "since we are concerned with integers between 1 and 20 , write down the primes till 40 . 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 ( you should be very comfortable with the first few primes . . . ) 2 , 3 , 5 , 7 , 11,12 , 13 , 17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11,13 ) , ( 7,17 ) , ( 5 , 19 ) 2 , 3 , 5 , 7 , 11 , 13 , 15,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 13 , 17 ) , ( 11 , 19 ) , ( 7 , 23 ) 2 , 3 , 5 , 7 , 11 , 13,17 , 19 , 23 , 29 , 31 , 37 - three pairs ( 11 , 23 ) , ( 5 , 29 ) , ( 3 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 18,19 , 23 , 29 , 31 , 37 - four pairs ( 17 , 19 ) , ( 13 , 23 ) , ( 7 , 29 ) , ( 5 , 31 ) 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 , 20,23 , 29 , 31 , 37 - definitely can not be more than 4 since there are only 4 primes more than 20 . so must be less than 4 pairs . ignore . answer ( d ) ."
Answer: d
Question (gain): a merchant purchased a jacket for $ 60 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 25 percent of the selling price . during a sale , the merchant discounted the selling price by 20 percent and sold the jacket . what was the merchant ’ s gross profit on this sale ?
Options: a ) $ 0 , b ) $ 3 , c ) $ 4 , d ) $ 12 , e ) $ 15
Rationale: "markup = x x = 0.25 ( 60 + x ) = > 3 x / 4 = 15 = > x = 20 so sp = 80 but actual sp = 0.8 * 80 = 64 so profit = $ 4 answer - c"
Answer: c
Question (physics): a car travels at a speed of 65 miles per hour . how far will it travel in 7 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 455 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 7 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 + 65 = 7 × 65 = 455 miles correct answer is c ) 455 miles"
Answer: c
Question (gain): the percentage profit earned by selling an article for rs . 1720 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 25 % profit ?
Options: a ) 3000 , b ) 1230 , c ) 1875 , d ) 5600 , e ) 3400
Rationale: "then , ( 1720 - x ) / x * 100 = ( x - 1280 ) / x * 100 1720 - x = x - 1280 2 x = 3000 = > x = 1500 required s . p . = 125 % of rs . 1500 = 125 / 100 * 1500 = rs . 1875 . answer c"
Answer: c
Question (geometry): find the surface area of a 10 cm x 4 cm x 2 cm brick .
Options: a ) 136 cu cm , b ) 124 cu cm , c ) 164 cu cm , d ) 180 cu cm , e ) none
Rationale: "sol . surface area = [ 2 ( 10 x 4 + 4 x 2 + 10 x 2 ) ] = ( 2 x 68 ) = 136 cu cm answer a"
Answer: a
Question (physics): a motorcyclist goes from bombay to pune , a distance of 192 kms at an average of 32 kmph speed . another man starts from bombay by car 2 â ½ hours after the first , and reaches pune â ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 1 : 3 , c ) 10 : 27 , d ) 5 : 4 , e ) 10 : 40
Rationale: "explanation : t = 192 / 32 = 6 h t = 6 - 3 = 3 time ratio = 6 : 3 = 2 : 1 speed ratio = 1 : 2 answer is a"
Answer: a
Question (general): a certain country is divided into 4 provinces . each province consists entirely of progressives and traditionalists . if each province contains the same number of traditionalists and the number of traditionalists in any given province is 1 / 12 the total number of progressives in the entire country , what fraction of the country is traditionalist ?
Options: a ) 1 / 5 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 4
Rationale: "let p be the number of progressives in the country as a whole . in each province , the number of traditionalists is p / 12 the total number of traditionalists is 4 p / 12 = p / 3 . the total population is p + p / 3 = 4 p / 3 p / ( 4 p / 3 ) = 3 / 4 the answer is e ."
Answer: e
Question (general): 12.5 * 3.2 * 8.8 = ?
Options: a ) 352 , b ) 435 , c ) 224 , d ) 646 , e ) 742
Rationale: "a 352 ? = 12.5 * 3.2 * 8.8 = 352"
Answer: a
Question (general): vishal invested 10 % more than trishul . trishul invested 10 % less than raghu . if the total sum of their investments is rs . 6069 , how much amount did raghu invest ?
Options: a ) 1287 , b ) 2887 , c ) 2100 , d ) 1129 , e ) 1192
Rationale: "let money invested by raghu = rs . x money invested by trishul = 9 / 10 x = 0.9 x money invested by vishal = 9 / 10 x * 110 / 100 = 0.99 x also , x + 0.9 x + 0.99 x = 6069 = x = 6069 / 2.89 = 2100 therefore , amount invested by raghu is rs . 2100 . answer : c"
Answer: c
Question (physics): a train 125 m long passes a man , running at 7 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 11 , b ) 50 , c ) 52 , d ) 65 , e ) 22
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 7 ) km / hr . x - 7 = 45 = = > x = 52 km / hr . answer : c"
Answer: c
Question (general): one - third of rahul ' s savings in national savings certificate is equal to one - half of his savings in public provident fund . if he has rs . 1 , 25,000 as total savings , how much has he saved in public provident fund ?
Options: a ) 80000 , b ) 60000 , c ) 50000 , d ) 75000 , e ) 90000
Rationale: "let savings in n . s . c and p . p . f . be rs . x and rs . ( 125000 - x ) respectively . then , = 1 / 3 x = 1 / 2 ( 125000 - x ) = x / 3 + x / 2 = 62500 = 5 x / 6 = 62500 = x = 62500 x 6 / 5 = 75000 savings in public provident fund = rs . ( 125000 - 75000 ) = rs . 50000 answer is c ."
Answer: c
Question (physics): an industrial loom weaves 0.128 metres of cloth every second . approximately , how many seconds will it take for the loom to weave 25 metres of cloth ?
Options: a ) 488 , b ) 204 , c ) 195 , d ) 178 , e ) 133
Rationale: let the required time be x seconds . more metres , more time ( direct proportion ) 0.128 : 25 : : 1 : x 0.128 x = 25 x 1 x = 25 / 0.128 = ( 25 x 1000 ) / 128 x = 195.31 . required time = 195 sec ( approximately ) . answer is c .
Answer: c
Question (general): the sum of two numbers is 45 . the sum of their quotient and is reciprocal is 2.05 , the product of the numbers is ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: a + b = 45 a / b + b / a = 2.05 = > ( a ^ 2 + b ^ 2 ) / ab = 2.05 = > ( ( a + b ) ^ 2 − 2 ab ) / ab = 2.05 = > ( a + b ) ^ 2 = 2.05 ab + 2 ab = 4.05 ab = > ab = 45 ^ 2 / 4.05 = 500 answer : c
Answer: c
Question (general): george went to a fruit market with certain amount of money . with this money he can buy either 50 oranges or 40 mangoes . he retains 15 % of the money for taxi fare and buys 15 mangoes . how many oranges can he buy ?
Options: a ) 25 , b ) 17.5 , c ) 20 , d ) 16 , e ) 12
Rationale: "let the amount of money be 200 let cost of 1 orange be 4 let cost of 1 mango be 5 he decides to retain 15 % of 200 = 30 for taxi fare , so he is left with 170 he buys 20 mangoes ( @ 5 ) so he spends 100 money left is 70 ( 170 - 100 ) no of oranges he can buy = 70 / 4 = > 17,5 so , george can buy 15 oranges . b"
Answer: b
Question (gain): daal is now being sold at rate rs . 20 a kg . during last month its rate was rs 16 per kg . by how reduce percent should a family its consumption so as to keep the expenditure fixed ?
Options: a ) 10 % , b ) 20 % , c ) 30 % , d ) 40 % , e ) 50 %
Rationale: last month rate = 16 per kg this month rate = 20 per kg if 20 = 100 % then 16 = ? therefore % = ( 16 * 100 ) / 20 = 80 % to reduce consumption 100 - 80 = 20 % answer : b
Answer: b
Question (gain): a certain maroon paint contains 70 percent blue pigment and 30 percent red pigment by weight . a certain green paint contains 10 percent blue pigment and 90 percent yellow pigment . when these paints are mixed to produce a brown paint , the brown paint contains 40 percent blue pigment . if the brown paint weighs 10 grams , then the red pigment contributes how many grams of that weight ?
Options: a ) 1.5 , b ) 2 , c ) 2.5 , d ) 3 , e ) 3.5
Rationale: 10 grams of combined mixture and 40 % blue pigment means that the mixtures were mixed 50 % each . thus 5 grams a piece . out of the 5 grams of the dark blue paint , 60 % is red . therefore , 5 * . 3 = 1.5 grams of red pigment
Answer: a
Question (general): before 4 years , dog a ’ s age was 4 times of dog b ’ s age and after 4 years , dog a ’ s age will be 3 times of dog b ’ s age . what is the difference of dog a ’ s age and dog b ’ s now ?
Options: a ) 36 , b ) 42 , c ) 52 , d ) 60 , e ) 64
Rationale: "a - 4 = 4 ( b - 4 ) - - > a - 4 b = - 12 . . . . . . . . . . . . . 1 a + 4 = 3 ( b + 4 ) - - > a - 3 b = 8 . . . . . . . . . . . . . 2 ( 2 ) - ( 1 ) - - > b = 20 - - > a = 3 ( 24 ) = 72 a - b = 72 - 20 = 52 answer : c"
Answer: c
Question (gain): a cricket bat is sold for $ 850 , making a profit of $ 225 . the profit percentage would be
Options: a ) 24 % , b ) 25 % , c ) 30 % , d ) 36 % , e ) 40 %
Rationale: "225 / ( 850 - 225 ) = 225 / 625 = 9 / 25 bit more than 33 % . answer : d"
Answer: d
Question (general): what is the least number to be added to 661 to make it a perfect square ?
Options: a ) 13 , b ) 15 , c ) 20 , d ) 16 , e ) 45
Rationale: "the numbers greater than 661 and are square of number is 676 . the least number that should be added 661 to make it perfect square = 676 - 661 = 15 . answer : b"
Answer: b
Question (general): joe ’ s average ( arithmetic mean ) test score across 4 equally weighted tests was 40 . he was allowed to drop his lowest score . after doing so , his average test score improved to 45 . what is the lowest test score that was dropped ?
Options: a ) 20 , b ) 25 , c ) 55 , d ) 65 , e ) 80
Rationale: "the arithmetic mean of 4 equally weighted tests was 40 . so what we can assume is that we have 4 test scores , each 40 . he dropped his lowest score and the avg went to 45 . this means that the lowest score was not 40 and other three scores had given the lowest score 5 each to make it up to 40 too . when the lowest score was removed , the other 3 scores got their 5 back . so the lowest score was 3 * 5 = 15 less than 40 . so the lowest score = 40 - 15 = 25 answer ( b )"
Answer: b
Question (general): the ages of patrick and michael are in the ratio of 3 : 5 and that of michael and monica are in the ratio of 3 : 5 . if the sum of their ages is 147 , what is the difference between the ages of patrick and monica ?
Options: a ) 48 , b ) 47 , c ) 46 , d ) 49 , e ) 52
Rationale: "let their ages are 9 x , 15 x and 25 x respectively . difference between the ages of patrick and monica = 25 x - 9 x = 16 x where 49 x = 147 or x = 3 so diff in ages = 16 x = 16 * 3 = 48 yrs answer : a"
Answer: a
Question (general): if the price of a certain bond on may 1 st was 2 / 3 the price of the bond on june 1 st and the price of the bond on july 1 st was 50 % greater than the price of the bond on may 1 st . then the price of the bond on june 1 st st was what percent of the average ( arithmetic mean ) price of the bond on may 1 st and july 1 st ?
Options: a ) 50 % , b ) 75 % , c ) 120 % , d ) 133 1 / 3 % , e ) 150 %
Rationale: "the price on june 1 st = 12 ( assume ) ; the price on may 1 st = 2 / 3 * 12 = 8 ; the price on july 1 st = 8 * 1.50 = 12 . the average price of the bond on may 1 st and july 1 st = ( 8 + 12 ) / 2 = 10 . the price of the bond on june 1 st ( 12 ) is 6 / 5 times ( 120 % ) the average price of the bond on may 1 st and july 1 st . answer : c ."
Answer: c
Question (gain): cricket match is conducted in us . the run rate of a cricket game was only 3.2 in first 10 over . what should be the run rate in the remaining 40 overs to reach the target of 252 runs ?
Options: a ) 6 , b ) 6.25 , c ) 7.25 , d ) 5.5 , e ) 8
Rationale: "required run rate = 252 - ( 3.2 x 10 ) = 220 = 5.5 40 40 d"
Answer: d
Question (geometry): the area of a square is equal to nine times the area of a rectangle of dimensions 121 cm * 144 cm . what is the perimeter of the square ?
Options: a ) 1500 cm , b ) 1800 cm , c ) 1584 cm , d ) 1718 cm , e ) 1086 cm
Rationale: "area of the square = s * s = 9 ( 121 * 144 ) = > s = 3 * 11 * 12 = 396 cm perimeter of the square = 4 * 396 = 1584 cm . answer : c"
Answer: c
Question (gain): the credit card and a global payment processing companies have been suffering losses for some time now . a well known company recently announced its quarterly results . according to the results , the revenue fell to $ 48.0 billion from $ 69.0 billion , a year ago . by what percent did the revenue fall ?
Options: a ) 20.8 , b ) 30.4 , c ) 31.8 , d ) 32.5 , e ) 33.8
Rationale: "$ 69 - $ 48 = 21 $ ( 21 / 69 ) * 100 = 30.434 % answer : b"
Answer: b
Question (gain): a and b started a business investing rs . 90,000 and rs 30,000 respectively . in what ratio the profit earned after 2 years be divided between a and b respectively ?
Options: a ) 9 : 2 , b ) 3 : 1 , c ) 18 : 20 , d ) 18 : 4 , e ) 17 : 4
Rationale: "a : b = 90000 : 30000 = 9 : 3 = 3 : 1 answer : b"
Answer: b
Question (physics): what is the time required for a bike to cover a distance of 450 km with a speed of 90 kmh ?
Options: a ) 5 hours , b ) 3 hours , c ) 8 hours , d ) 6 hours , e ) 4 hours
Rationale: time = distance / speed time = 450 / 90 = 5 answer : a
Answer: a
Question (general): how many even multiples of 25 are there between 249 and 501 ?
Options: a ) 5 , b ) 6 , c ) 9 , d ) 10 , e ) 11
Rationale: "250 = 10 * 25 500 = 20 * 25 the even multiples are 25 multiplied by 10 , 12 , 14 , 16 , 18 , and 20 for a total of 6 . the answer is b ."
Answer: b
Question (physics): tanks a and b are each in the shape of a right circular cylinder . the interior of tank a has a height of 8 meters and a circumference of 8 meters , and the interior of tank b has a height of 8 meters and a circumference of 10 meters . the capacity of tank a is what percent of the capacity of tank b ?
Options: a ) 64 % , b ) 80 % , c ) 100 % , d ) 120 % , e ) 125 %
Rationale: "for a , r = 8 / 2 pi . its capacity = ( 4 pi ) ^ 2 * 8 = 128 pi for b , r = 10 / pi . its capacity = ( 5 pi ) ^ 2 * 8 = 200 pi a / b = 128 pi / 200 pi = 0.64 a"
Answer: a
Question (general): in n is a positive integer less than 200 , and 14 n / 60 is an integer , then n has how many different positive prime factors c ?
Options: a ) 2 , b ) 3 , c ) 5 , d ) 6 , e ) 8
Rationale: "i like to put the numbers in prime factors so it is easier and faster to visualize . 14 * n / 60 if we write the factors of 14 - - > 2 , 7 , and the factors of 60 - - > 2 , 2 , 3 , 5 , we have ( 2 * 7 * n ) / ( 2 ^ 2 * 3 * 5 ) simplifying 7 * n / ( 2 * 3 * 5 ) the only way the equation above has an integer value is if n has at least the factors 2 , 3 and 5 , so we can simplify again and we have the number 7 . the number could be 2 * 3 * 5 , or 2 * 3 * 5 * 2 , or 2 * 3 * 5 * . . . . . however to be less than 200 we can not add any prime number . 2 * 3 * 5 = 120 if we added the next prime factor 7 , we would have c = 2 * 3 * 5 * 7 = 840 thus , answer b"
Answer: b
Question (general): if the average ( arithmetic mean ) of a and b is 110 , and the average of b and c is 150 , what is the value of a − c ?
Options: a ) − 220 , b ) − 100 , c ) 100 , d ) − 80 , e ) it can not be determined from the information given
Rationale: "question : a - c = ? ( a + b ) / 2 = 110 = = = > a + b = 220 ( b + c ) / 2 = 150 = = = > b + c = 300 ( a + b ) - ( b + c ) = 220 - 300 = = = > a + b - b - c = - 80 = = = > a - c = - 80 answer : d"
Answer: d
Question (general): the average of marks obtained by 120 boys was 40 . if the average of marks of passed boys was 39 and that of failed boys was 15 , the number of boys who passed the examination is ?
Options: a ) 100 , b ) 110 , c ) 125 , d ) 130 , e ) 145
Rationale: "let the number of boys who passed = x . then , 39 x x + 15 x ( 120 - x ) = 120 x 40 24 x = 4800 - 1800 = > x = 3000 / 24 x = 125 hence , the number of boys passed = 125 . answer : c"
Answer: c
Question (other): in a group of 27 junior high school students , 7 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 6 , c ) 9 , d ) 4 , e ) 6
Rationale: "a 7 add 7 + 10 + 4 to get 21 . then subtract 21 from the total students ⇒ 27 – 21 = 6 . answer is e"
Answer: e
Question (general): angelo and isabella are both salespersons . in any given week , angelo makes $ 550 in base salary plus 8 percent of the portion of his sales above $ 4,000 for that week . isabella makes 10 percent of her total sales for any given week . for what amount of weekly sales would angelo and isabella earn the same amount of money ?
Options: a ) 11,500 , b ) 24,500 , c ) 25,500 , d ) 26,500 , e ) 27,500
Rationale: "official solution : the problem asks for the amount of weekly sales it takes for angelo and isabella to earn the same amount of money . you can write an equation that sets angelo ’ s and isabella ’ s weekly earnings equal to each other , with x representing weekly sales . weekly earnings for each salesperson equal base salary plus commission . so angelo ’ s earnings are 550 + ( 0.08 ) ( x – 4,000 ) , and isabella ’ s are 0.10 x . set up the equation and solve : 550 + ( 0.08 ) ( x – 4,000 ) = 0.10 x distribute the 0.08 : 550 + 0.08 x – 320 = 0.10 x combine terms and subtract 0.08 x from both sides : 230 = 0.02 x divide both sides by 0.02 : 11,500 = x your answer is a ."
Answer: a