Cheukting/mathqa huggingface dataset:
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 31.1 % . what would have been the percentage of profit earned if no discount had been offered ?
Options: a ) 38 , b ) 27.675 , c ) 30 , d ) data inadequate , e ) none of these
Rationale: "giving no discount to customer implies selling the product on printed price . suppose the cost price of the article is 100 . then printed price = 100 ã — ( 100 + 31.1 ) / ( 100 â ˆ ’ 5 ) = 138 hence , required % profit = 138 â € “ 100 = 38 % answer a"
Answer: a
Question (gain): what will be the difference between simple and compound interest at 14 % per annum on a sum of rs . 1000 after 4 years ?
Options: a ) 129 , b ) 130 , c ) 124 , d ) 133 , e ) 145
Rationale: "s . i . = ( 1000 * 14 * 4 ) / 100 = rs . 560 c . i . = [ 1000 * ( 1 + 14 / 100 ) 4 - 1000 ] = rs . 689 difference = ( 689 - 560 ) = rs . 129 answer : a"
Answer: a
Question (physics): there are 28 stations between hyderabad and bangalore . how many second class tickets have to be printed , so that a passenger can travel from any station to any other station ?
Options: a ) 156 , b ) 167 , c ) 870 , d ) 352 , e ) 380
Rationale: "the total number of stations = 30 from 30 stations we have to choose any two stations and the direction of travel ( i . e . , hyderabad to bangalore is different from bangalore to hyderabad ) in 3 ⁰ p ₂ ways . 30 p ₂ = 30 * 29 = 870 . answer : c"
Answer: c
Question (gain): the present population of a town is 3888 . population increase rate is 20 % p . a . find the population of town before 2 years ?
Options: a ) 2500 , b ) 2100 , c ) 3500 , d ) 3600 , e ) 2700
Rationale: "p = 3888 r = 20 % required population of town = p / ( 1 + r / 100 ) ^ t = 3888 / ( 1 + 20 / 100 ) ^ 2 = 3888 / ( 6 / 5 ) ^ 2 = 2700 ( approximately ) answer is e"
Answer: e
Question (other): the triplicate ratio of 1 : 9 is ?
Options: a ) 1 : 0 , b ) 1 : 8 , c ) 1 : 7 , d ) 1 : 2 , e ) 1 : 729
Rationale: "13 : 93 = 1 : 729 answer : e"
Answer: e
Question (general): the sum of all the integers s such that - 26 < s < 24 is
Options: a ) 0 , b ) - 2 , c ) - 25 , d ) - 49 , e ) - 51
Rationale: "easy one - - 25 , - 24 , - 23 , - 22 , . . . . . . - 1,0 , 1 , 2 . . . . , 22 , 23 cancel everyhitng and we ' re left with - - 25 and - 24 s = - 49 . d is the answer ."
Answer: d
Question (geometry): a full stationary oil tank that is a right circular cylinder has a radius of 100 feet and a height of 25 feet . oil is pumped from the stationary tank to an oil truck that has a tank that is a right circular cylinder until the truck ' s tank is completely filled . if the truck ' s tank has a radius of 6 feet and a height of 10 feet , how far ( in feet ) did the oil level drop in the stationary tank ?
Options: a ) 0.036 , b ) 0.36 , c ) 0.6 , d ) 6 , e ) 3.6
Rationale: "the volume of oil pumped to the tank = the volume of oil taken away from stationary cylinder . pi * 36 * 10 = pi * h * 100 * 100 ( h is distance that the oil level dropped ) h = 360 / 10,000 = 36 / 1000 = 0.036 ft the answer is a ."
Answer: a
Question (general): each week a restaurant serving mexican food uses the same volume of chili paste , which comes in either 35 - ounce cans or 25 - ounce cans of chili paste . if the restaurant must order 20 more of the smaller cans than the larger cans to fulfill its weekly needs , then how manysmallercans are required to fulfill its weekly needs ?
Options: a ) 60 , b ) 70 , c ) 80 , d ) 100 , e ) 120
Rationale: "let x be the number of 35 ounce cans . therefore ( x + 20 ) is the number of 25 ounce cans . total volume is same , therefore 35 x = 25 ( x + 20 ) 10 x = 500 x = 50 therefore , number of 15 ounce cans = 50 + 20 = 70 ans - b"
Answer: b
Question (general): if n is an integer and 101 n ^ 2 is less than or equal to 10000 , what is the greatest possible value of n ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "101 * n ^ 2 < = 10000 n ^ 2 < = 10000 / 101 which will be less than 100 since 10000 / 100 = 100 which is the square of 9 next closest value of n where n ^ 2 < = 100 is 9 ans c"
Answer: c
Question (physics): a constructor estimates that 10 people can paint mr khans house in 4 days . if he uses 5 people instead of 10 , how long will they take to complete the job ?
Options: a ) 10 , b ) 4 , c ) 5 , d ) 8 , e ) 6
Rationale: "explanation : use formula for a work members ã — days = constant 10 ã — 4 = 5 ã — a a = 8 so answer is 8 days answer : d"
Answer: d
Question (gain): the population of a town is 8000 . it decreases annually at the rate of 20 % p . a . what will be its population after 3 years ?
Options: a ) 5100 , b ) 4096 , c ) 5200 , d ) 5400 , e ) 5500
Rationale: "formula : ( after = 100 denominator ago = 100 numerator ) 8000 ã — 80 / 100 ã — 80 / 100 x 80 / 100 = 4096 answer : b"
Answer: b
Question (gain): the percentage profit earned by selling an article for rs . 1920 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 40 % profit ?
Options: a ) 2000 , b ) 2778 , c ) 2299 , d ) 2778 , e ) 2240
Rationale: "let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 140 % of rs . 1600 = 140 / 100 * 1600 = rs . 2240 . answer : e"
Answer: e
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 360 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2400 , d ) 10800 , e ) 10900
Rationale: "let the required number of bottles be x . more machines , more bottles ( direct proportion ) more minutes , more bottles ( direct proportion ) machines 6 : 10 : : 360 : x time ( in minutes ) 1 : 4 6 x 1 x x = 10 x 4 x 360 x = ( 10 x 4 x 360 ) / ( 6 ) x = 2400 . answer : c"
Answer: c
Question (general): there are 1000 buildings in a street . a sign - maker is contracted to number the houses from 1 to 1000 . how many zeroes will he need ?
Options: a ) 190 , b ) 191 , c ) 192 , d ) 193 , e ) 194
Rationale: divide as ( 1 - 100 ) ( 100 - 200 ) . . . . ( 900 - 1000 ) total 192 answer : c
Answer: c
Question (gain): a man bought 20 shares of rs . 50 at 5 discount , the rate of dividend being 13 . the rate of interest obtained is :
Options: a ) 27 % , b ) 87 % , c ) 15 % , d ) 66 % , e ) 88 %
Rationale: "investment = rs . [ 20 x ( 50 - 5 ) ] = rs . 900 . face value = rs . ( 50 x 20 ) = rs . 1000 . dividend = rs . 27 x 1000 = rs . 135 . 2 100 interest obtained = 135 x 100 % = 15 % 900 view answer discuss in forum answer : c"
Answer: c
Question (gain): ? % of 360 = 108
Options: a ) 30 , b ) 36 , c ) 64 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 108 or , ? = 108 × 100 / 360 = 30 answer a"
Answer: a
Question (physics): a train 300 m long is running at a speed of 45 km / hr . in what time will it pass a bridge 150 m long ?
Options: a ) 40 , b ) 36 , c ) 41 , d ) 42 , e ) 34
Rationale: "speed = 45 * 5 / 18 = 25 / 2 m / sec total distance covered = 300 + 150 = 450 m required time = 450 * 2 / 25 = 36 sec answer : option b"
Answer: b
Question (general): what is the sum of all digits for the number 10 ^ 29 - 41 ?
Options: a ) 257 , b ) 242 , c ) 231 , d ) 202 , e ) 187
Rationale: "10 ^ 29 is a 30 - digit number : 1 followed by 29 zeros . 10 ^ 29 - 41 is a 29 - digit number : 27 9 ' s and 59 at the end . the sum of the digits is 27 * 9 + 5 + 9 = 257 . the answer is a ."
Answer: a
Question (physics): a train running at the speed of 120 km / hr crosses a pole in 18 seconds . what is the length of the train ?
Options: a ) 560 , b ) 570 , c ) 580 , d ) 590 , e ) 600
Rationale: "speed = ( 120 x ( 5 / 18 ) m / sec = ( 100 / 3 ) m / sec . length of the train = ( speed x time ) . length of the train = ( ( 100 / 3 ) x 18 ) m = 600 m e"
Answer: e
Question (physics): a train 100 meters long completely crosses a 300 meters long bridge in 45 seconds . what is the speed of the train is ?
Options: a ) 32 kmph , b ) 76 kmph , c ) 34 kmph , d ) 43 kmph , e ) 40 kmph
Rationale: "s = ( 100 + 300 ) / 45 = 400 / 45 * 18 / 5 = 32 answer : a"
Answer: a
Question (gain): each month a retailer sells 100 identical items . on each item he makes a profit of $ 40 that constitutes 10 % of the item ' s price to the retailer . if the retailer contemplates giving a 5 % discount on the items he sells , what is the least number of items he will have to sell each month to justify the policy of the discount ?
Options: a ) 191 , b ) 213 , c ) 221 , d ) 223 , e ) 226
Rationale: "for this question , we ' ll need the following formula : sell price = cost + profit we ' re told that the profit on 1 item is $ 20 and that this represents 10 % of the cost : sell price = cost + $ 40 sell price = $ 400 + $ 40 thus , the sell price is $ 440 for each item . selling all 100 items gives the retailer . . . 100 ( $ 40 ) = $ 2,000 of profit if the retailer offers a 5 % discount on the sell price , then the equation changes . . . 5 % ( 440 ) = $ 22 discount $ 418 = $ 400 + $ 18 now , the retailer makes a profit of just $ 18 per item sold . to earn $ 2,000 in profit , the retailer must sell . . . . $ 18 ( x ) = $ 2,000 x = 2,000 / 18 x = 222.222222 items you ' ll notice that this is not among the answer choices . . . . 221 and 223 are . selling 221 items would get us 9 ( 221 ) = $ 1989 which is not enough money . to get back to at least $ 2,000 , we need to sell 223 items . final answer : d"
Answer: d
Question (general): the average age of 15 students of a class is 14 years . out of these , the average age of 5 students is 14 years and that of the other 9 students is 16 years . tee age of the 15 th student is ?
Options: a ) 3 years , b ) 4 years , c ) 5 years , d ) 6 years , e ) 7 years
Rationale: "age of the 15 th student = [ 15 * 14 - ( 14 * 5 + 16 * 9 ) ] = ( 210 - 214 ) = 4 years . answer : b"
Answer: b
Question (general): bookman purchased 55 copies of a new book released recently , 10 of which are hardback and sold for $ 20 each , and rest are paperback and sold for $ 10 each . if 14 copies were sold and the total value of the remaining books was 460 , how many paperback copies were sold ?
Options: a ) 10 , b ) 11 , c ) 12 , d ) 13 , e ) 9
Rationale: "the bookman had 10 hardback ad 55 - 10 = 45 paperback copies ; 14 copies were sold , hence 55 - 14 = 41 copies were left . let # of paperback copies left be p then 10 p + 20 ( 41 - p ) = 460 - - > 10 p = 360 - - > p = 36 # of paperback copies sold is 45 - 36 = 9 answer : e"
Answer: e
Question (general): diana is painting statues . she has 1 / 2 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?
Options: a ) 8 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: "number of statues = all the paint ÷ amount used per statue = 1 / 2 ÷ 1 / 16 = 8 / 16 * 16 / 1 = 8 / 1 = 8 answer is a ."
Answer: a
Question (general): if the price of gasoline increases by 25 % and a driver intends to spend only 20 % more on gasoline , by how much percent should the driver reduce the quantity of gasoline that he buys ?
Options: a ) 2 % , b ) 3 % , c ) 4 % , d ) 5 % , e ) 6 %
Rationale: "let x be the amount of gasoline the driver buys originally . let y be the new amount of gasoline the driver should buy . let p be the original price per liter . ( 1.25 * p ) y = 1.2 ( p * x ) y = ( 1.2 / 1.25 ) x = 0.96 x which is a reduction of 4 % . the answer is c ."
Answer: c
Question (general): an art gallery has only paintings and sculptures . currently , 1 / 3 of the pieces of art are displayed , and 1 / 6 of the pieces on display are sculptures . if 1 / 3 of the pieces not on display are paintings , and 1000 sculptures are not on display , how many pieces of art does the gallery have ?
Options: a ) 360 , b ) 2250 , c ) 540 , d ) 640 , e ) 720
Rationale: too many words and redundant info there . ( i ) 1 / 3 of the pieces of art are displayed , hence 2 / 3 of the pieces of art are not displayed . ( ii ) 1 / 6 of the pieces on display are sculptures , hence 5 / 6 of the pieces on display are paintings . ( iii ) 1 / 3 of the pieces not on display are paintings , hence 2 / 3 of the pieces not on display are sculptures . 1000 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 1000 - - > { not on display } = 1500 . according to ( i ) 2 / 3 * { total } = 1500 - - > { total } = 2250 . answer : b .
Answer: b
Question (gain): john and ingrid pay 30 % and 40 % tax annually , respectively . if john makes $ 60000 and ingrid makes $ 72000 , what is their combined tax rate ?
Options: a ) 32 % , b ) 34.4 % , c ) 35 % , d ) 35.6 % , e ) 36.4 %
Rationale: "( 1 ) when 30 and 40 has equal weight or weight = 1 / 2 , the answer would be 35 . ( 2 ) when 40 has larger weight than 30 , the answer would be in between 35 and 40 . unfortunately , we have 2 answer choices d and e that fit that condition so we need to narrow down our range . ( 3 ) get 72000 / 132000 = 6 / 11 . 6 / 11 is a little above 6 / 12 = 1 / 2 . thus , our answer is just a little above 35 . answer : d"
Answer: d
Question (physics): the lenght of a room is 5.5 m and width is 4 m . find the cost of paving the floor by slabs at the rate of rs . 900 per sq . metre .
Options: a ) s . 19,800 , b ) s . 15,600 , c ) s . 16,500 , d ) s . 17,600 , e ) s . 17,900
Rationale: "area of the floor = ( 5.5 ã — 4 ) m 2 = 22 m 2 . cost of paving = rs . ( 900 ã — 22 ) = rs . 19800 answer : option a"
Answer: a
Question (general): a factory that employs 1000 assembly line workers pays each of these workers $ 5 per hour for the first 40 hours worked during a week and 1 ½ times that rate for hours worked in excess of 40 . what was the total payroll for the assembly - line workers for a week in which 30 percent of them worked 15 hours , 50 percent worked 40 hours , and the rest worked 50 hours ?
Options: a ) $ 180,000 , b ) $ 185,000 , c ) $ 190,000 , d ) $ 177,500 , e ) $ 205,000
Rationale: "30 % of 1000 = 300 worked for 15 hours payment @ 5 / hr total payment = 300 * 15 * 5 = 22500 50 % of 1000 = 500 worked for 40 hours payment @ 5 / hr total payment = 500 * 40 * 5 = 100000 remaining 200 worked for 50 hours payment for first 40 hours @ 5 / hr payment = 200 * 40 * 5 = 40000 payment for next 10 hr @ 7.5 / hr payment = 200 * 10 * 7.5 = 15000 total payment = 22500 + 100000 + 40000 + 15000 = 1775000 hence , answer is d"
Answer: d
Question (general): a corporation double its annual bonus to 100 of its employees . what percent of the employees ’ new bonus is the increase ?
Options: a ) 50 % , b ) 12 % , c ) 8 % , d ) 6 % , e ) 5 %
Rationale: let the annual bonus be x . a corporation double its annual bonus . so new bonus = 2 x . increase = 2 x - x = x the increase is what percent of the employees ’ new bonus = ( x / 2 x ) * 100 = 50 % hence a .
Answer: a
Question (physics): a and b together do a work in 20 days . b and c together in 15 days and c and a in 12 days . then b alone can finish same work in how many days ?
Options: a ) 50 , b ) 60 , c ) 45 , d ) 35 , e ) 48
Rationale: "( a + b ) work in 1 day = 1 / 20 , ( b + c ) work in 1 days = 1 / 15 . , ( c + a ) work in 1 days = 1 / 12 ( 1 ) adding = 2 [ a + b + c ] in 1 day work = [ 1 / 20 + 1 / 15 + 1 / 12 ] = 1 / 5 ( a + b + c ) work in 1 day = 1 / 10 b work in 1 days = [ a + b + c ] work in 1 days - work of ( a + c ) in 1 days = [ 1 / 10 - 1 / 12 ] = 1 / 60 b alone finish work in 60 days answer b"
Answer: b
Question (physics): two trains of equal length , running with the speeds of 60 and 16 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 ) 10.11 , b ) 8.11 , c ) 77.2 , d ) 13.15 , e ) 22.22
Rationale: "rs = 60 - 40 = 20 * 5 / 18 = 100 / 18 t = 50 d = 50 * 100 / 18 = 2500 / 9 rs = 60 + 16 = 76 * 5 / 18 t = 2500 / 9 * 18 / 380 = 13.15 sec . answer : d"
Answer: d
Question (general): calculate the ratio between x and y if 30 % of x equal to 50 % of y ?
Options: a ) 4 : 5 , b ) 3 : 5 , c ) 3 : 7 , d ) 3 : 2 , e ) 4 : 5
Rationale: "explanation : 30 x = 50 y x : y = 30 : 50 = 3 : 5 answer : b"
Answer: b
Question (geometry): three walls have wallpaper covering a combined area of 300 square meters . by overlapping the wallpaper to cover a wall with an area of 180 square meters , the area that is covered by exactly two layers of wallpaper is 34 square meters . what is the area that is covered with three layers of wallpaper ?
Options: a ) 43 square meters , b ) 36 square meters , c ) 42 square meters , d ) 83.3 square meters , e ) 120 square meters
Rationale: "300 - 180 = 120 sq m of the wallpaper overlaps ( in either two layers or three layers ) if 36 sq m has two layers , 120 - 34 = 86 sq m of the wallpaper overlaps in three layers . 86 sq m makes two extra layers hence the area over which it makes two extra layers is 43 sq m . answer ( a ) ."
Answer: a
Question (probability): a meeting has to be conducted with 6 managers . find the number of ways in which the managers may be selected from among 9 managers , if there are 2 managers who refuse to attend the meeting together .
Options: a ) 36 , b ) 40 , c ) 42 , d ) 45 , e ) 49
Rationale: "the total number of ways to choose 6 managers is 9 c 6 = 84 we need to subtract the number of groups which include the two managers , which is 7 c 4 = 35 . 84 - 35 = 49 the answer is e ."
Answer: e
Question (gain): a trader bought a car at 20 % discount on its original price . he sold it at a 40 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 82 % , b ) 52 % , c ) 12 % , d ) 19 % , e ) 22 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 140 / 100 ) = 112 100 - 112 = 12 % answer : c"
Answer: c
Question (general): what is the unit digit in the product ( 3 ^ 65 x 6 ^ 59 x 7 ^ 71 ) ?
Options: a ) 18 , b ) 12 , c ) 69 , d ) 32 , e ) 4
Rationale: explanation : unit digit in 3 ^ 4 = 1 unit digit in ( 3 ^ 4 ) 16 = 1 unit digit in 3 ^ 65 = unit digit in [ ( 3 ^ 4 ) 16 x 3 ] = ( 1 x 3 ) = 3 unit digit in 6 ^ 59 = 6 unit digit in 7 ^ 4 unit digit in ( 7 ^ 4 ) 17 is 1 . unit digit in 7 ^ 71 = unit digit in [ ( 7 ^ 4 ) 17 x 73 ] = ( 1 x 3 ) = 3 required digit = unit digit in ( 3 x 6 x 3 ) = 4 e
Answer: e
Question (physics): a start walking from a place at a uniform speed of 6 kmph in a particular direction . after half an hour , b starts from the same place and walks in the same direction as a at a uniform speed and overtakes a after 1 hour 48 minutes . find the speed of b .
Options: a ) 4.7 kmph , b ) 6.6 kmph , c ) 4 kmph , d ) 7 kmph , e ) 5.3 kmph
Rationale: "distance covered by a in 30 min = 1 km b covers extra 1 km in 1 hour 48 minutes ( 9 / 5 hr ) i . e . relative speed of b over a = 1 / ( 9 / 5 ) = 5 / 9 so the speed of b = speed of a + 5 / 9 = 6 + 5 / 9 = 6.55 answer b"
Answer: b
Question (physics): oak street begins at pine street and runs directly east for 2 kilometers until it ends when it meets maple street . oak street is intersected every 400 meters by a perpendicular street , and each of those streets other than pine street and maple street is given a number beginning at 1 st street ( one block east of pine street ) and continuing consecutively ( 2 nd street , 3 rd street , etc . . . ) until the highest - numbered street one block west of maple street . what is the highest - numbered street that intersects oak street ?
Options: a ) 4 th , b ) 5 th , c ) 6 th , d ) 7 th , e ) 8 th
Rationale: 2 km / 400 m = 5 . however , the street at the 2 - km mark is not 5 th street ; it is maple street . therefore , the highest numbered street is 4 th street . the answer is a .
Answer: a
Question (gain): 50 percent of the members of a study group are women , and 30 percent of those women are lawyers . if one member of the study group is to be selected at random , what is the probability that the member selected is a woman lawyer ?
Options: a ) 0.16 , b ) 0.25 , c ) 0.45 , d ) 0.35 , e ) 0.15
Rationale: "say there are 100 people in that group , then there would be 0.5 * 0.30 * 100 = 15 women lawyers , which means that the probability that the member selected is a woman lawyer is favorable / total = 15 / 100 . answer : e"
Answer: e
Question (physics): the cross - section of a cannel is a trapezium in shape . if the cannel is 14 m wide at the top and 8 m wide at the bottom and the area of cross - section is 550 sq m , the depth of cannel is ?
Options: a ) 76 , b ) 28 , c ) 50 , d ) 80 , e ) 25
Rationale: "1 / 2 * d ( 14 + 8 ) = 550 d = 50 answer : c"
Answer: c
Question (physics): kim finds a 4 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?
Options: a ) 2 / 5 , b ) 7 / 5 , c ) 3 / 5 , d ) 8 / 15 , e ) 1 / 2
Rationale: "3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is c"
Answer: c
Question (general): $ 350 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?
Options: a ) $ 200 , b ) $ 225 , c ) $ 250 , d ) $ 275 , e ) $ 300
Rationale: "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 350 x = 50 4 x = 200 the answer is c ."
Answer: c
Question (general): in an it company , there are a total of 90 employees including 50 programmers . the number of male employees is 80 , including 35 male programmers . how many employees must be selected to guaranty that we have 3 programmers of the same sex ?
Options: a ) 10 , b ) 45 , c ) 55 , d ) 35 , e ) 65
Rationale: "you could pick 40 non - programmers , 2 male programmers , and 2 female programmers , and still not have 3 programmers of the same sex . but if you pick one more person , you must either pick a male or a female programmer , so the answer is 45 . b"
Answer: b
Question (gain): the cost of one photocopy is $ 0.02 . however , a 25 % discount is offered on orders of more than 100 photocopies . if arthur and david have to make 80 copies each , how much will each of them save if they submit a single order of 160 copies ?
Options: a ) $ 0.32 , b ) $ 0.40 , c ) $ 0.45 , d ) $ 0.48 , e ) $ 0.54
Rationale: "if arthur and david submit separate orders , each would be smaller than 100 photocopies , so no discount . each would pay ( 80 ) * ( $ 0.02 ) = $ 1.60 , or together , a cost of $ 3.20 - - - that ' s the combined no discount cost . if they submit things together as one big order , they get a discount off of that $ 3.20 price - - - - 25 % or 1 / 4 of that is $ 0.80 , the discount on the combined sale . they each effective save half that amount , or $ 0.40 . answer = ( b ) ."
Answer: b
Question (general): ( 3 x + 1 ) ( 2 x - 5 ) = ax ^ 2 + kx + n . what is the value of a - n + k ?
Options: a ) 5 , b ) 8 , c ) 9 , d ) 14 , e ) 11
Rationale: "expanding we have 6 x ^ 2 - 15 x + 2 x - 5 6 x ^ 2 - 13 x - 5 taking coefficients , a = 6 , k = - 13 , n = - 5 therefore a - n + k = 6 - ( - 13 ) - 5 = 19 - 5 = 14 the answer is d ."
Answer: d
Question (physics): if 6 men and 8 women can do a piece of work in 10 days while 26 men and 48 women can do the same in 2 days , the time taken by 15 men and 20 women in doing the same type of work will be ?
Options: a ) 5 , b ) 4 , c ) 6 , d ) 7 , e ) 8
Rationale: let 1 man ' s 1 day ' s work = x and 1 women ' s 1 day ' s work = y . then , 6 x + 8 y = 1 and 26 x + 48 y = 1 . 10 2 solving these two equations , we get : x = 1 and y = 1 . 100 200 ( 15 men + 20 women ) ' s 1 day ' s work = 15 + 20 = 1 . 100 200 4 15 men and 20 women can do the work in 4 days . hence answer will be b
Answer: b
Question (general): the maximum number of students among them 1345 pens and 775 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
Options: a ) 91 , b ) 10 , c ) 6 , d ) 5 , e ) none of these
Rationale: "explanation : required number of students = h . c . f of 1345 and 775 = 5 . answer : d"
Answer: d