Cheukting/mathqa huggingface dataset:
Question (general): the average age of 32 students in a group is 10 years . when teacher ' s age is included to it , the average increases by one . what is the teacher ' s age in years ?
Options: a ) 45 , b ) 43 , c ) 51 , d ) 53 , e ) 57
Rationale: "age of the teacher = ( 33 * 11 - 32 * 10 ) = 43 years . answer : b"
Answer: b
Question (gain): mohit sold an article for $ 21000 . had he offered a discount of 10 % on the selling price , he would have earned a profit of 8 % . what is the cost price of the article ?
Options: a ) 16000 , b ) 25000 , c ) 15000 , d ) 18000 , e ) 17500
Rationale: "let the cp be $ x . had he offered 10 % discount , profit = 8 % profit = 8 / 100 x and hence his sp = x + 8 / 100 x = $ 1.08 x = 21000 - 10 / 100 ( 21000 ) = 21000 - 2100 = $ 18900 = > 1.08 x = 18900 = > x = 17500 e"
Answer: e
Question (other): a marketing firm determined that , of 200 households surveyed , 80 used neither brand k nor brand b soap , 60 used only brand k soap , and for every household that used both brands of soap , 3 used only brand b soap . how many of the 200 households surveyed used both brands of soap ?
Options: a ) 15 , b ) 20 , c ) 30 , d ) 40 , e ) 45
Rationale: solution for soap k and soap b ( d ) 40
Answer: d
Question (gain): a shopkeeper cheats to the extent of 10 % while buying and selling , by using false weights . his total gain is .
Options: a ) 22 , b ) 21 , c ) 8 , d ) 9 , e ) 81
Rationale: answer : b ) 21 %
Answer: b
Question (general): the number of singles that a baseball player hit increased 15 percent from her first season to her second season , and the number of doubles that she hit in the same time period decreased by 5 percent . if the total number of singles and doubles that she hit increased 4 percent from her first season to her second season , what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season ?
Options: a ) 3 : 5 , b ) 5 : 7 , c ) 7 : 11 , d ) 9 : 11 , e ) 11 : 15
Rationale: soln : - 1.15 s + 0.95 d = 1.04 [ s + d ] 0.11 s = 0.09 d s / d = 9 / 11 answer : d
Answer: d
Question (general): the product x of two prime numbers is between 17 and 55 . if one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25 , then x =
Options: a ) 18 , b ) 29 , c ) 37 , d ) 44 , e ) 51
Rationale: "option b & c can be ruled out as they themselves are prime numbers 18 = 2 * 9 = 3 * 6 > > ignore 44 = 2 * 22 = 4 * 11 > > ignore 51 = 3 * 17 > > answer answer e"
Answer: e
Question (general): the average of first 6 prime numbers which are between 60 and 90 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 57 , e ) 72.33
Rationale: explanation : first six prime numbers which are between 60 and 90 = 61 , 67 , 71 , 73 , 79 , 83 average = ( 61 + 67 + 71 + 73 + 79 + 83 ) / 6 = 72.33 answer : e
Answer: e
Question (geometry): a rectangular grass field is 95 m * 55 m , it has a path of 2.5 m wide all round it on the outside . find the area of the path and the cost of constructing it at rs . 2 per sq m ?
Options: a ) 1350 , b ) 1550 , c ) 9676 , d ) 1679 , e ) 2691
Rationale: "area = ( l + b + 2 d ) 2 d = ( 95 + 55 + 2.5 * 2 ) 2 * 2.5 = > 775 775 * 2 = rs . 1550 answer : b"
Answer: b
Question (gain): the sale price sarees listed for rs . 350 after successive discount is 20 % and 5 % is ?
Options: a ) 266 , b ) 278 , c ) 342 , d ) 787 , e ) 191
Rationale: "350 * ( 80 / 100 ) * ( 95 / 100 ) = 266 answer : a"
Answer: a
Question (physics): a train is 360 meter long is running at a speed of 56 km / hour . in what time will it pass a bridge of 140 meter length .
Options: a ) 20.14 seconds , b ) 12.14 seconds , c ) 22.14 seconds , d ) 32.14 seconds , e ) none of these
Rationale: "explanation : speed = 56 km / hr = 56 * ( 5 / 18 ) m / sec = 140 / 9 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 / 140 / 9 = 32.14 seconds answer : d"
Answer: d
Question (gain): a reduction of 25 % in the price of oil enables a house wife to obtain 5 kgs more for rs . 1100 , what is the reduced price for kg ?
Options: a ) s . 40 , b ) s . 46 , c ) s . 55 , d ) s . 41 , e ) s . 42
Rationale: "800 * ( 25 / 100 ) = 275 - - - - 5 ? - - - - 1 = > rs . 55 answer : c"
Answer: c
Question (general): in a college , 280 students study hindi , 254 students study sanskrit and 280 students study english . 97 students study hindi as well as physics , 138 students study sanskrit as well as english and 152 students study hindi as well as english . 73 students study all the 3 languages . how many total number of students are there in that college ?
Options: a ) 350 , b ) 500 , c ) 650 , d ) 235 , e ) 450
Rationale: b
Answer: b
Question (general): 20 men shake hands with each other . maximum no of handshakes without cyclic handshakes .
Options: a ) 190 , b ) 200 , c ) 210 , d ) 220 , e ) 230
Rationale: "1 st person will shake hand with 19 people 2 nd person will shake hand with 18 people 3 rd person will shake hand with 17 people . . . . . . total no . of handshakes = 19 + 18 + 17 + . . . + 3 + 2 + 1 = 19 * ( 19 + 1 ) / 2 = 190 or , if there are n persons then no . of shakehands = nc 2 = 20 c 2 = 190 answer : a"
Answer: a
Question (physics): a and b complete a work in 8 days . a alone can do it in 16 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.78 days , c ) 5.3 days , d ) 3.15 days , e ) 2.75 days
Rationale: "1 / 8 + 1 / 16 = 3 / 16 16 / 3 = 5.3 days answer : c"
Answer: c
Question (physics): suppose 8 monkeys take 8 minutes to eat 8 bananas . how many monkeys would it take to eat 48 bananas in 48 minutes
Options: a ) 5 monkeys , b ) 6 monkeys , c ) 7 monkeys , d ) 8 monkeys , e ) 9 monkeys
Rationale: "8 monkeys take 8 minutes to eat 8 bananas means each monkey takes 8 min for 1 banana in 48 mins one monkey can eat 6 bananas . . . . which means that 8 monkeys can eat 48 bananas in 48 minutes so answer is 8 monkeys answer : d"
Answer: d
Question (general): a certain company has records stored with a record storage firm in 15 - inch by 12 - inch by 10 - inch boxes . the boxes occupy 1.08 million cubic inches of space . if the company pays $ 0.2 per box per month for the record storage , what is the total amount that the company pays each month for record storage ?
Options: a ) a . 150 , b ) b . 300 , c ) c . 600 , d ) d . 120 , e ) e . 200
Rationale: volume per box : 15 x 12 x 10 = 1,800 total volume : 1 , 080,000 number of boxes : total volume / volume per box = 1 , 080,000 / 1,800 = 600 price per month : number of boxes * price per box = 600 * 0.2 = 120 answer : d
Answer: d
Question (general): company s produces two kinds of stereos : basic and deluxe . of the stereos produced by company s last month , 2 / 3 were basic and the rest were deluxe . if it takes 1.3 as many hours to produce a deluxe stereo as it does to produce a basic stereo , then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos ?
Options: a ) 7 / 17 , b ) 13 / 33 , c ) 7 / 15 , d ) 17 / 35 , e ) 1 / 2
Rationale: "the easiest way for me is to plug in numbers . let the number of basic stereos produced be 40 , and number of delux stereos produced be 20 . total of 60 stereos . if it takes an hour to produce a basic stereo then it will take 1.3 hours to produce a deluxe stereo . 40 basic stereos = 40 hours . 20 delux stereos = 26 hours . total hours = 66 . then the fraction would be 26 / 66 = 13 / 33 . therefore answer b b ."
Answer: b
Question (general): two employees x and y are paid a total of rs . 528 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
Options: a ) s . 250 , b ) s . 280 , c ) s . 290 , d ) s . 299 , e ) s . 240
Rationale: "let the amount paid to x per week = x and the amount paid to y per week = y then x + y = 528 but x = 120 % of y = 120 y / 100 = 12 y / 10 ∴ 12 y / 10 + y = 528 ⇒ y [ 12 / 10 + 1 ] = 528 ⇒ 22 y / 10 = 528 ⇒ 22 y = 5280 ⇒ y = 5280 / 22 = 480 / 2 = rs . 240 e"
Answer: e
Question (physics): 8 identical machines , working alone and at their constant rates , take 6 hours to complete a job lot . how long would it take for 2 such machines to perform the same job ?
Options: a ) 2.25 hours , b ) 8.75 hours , c ) 12 hours , d ) 24 hours , e ) 16 hours
Rationale: "let each machine do 1 unit of work for 1 hour 8 machines - - > 8 units of work in 1 hour for 6 hours = 8 * 6 = 48 units of total work is done . now this 48 units of total work must be done by 2 machines 2 units of work ( 2 machines ) - - - > 1 hour for 48 units of work 2 * 24 - - - > 1 * 24 hours d 24 hours"
Answer: d
Question (physics): in a lake , there is a patch of lily pads . every day , the patch doubles in size . it takes 50 days for the patch to cover the entire lake , how many days would it take the patch to cover half of the lake ?
Options: a ) 36 , b ) 2 ^ 4 * 3 , c ) 24 , d ) 49 , e ) 47
Rationale: "working backward from the day it ' s covered : day 50 : fully covered day 49 : half covered so 49 days answer : d"
Answer: d
Question (gain): a shopkeeper sold an article for rs 2564.36 . approximately what was his profit percent if the cost price of the article was rs 2200
Options: a ) 17 % , b ) 5 % , c ) 6 % , d ) 7 % , e ) 8 %
Rationale: "explanation : gain % = ( 364.36 * 100 / 2200 ) = 16.56 % = 17 % approx option a"
Answer: a
Question (general): if a ( a - 6 ) = 27 and b ( b - 6 ) = 27 , where a ≠ b , then a + b = ?
Options: a ) − 48 , b ) − 2 , c ) 46 , d ) 6 , e ) 48
Rationale: "i . e . if a = - 3 then b = 9 or if a = 9 then b = - 3 but in each case a + b = - 3 + 9 = 6 answer : option d"
Answer: d
Question (gain): fox jeans regularly sell for $ 15 a pair and pony jeans regularly sell for $ 18 a pair . during a sale these regular unit prices are discounted at different rates so that a total of $ 8.64 is saved by purchasing 5 pairs of jeans : 3 pairs of fox jeans and 2 pairs of pony jeans . if the sum of the two discount rates is 22 percent , what is the discount rate on pony jeans ?
Options: a ) 8 % , b ) 10 % , c ) 11 % , d ) 12 % , e ) 14 %
Rationale: let x be the discount on pony jeans . then 0.22 - x is the discount on fox jeans . 3 ( 0.22 - x ) ( 15 ) + 2 x ( 18 ) = 8.64 9.9 - 45 x + 36 x = 8.64 9 x = 1.26 x = 0.14 the answer is e .
Answer: e
Question (geometry): a cylindrical can has a radius of 4 centimeters and a height of 18 centimeters . what is the area , in square centimeters , of a rectangular label that completely covers the curved surface of the can without over - lapping ?
Options: a ) 16 pi , b ) 64 pi , c ) 96 pi , d ) 144 pi , e ) 576 pi
Rationale: "they are asking the lateral surface area of the cylinder . the lateral surface area = 2 * pi * r * h = 2 * pi * 4 * 18 = 144 pi answer is d ."
Answer: d
Question (general): what is 5 2 / 3 - 3 5 / 4 divided by 5 / 2 - 7 / 6 ?
Options: a ) 2 , b ) 6 , c ) 4 , d ) 5 , e ) 1
Rationale: "5 2 / 3 - 3 5 / 4 = 17 / 3 - 20 / 4 = ( 68 - 60 ) / 12 = 8 / 12 = 4 / 3 5 / 2 - 7 / 6 = ( 15 - 7 ) / 6 = 8 / 6 = 4 / 3 so 4 / 3 / 4 / 3 = 1 answer - e"
Answer: e
Question (geometry): the perimeter of a triangle is 36 cm and the inradius of the triangle is 2.5 cm . what is the area of the triangle ?
Options: a ) 38 cm 2 , b ) 27 cm 2 , c ) 45 cm 2 , d ) 25 cm 2 , e ) 35 cm 2
Rationale: "area of a triangle = r * s where r is the inradius and s is the semi perimeter of the triangle . area of triangle = 2.5 * 36 / 2 = 45 cm 2 answer : c"
Answer: c
Question (general): sum of the squares of 3 no . ' s is 222 and the sum of their products taken two at a time is 131 . find the sum ?
Options: a ) 22 , b ) 24 , c ) 26 , d ) 28 , e ) 30
Rationale: "( a + b + c ) 2 = a 2 + b 2 + c 2 + 2 ( ab + bc + ca ) = 222 + 2 * 131 a + b + c = √ 484 = 22 a"
Answer: a
Question (general): a salesman ' s income consists of a commission and a base salary of $ 450 per week . over the past 5 weeks , his weekly income totals have been $ 406 , $ 413 , $ 420 , $ 436 and $ 395 . what must his average ( arithmetic mean ) commission be per week over the next two weeks so that his average weekly income is $ 500 over the 7 - week period ?
Options: a ) $ 150 , b ) $ 245 , c ) $ 365 , d ) $ 715 , e ) $ 265
Rationale: "total weekly income over 5 weeks = $ 406 + $ 413 + $ 420 + $ 436 + $ 395 = $ 2070 for avg weekly income to be $ 500 over 7 weeks , we need total weekly income over 7 weeks = $ 3500 now , $ 3500 - $ 2070 = $ 1430 from this , we subtract base salary for 2 weeks i . e $ 450 * 2 = $ 900 therefore , commission = $ 1430 - $ 900 = $ 530 for 2 weeks avg weekly commission = $ 265 answer e"
Answer: e
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 400 sculptures are not on display , how many pieces of art does the gallery have ?
Options: a ) 360 , b ) 900 , 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 . 400 sculptures are not on display , so according to ( iii ) 2 / 3 * { not on display } = 400 - - > { not on display } = 600 . according to ( i ) 2 / 3 * { total } = 600 - - > { total } = 900 . answer : b ."
Answer: b
Question (general): what is ( 25 ^ 7 + 25 ) / 25 ?
Options: a ) 244140626 , b ) 243120617 , c ) 242580531 , d ) 241230438 , e ) 240760355
Rationale: "( 25 ^ 7 + 25 ) / 25 = 25 * ( 25 ^ 6 + 1 ) / 25 = 25 ^ 6 + 1 clearly this is a number which ends with a 6 in the units place . the answer is a ."
Answer: a
Question (general): chris mixed 5 pounds of raisins with 4 pounds of nuts . if a pound of nuts costs 3 times as much as a pound of raisins , then the total cost of the raisins was what fraction of the total cost of the mixture ?
Options: a ) 5 / 17 , b ) 1 / 5 , c ) 1 / 4 , d ) 1 / 3 , e ) 3 / 7
Rationale: "1 lbs of raisin = $ 1 5 lbs of raisin = $ 5 1 lbs of nuts = $ 3 4 lbs of nuts = $ 12 total value of mixture = 12 + 5 = 17 fraction of the value of raisin = 5 / 17 = 1 / 5 ans : a"
Answer: a
Question (physics): a train running at the speed of 60 km / hr crosses a pole in 18 sec . what is the length of the train ?
Options: a ) 118 , b ) 150 , c ) 300 , d ) 258 , e ) 191
Rationale: "speed = 60 * 5 / 18 = 50 / 3 m / sec length of the train = speed * time = 50 / 3 * 18 = 300 m answer : c"
Answer: c
Question (general): find the value for x from below equation : x / 3 = - 5 ?
Options: a ) - 66 , b ) 13 , c ) - 15 , d ) - 31 , e ) 40
Rationale: "1 . multiply both sides by 3 : x * 3 / 3 = - 5 / 3 simplify both sides : x = - 15 c"
Answer: c
Question (general): if an average hard drive had a capacity of 0.7 tb in 2000 , and average hard drive capacities double every 5 years , what will be the average hard drive capacity in 2050 ?
Options: a ) 256 , b ) 512 , c ) 768 , d ) 1024 , e ) 7168
Rationale: 0.7 * 2 ^ 10 = 0.7 * 1024 = 716.8 the answer is e .
Answer: e
Question (general): 9 men went to a hotel . 8 of them spent rs . 3 each over their meals and the ninth spent rs . 2 more than the average expenditure of all the 9 . determine the total money spent by them ? a . rs . 29.25
Options: a ) 29.25 , b ) 29.28 , c ) 29.27 , d ) 29.22 , e ) 29.21
Rationale: average of 9 = x 9 x = 8 * 3 + x * 2 x = 3.25 total = 9 * 3.25 = 29.25 . answer : a
Answer: a
Question (other): a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 10 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 315
Rationale: "1 c 7 * 2 c 10 = 7 * 45 = 315 the answer is ( e )"
Answer: e
Question (general): find the average of all the numbers between 6 and 34 which are divisible by 5
Options: a ) 18 , b ) 20 , c ) 24 , d ) 30 , e ) 40
Rationale: "exp . multiples of 5 between 6 and 34 are 10 , 15,20 , 25,30 average = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 5 ( 10 + 30 ) / 2 * 5 = 40 / 2 = 20 answer : b"
Answer: b
Question (physics): how much time will a train of length 420 m moving at a speed of 72 kmph take to cross another train of length 640 m , moving at 36 kmph in the same direction ?
Options: a ) 50 , b ) 99 , c ) 88 , d ) 76 , e ) 106
Rationale: "the distance to be covered = sum of their lengths = 420 + 640 = 1060 m . relative speed = 72 - 36 = 36 kmph = 36 * 5 / 18 = 10 mps . time required = d / s = 1060 / 10 = 106 sec . answer : e"
Answer: e
Question (gain): machine p and machine q are each used to manufacture 110 sprockets . it takes machine p 10 hours longer to produce 110 sprockets than machine q . machine q produces 10 % more sprockets per hour than machine a . how many sprockets per hour does machine a produce ?
Options: a ) 5 , b ) 15 , c ) 55 , d ) 95 , e ) 1
Rationale: p makes x sprockets per hour . then q makes 1.1 x sprockets per hour . 10 / x = 110 / 1.1 x + 10 1.1 ( 110 ) = 110 + 11 x 11 x = 11 x = 1 the answer is e
Answer: e
Question (physics): a spider web consists of 3 concurrent lines forming radial support for 20 concentric regular hexagon . the hexagon vertices are 5 mm from their immidiate neighbour . if the innermost hexagon has a side length 3 mm how many meters is the length of the entire web including the 3 diagonals ?
Options: a ) 7.354 m
b ) 8.354 m
c ) 6.354 m
d ) 9.354 m
e ) 5.354 m
Rationale: for perimeter of all hexagon = 6 * ( 3 + 8 + 13 + . . . . . . . . . . . 20 th term . ) sum will be 6060 mm and for length of one diagonal find 20 th term = 98 so total length = 6060 + 294 = 6354 mm = 6.354 m answer : c
Answer: c
Question (general): when processing flower - nectar into honey bees ' extract , a considerable amount of water gets reduced . how much flower - nectar must be processed to yield 1 kg of honey , if nectar contains 50 % water , and the honey obtained from this nectar contains 25 % water ?
Options: a ) 1.2 kg , b ) 1.5 kg , c ) 1.7 kg , d ) 1.9 kg , e ) none of these
Rationale: "explanation : flower - nectar contains 50 % of non - water part . in honey this non - water part constitutes 75 % ( 100 - 25 ) . therefore 0.5 x amount of flower - nectar = 0.75 x amount of honey = 0.75 x 1 kg therefore amount of flower - nectar needed = ( 0.75 / 0.51 ) kg = 1.5 kgs answer : b"
Answer: b
Question (general): a dishonest dealer claims to sell a product at its cost price . he uses a counterfeit weight which is 20 % less than the real weight . further greed overtook him and he added 30 % impurities to the product . find the net profit percentage of the dealer ?
Options: a ) 44 % , b ) 40 % , c ) 50 % , d ) 56.25 % , e ) 37.5 %
Rationale: "the dealer uses weight which is 20 % less than the real weight . or ( 1 - 1 / 5 ) or 4 / 5 of real weight . it means that he is selling $ 4 worth of product for $ 5 . the dealer then further added 30 % impurities to the product . it means that he is selling $ 5 worth of product for $ 5.5 . so his profit is $ 5.5 - $ 4 = $ 1.5 and his profit percent is ( 1.5 / 4 ) * 100 = 37.5 % answer : - e"
Answer: e
Question (gain): in a certain company , a third of the workers do not have a retirement plan . 20 % of the workers who do not have a retirement plan are women , and 40 % of the workers who do have a retirement plan are men . if 144 of the workers of that company are men , how many of the workers are women ?
Options: a ) 80 , b ) 95 , c ) 105 , d ) 120 , e ) 126
Rationale: "set up equation : x = total number of workers 144 = 0,4 * 2 / 3 * x + 0,8 * 1 / 3 * x 144 = 16 / 30 x x = 270 270 - 144 = 126 answer e"
Answer: e
Question (general): 95 white and black tiles will be used to form a 10 x 10 square pattern . if there must be at least one black tile in every row and at least one white tile in every column , what is the maximum difference between the number of black and white tiles that can be used ?
Options: a ) 75 , b ) 80 , c ) 85 , d ) 90 , e ) 95
Rationale: answer = c please refer diagram below 95 - 10 = 85
Answer: c
Question (physics): in what time will a railway train 20 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 6 sec , b ) 7 sec , c ) 8 sec , d ) 9 sec , e ) 2 sec
Rationale: "t = 60 / 36 * 18 / 5 = 2 sec answer : e"
Answer: e
Question (gain): what is the rate percent when the simple interest on rs . 800 amount to rs . 400 in 2 years ?
Options: a ) 5 % , b ) 6 % , c ) 2 % , d ) 25 % , e ) 1 %
Rationale: interest for 2 yrs = 400 interest for 1 yr = 200 interest rate = 200 / 800 x 100 = 25 % answer : d
Answer: d
Question (geometry): if the area of a square with sides of length 9 centimeters is equal to the area of a rectangle with a width of 3 centimeters , what is the length of the rectangle , in centimeters ?
Options: a ) 4
b ) 27
c ) 12
d ) 16
e ) 18
Rationale: let length of rectangle = l 9 ^ 2 = l * 3 = > l = 81 / 3 = 27 answer b
Answer: b
Question (general): taequan is playing a dice game where he rolls two , fair , 6 - sided dice twice . if he gets the same roll on his second try as his first , he wins . if he rolled an 8 on his first try , what is the probability that he will win with his second roll ?
Options: a ) 1 / 18 , b ) 1 / 12 , c ) 1 / 9 , d ) 1 / 6 , e ) 5 / 36
Rationale: there are 5 ways to roll an 8 : 2 and 6 , 6 and 2 , 3 and 5 , 5 and 3 , 4 and 4 ( 4 and 4 is counted just once ) . there are 6 * 6 = 36 ways to roll two six - sided dice . the dice are fair , so the probability of rolling an 8 is 5 / 36 . e
Answer: e
Question (physics): car a runs at the speed of 100 km / hr & reaches its destination in 5 hr . car b runs at the speed of 80 km / h & reaches its destination in 6 h . what is the respective ratio of distances covered by car a & car b ?
Options: a ) 11 : 5 , b ) 11 : 8 , c ) 13 : 7 , d ) 25 : 24 , e ) 16 : 9
Rationale: "sol . distance travelled by car a = 100 × 5 = 500 km distance travelled by car b = 80 × 6 = 480 km ratio = 500 / 480 = 25 : 24 answer : d"
Answer: d
Question (general): george baked a total of 100 pizzas for 7 straight days , beginning on saturday . he baked 3 / 5 of the pizzas the first day , and 3 / 5 of the remaining pizzas the second day . if each successive day he baked fewer pizzas than the previous day , what is the maximum number of pizzas he could have baked on wednesday ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "3 / 5 of the 100 pizzas cooked on saturday = 60 pizzas 3 / 5 of the remaining pizzas on sunday = 24 pizzas we ' re left with ( 100 - 60 - 24 ) = 16 pizzas for the remaining 5 days . the prompt tells us that each day has fewer pizzas than the day before it , so we ca n ' t have duplicate numbers . m t w th f 6 4 3 2 1 = 16 w = 3 a"
Answer: a