Cheukting/mathqa huggingface dataset:
Question (physics): a train 270 metres long is moving at a speed of 25 kmph . it will cross a man coming from the opposite direction at a speed of 2 km per hour in :
Options: a ) 30 sec , b ) 32 sec , c ) 36 sec , d ) 38 sec , e ) 40 sec
Rationale: "relative speed = ( 25 + 2 ) km / hr = 27 km / hr = ( 27 × 5 / 18 ) m / sec = 15 / 2 m / sec . time taken by the train to pass the man = ( 270 × 2 / 15 ) sec = 36 sec answer : c"
Answer: c
Question (physics): speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph . a man rows to a place at a distance of 4864 km and comes back to the starting point . the total time taken by him is :
Options: a ) 700 , b ) 200 , c ) 540 , d ) 120 , e ) 635
Rationale: "explanation : speed downstream = ( 14 + 1.2 ) = 15.2 kmph speed upstream = ( 14 - 1.2 ) = 12.8 kmph total time taken = 4864 / 15.2 + 4864 / 12.8 = 320 + 380 = 700 hours . answer : a"
Answer: a
Question (gain): you enter a weight loss challenge game and manage to lose 13 % of your body weight . for the final weigh in you are forced to wear clothes that add 2 % to your weight . what percentage of weight loss is measured at the final weigh in ?
Options: a ) 13 % , b ) 9.22 % , c ) 11.26 % , d ) 14 % , e ) 12 %
Rationale: ( 100 % - 13 % ) * ( 100 % + 2 % ) = 0.87 * 1.02 = 11.26 % the weigh in records your weight loss at 11.26 % ! the answer is c
Answer: c
Question (gain): i bought two books ; for rs . 500 . i sold one at a loss of 15 % and other at a gain of 19 % and then i found each book was sold at the same price . find the cost of the book sold at a loss ?
Options: a ) 337 , b ) 280 , c ) 299.67 , d ) 266.67 , e ) 291.67
Rationale: "x * ( 85 / 100 ) = ( 500 - x ) 119 / 100 x = 291.67 answer : e"
Answer: e
Question (general): 252 ã · ? ã — 15 + 270 = 405
Options: a ) 24 , b ) 25 , c ) 28 , d ) 39 , e ) 43
Rationale: "explanation : 252 ã · ? ã — 15 = 405 - 270 = 135 ( 252 ã — 15 ) / ? = 135 ? = ( 252 ã — 15 ) / 135 = 28 answer : option c"
Answer: c
Question (gain): a and b put in rs . 300 and rs . 400 respectively into a business . a reinvests into the business his share of the first year ' s profit of rs . 196 where as b does not . in what ratio should they divide the second year ' s profit ?
Options: a ) 39 : 40 , b ) 39 : 49 , c ) 24 : 25 , d ) 39 : 47 , e ) 39 : 41
Rationale: "explanation : 3 : 4 a = 3 / 7 * 196 = 84 384 : 400 24 : 25 answer : c"
Answer: c
Question (general): in a group of ducks and cows , the total number of legs are 40 more than twice the number of heads . find the total number of cows .
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "let the number of ducks be d and number of cows be c then , total number of legs = 2 d + 4 c = 2 ( d + 2 c ) total number of heads = c + d given that total number of legs are 40 more than twice the number of heads = > 2 ( d + 2 c ) = 40 + 2 ( c + d ) = > d + 2 c = 20 + c + d = > 2 c = 20 + c = > c = 20 i . e . , total number of cows = 20 answer is e ."
Answer: e
Question (general): a student chose a number , multiplied it by 2 , then subtracted 138 from the result and got 102 . what was the number he chose ?
Options: a ) 90 , b ) 100 , c ) 120 , d ) 160 , e ) 200
Rationale: "solution : let x be the number he chose , then 2 * x * 138 = 102 2 x = 240 x = 120 correct answer c"
Answer: c
Question (general): the product of two successive numbers is 4160 . which is the smaller of the two numbers ?
Options: a ) 78 , b ) 64 , c ) 88 , d ) 67 , e ) 37
Rationale: "b 4160 from the given alternatives , 64 × 65 = 4160 ∴ smaller number = 64"
Answer: b
Question (general): soymilk are sold in packages of two or 3 only . if hannah bought 17 soymilk exactly , what could be the number of large packs hannah bought ?
Options: a ) 1 , b ) 4 , c ) 3 , d ) 5 , e ) 8
Rationale: let number of packs of three = t let number of packs of two = w 3 t + 2 w = 17 now , we need to test for values of w . since sum 17 is odd and 2 w will always be even , therefore w ca n ' t be even . now , we can test for values w = 1 , 3 and 5 2 * 4 + 3 * 3 = 8 + 9 = 17 answer c
Answer: c
Question (general): what ratio must a shopkeeper mix peas and soybean of rs . 16 and rs . 25 / kg , as to obtain a mixture of rs . 21.50 ?
Options: a ) 10 : 7 , b ) 9 : 8 , c ) 7 : 11 , d ) 13 : 11 , e ) 14 : 8
Rationale: "correct option : ( c ) use rule of alligation , to determine the ratio the required ratio of soybean and peas = 3.50 : 5.50 = 7 : 11"
Answer: c
Question (physics): a 300 meter long train crosses a platform in 33 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 250 , b ) 266 , c ) 230 , d ) 288 , e ) 271
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 33 = 50 / 3 3 ( x + 300 ) = 1650 è x = 250 m . answer : a"
Answer: a
Question (other): bucket p has thrice the capacity as bucket q . it takes 60 turns for bucket p to fill the empty drum . how many turns it will take for both the buckets p and q , having each turn together to fill the empty drum ?
Options: a ) 30 , b ) 45 , c ) 50 , d ) 25 , e ) 60
Rationale: "let capacity of p be x liters then capacity of q = x / 3 liters capacity of the drum = 60 x required number of turns = 60 x / ( x + x / 3 ) = 60 x * 3 / 4 x = 45 answer is b"
Answer: b
Question (geometry): mr . loyd wants to fence his square shaped land of 120 sqft each side . if a pole is laid every 10 ft how many poles do he need ?
Options: a ) 20 , b ) 30 , c ) 48 , d ) 50 , e ) 60
Rationale: "if each side is 120 feet . . then total perimeter is 120 * 4 = 480 poles every 10 feet hence no of poles = 480 / 10 = 48 answer : c"
Answer: c
Question (general): if 4 / ( 1 + 3 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3
Rationale: "the expression 4 / ( 1 + 3 / x ) = 1 should have been equal to something . if 4 / ( 1 + 3 / x ) = 1 = > 4 x / ( x + 3 ) = 1 = > 4 x = x + 3 = > 3 x = 3 = > x = 1 correct option : b"
Answer: b
Question (gain): a 16 % stock yielding 10 % is quoted at :
Options: a ) 83.33 , b ) 110 , c ) 112 , d ) 120 , e ) 160
Rationale: "solution to earn rs . 10 , money invested = rs . 100 . to earn rs . 16 , money invested = rs . ( 100 / 10 x 16 ) = rs . 160 . â ˆ ´ market value of rs . 100 stock = rs . 160 answer e"
Answer: e
Question (general): there are , in a certain league , 20 teams , and each team face another team for a total of 10 times . how many games are played in the season ?
Options: a ) 1900 , b ) 3600 , c ) 2400 , d ) 180 , e ) 5400
Rationale: "1 st team : 190 2 nd team : 180 3 rd team : 170 similarly the last team will play 0 therefore ( 190 + 180 + 170 . . . . 10 ) 10 ( 19 + 18 + 17 + 16 . . . . 1 ) 10 ( n ( n + 1 ) / 2 ) = 10 ( 19 * 20 / 2 ) = 1900 answer : a"
Answer: a
Question (general): if integer k is equal to the sum of all even multiples of 15 between 390 and 615 , what is the greatest prime factor of k ?
Options: a ) 5 , b ) 7 , c ) 8 , d ) 13 , e ) 17
Rationale: "if we break down what the stem is asking what is the sum of all mult of 30 between 390 and 600 . using arithmetic progression to find n : 600 = 390 + ( n - 1 ) 30 210 + 30 = 30 n 240 = 3 n = > n = 8 the sum would be : 8 * mean mean = [ 600 + 390 ] / 2 = 495 8 * 495 c"
Answer: c
Question (general): if x and y are positive integers and 3 + x + y + xy = 17 , what is the value of x + y ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "try each answer choice . for a : 3 + 3 + xy = 17 ; xy = 11 ( impossible , 11 prime number . 1 + 11 does n ' t equal 3 ) for b : 3 + 5 + xy = 17 ; xy = 9 ( no combination of xy = 9 and x + y = 5 ) for c : 3 + 6 + xy = 17 ; xy = 8 ( x + y = 6 ; x = 2 , y = 4 or x = 4 , y = 2 ) for d : 3 + 8 + xy = 17 ; xy = 6 ( no combination of xy = 6 and x + y = 8 ) for e : 3 + 9 + xy = 17 ; xy = 5 ( impossible , 5 prime number . 1 + 5 does n ' t equal 9 ) therefore , answer c ."
Answer: c
Question (general): a sun is divided among x , y and z in such a way that for each rupee x gets , y gets 45 paisa and z gets 30 paisa . if the share of y is rs . 54 , what is the total amount ?
Options: a ) 166 , b ) 105 , c ) 178 , d ) 177 , e ) 210
Rationale: "x : y : z = 100 : 45 : 30 20 : 9 : 6 9 - - - 54 35 - - - ? = > 210 answer : e"
Answer: e
Question (general): the expenditure of a businessman increase consistently by 10 % per year . if his present expenditure is rs . 20000 then what will his expenditure be after 2 years ?
Options: a ) 24500 , b ) 24400 , c ) 24300 , d ) 24200 , e ) 24100
Rationale: explanation : expenditure = 20000 x 1.1 x 1.1 = 24200 answer : option d
Answer: d
Question (general): farm tax is levied on the 25 % of the cultivated land . the tax department collected total $ 3840 through the farm tax from the village of mr . william . mr . william paid only $ 480 as farm tax . the percentage of total land of mr . willam over the total taxable land of the village is :
Options: a ) 15 % , b ) 25 % , c ) 50 % , d ) 0.2083 % , e ) none
Rationale: "this will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village . that leads to ( 480 / 3840 ) x 100 = 12.5 % in percentage terms . but the question asks ratio between his total land to total cultivated land . hence the answer is 12.5 % x ( 100 / 25 ) = 50 % the correct answer is ( c ) ."
Answer: c
Question (general): a textile manufacturing firm employees 100 looms . it makes fabrics for a branded company . the aggregate sales value of the output of the 100 looms is rs 5 , 00,000 and the monthly manufacturing expenses is rs 1 , 50,000 . assume that each loom contributes equally to the sales and manufacturing expenses are evenly spread over the number of looms . monthly establishment charges are rs 75000 . if one loom breaks down and remains idle for one month , the decrease in profit is :
Options: a ) 13000 , b ) 7000 , c ) 10000 , d ) 3500 , e ) none of these
Rationale: "explanation : profit = 5 , 00,000 â ˆ ’ ( 1 , 50,000 + 75,000 ) = rs . 2 , 75,000 . since , such loom contributes equally to sales and manufacturing expenses . but the monthly charges are fixed at rs 75,000 . if one loan breaks down sales and expenses will decrease . new profit : - = > 500000 ã — ( 99 / 100 ) â ˆ ’ 150000 ã — ( 99 / 100 ) â ˆ ’ 75000 . = > rs 2 , 68,000 . decrease in profit = > 2 , 75,000 â ˆ ’ 2 , 71,500 = > rs . 3,500 . answer : d"
Answer: d
Question (physics): it is the new year and mandy has made a resolution to lose weight this year . she plans to exercise and do yoga . for exercise she plans to workout at the gym and ride her bicycle in the ratio of 2 : 3 everyday . she will also do yoga in the ratio , yoga : exercise = 2 : 3 . if she rides her bike for 18 minutes , how much time will she spend doing yoga ? ( rounded to minutes )
Options: a ) 30 min . , b ) 41 min . , c ) 17 min . , d ) 23 min . , e ) 25 min .
Rationale: "the ratio is 2 : 3 = gym : ride , so ( 18 ) ( 3 / 2 ) = 27 minutes at the gym , and 27 + 18 = 45 minutes exercise , so ( 2 / 3 ) ( 45 ) = 30 minutes yoga . answer : a"
Answer: a
Question (general): when positive integer x is divided by 11 , the quotient is y and the remainder is 4 . when 2 x is divided by 8 , the quotient is 3 y and the remainder is 1 . what is the value of 13 y – x ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: ( 1 ) x = 11 y + 4 ( 2 ) 2 x = 24 y + 1 let ' s subtract equation ( 1 ) from equation ( 2 ) . 13 y - 3 = x 13 y - x = 3 the answer is b .
Answer: b
Question (physics): what is the least number of squares tiles required to pave the floor of a room 15.17 m long and 9.02 m broad ?
Options: a ) 814
b ) 266
c ) 287
d ) 999
e ) 661
Rationale: explanation : length of largest tile = h . c . f . of 1517 cm and 902 cm = 41 cm . area of each tile = required number of tiles = = 814 answer : a ) 814
Answer: a
Question (other): a bottle contains a certain solution . in the bottled solution , the ratio of water to soap is 3 : 2 , and the ratio of soap to salt is seven times this ratio . the solution is poured into an open container , and after some time , the ratio of water to soap in the open container is halved by water evaporation . at that time , what is the ratio of water to salt in the solution ?
Options: a ) 1 : 1 , b ) 2 : 3 , c ) 3 : 2 , d ) 9 : 4 , e ) 63 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 21 : 2 = > for 21 soap , salt = 2 = > for 2 soap , salt = ( 2 / 21 ) * 2 = 4 / 21 so , water : soap : salt = 3 : 2 : 4 / 21 = 63 : 42 : 4 after open container , water : soap : salt = 31.5 : 42 : 4 so , water : salt = 31.5 : 4 = 63 : 8 e"
Answer: e
Question (geometry): if a drawing has an outer circle of diameter 30 and an inner circle of diameter 24 , then what fraction of outer circle ' s surface is not covered by the inner circle ?
Options: a ) 3 / 6
b ) 8 / 24
c ) 14 / 16
d ) 9 / 25
e ) 2 / 3
Rationale: the questions asks us to find the surface which is not covered by the inner circle i . e . , area of the surface not covered . where as circumference is the length along the edge of the circle , 2 * pi * r implies the length of the curve pi * r ^ 2 implies area enclosed by that curve . . hence area of the circle is considered for this problem area of the inner circle = pi * r ^ 2 , where r = 12 = > pi * 144 area of the outer circle = pi * 225 surface not covered by the inner circle = pi * 225 - pi * 144 = pi * 81 fraction of outer circle ' s surface is not covered by the inner circle = pi * 81 / total area of the outer circle = > pi * 81 / pi * 225 = 9 / 25 answer is d
Answer: d
Question (physics): the sum of three consecutive even numbers is 366 . find the middle number of the three ?
Options: a ) 111 , b ) 123 , c ) 122 , d ) 152 , e ) 142
Rationale: "middle number = 366 / 3 = 122 ans c"
Answer: c
Question (physics): x can finish a work in 24 days . y can finish the same work in 16 days . yworked for 10 days and left the job . how many days does x alone need to finish the remaining work ?
Options: a ) 3 , b ) 5 , c ) 6 , d ) 8 , e ) 9
Rationale: "work done by x in 1 day = 1 / 24 work done by y in 1 day = 1 / 16 work done by y in 10 days = 10 / 16 = 5 / 8 remaining work = 1 – 5 / 8 = 3 / 8 number of days in which x can finish the remaining work = ( 3 / 8 ) / ( 1 / 24 ) = 9 e"
Answer: e
Question (gain): some of 45 % - intensity red paint is replaced with 25 % solution of red paint such that the new paint intensity is 40 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 5 , b ) 1 / 4 , c ) 1 / 5 , d ) 1 / 7 , e ) 2 / 3
Rationale: "let total paint = 1 let amount replaced = x 45 ( 1 - x ) + 25 x = 40 x = 1 / 4 answer : b"
Answer: b
Question (other): what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ?
Options: a ) e = 5 , b ) e = 9 , c ) e = 10 , d ) e = 20 , e ) 30
Rationale: "what is the greatest positive integer e such that 3 ^ e is a factor of 9 ^ 10 ? 9 ^ 10 = ( 3 ^ 2 ) ^ 10 = 3 ^ 20 d . 20"
Answer: d
Question (geometry): what will be the cost of building a fence around a square plot with area equal to 289 sq ft , if the price per foot of building the fence is rs . 59 ?
Options: a ) 3944 , b ) 920 , c ) 7290 , d ) 6928 , e ) 4012
Rationale: "explanation : let the side of the square plot be a ft . a 2 = 289 = > a = 17 length of the fence = perimeter of the plot = 4 a = 68 ft . cost of building the fence = 68 * 59 = rs . 4012 . answer : option e"
Answer: e
Question (general): if the sum of two numbers is 45 and the h . c . f and l . c . m of these numbers are 4 and 5 respectively , then the product of the reciprocals is equal to :
Options: a ) 20 / 20 , b ) 1 / 1 , c ) 2 / 30 , d ) 11 / 20 , e ) 1 / 20
Rationale: "let the numbers be a and b . then , a + b = 45 and ab = 5 * 4 = 20 . required product = 1 / a * 1 / b = 1 / ab = 1 / 20 = 1 / 20 . answer : e"
Answer: e
Question (physics): at jerri ’ s pet shop , 60 cups of bird seed are used every 5 days to feed 20 parakeets . how many cups of bird seed would be required to feed 10 parakeets for 5 days ?
Options: a ) 45.6 , b ) 20 , c ) 9 , d ) 30 , e ) 65
Rationale: let ' s go step - by - step . 60 cups are used over a 5 day period , which means 12 cups a day . this feeds 20 parakeets , which means each parakeet needs . 60 of a cup every day . for 10 parakeets , we need 10 * . 60 cups = 6 cups a day . over 5 days , we need 30 cups . choice d .
Answer: d
Question (general): find the value of x : 2 x ² − 4 .
Options: a ) 0,2 , b ) - 2,2 , c ) - 2,1 , d ) 0,4 , e ) - 1,4
Rationale: that quadratic is factored as follows : 2 x ² − 4 = ( 2 x − 2 ) ( x + 2 ) . now , it is easy to see that the second factor will be 0 when x = − 2 . as for the value of x that will make 2 x − 4 = 0 , we must solve that equation we have : 2 x = 4 x = 2 the solutions are : x = - 2 and 2 b
Answer: b
Question (general): a jar of 180 marbles is divided equally among a group of marble - players today . if 2 people joined the group in the future , each person would receive 1 marble less . how many people are there in the group today ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "180 = 18 * 10 = 20 * 9 there are 18 people in the group today . the answer is b ."
Answer: b
Question (general): a cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number age of the family now is :
Options: a ) 18 , b ) 17 , c ) 76 , d ) 85 , e ) 86
Rationale: "let the number of wickets taken till the last match be x . then , ( 12.4 x + 26 ) / ( x + 5 ) = 12 = 12.4 x + 26 = 12 x + 60 = 0.4 x = 34 = x = 340 / 4 = 85 . answer : d"
Answer: d
Question (general): the average of first 5 multiples of 5 is
Options: a ) 3 , b ) 6 , c ) 9 , d ) 12 , e ) 15
Rationale: solution average = 5 ( 1 + 2 + 3 + 4 + 5 ) / 5 = 75 / 5 . = 15 answer e
Answer: e
Question (gain): a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 50 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 70 , b ) 65 , c ) 60 , d ) 75 , e ) 80
Rationale: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 50 % of 50 % i . e 25 % . so he completed 50 + 25 = 75 % of total trip . d"
Answer: d
Question (general): the difference of two numbers is 1415 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) a ) 270 , b ) b ) 280 , c ) c ) 290 , d ) d ) 300 , e ) e ) 310
Rationale: let the smaller number be x . then larger number = ( x + 1415 ) . x + 1415 = 6 x + 15 5 x = 1400 x = 280 smaller number = 280 . b )
Answer: b
Question (gain): the price of a jacket is reduced by 25 % . during a special sale the price of the jacket is reduced another 25 % . by approximately what percent must the price of the jacket now be increased in order to restore it to its original amount ?
Options: a ) 32.5 , b ) 77.78 , c ) 48 , d ) 65 , e ) 67.5
Rationale: "1 ) let the price of jacket initially be $ 100 . 2 ) then it is decreased by 25 % , therefore bringing down the price to $ 75 . 3 ) again it is further discounted by 10 % , therefore bringing down the price to $ 56.25 4 ) now 56.25 has to be added byx % in order to equal the original price . 56.25 + ( x % ) 56.25 = 100 . solving this eq for x , we get x = 77.78 ans is b ."
Answer: b
Question (physics): there is a 50 cm line marked at each centimeter and an insect is placed at every centimeter . 9 frogs are trained to jump a constant distance . the first one jumps 2 cm in every leap , the second one jumps 3 cm and so on until the 9 th one jumps 10 cm in every leap and they eat any insect that is available at that spot . if all of them start from start line and finish the entire 50 cm , how many insects were still left after the race was over ?
Options: a ) 0 , b ) 4 , c ) 6 , d ) 8 , e ) 11
Rationale: "only the prime numbers greater than 10 and less than 50 were left . that is 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , and 47 . the total is 11 . the answer is e ."
Answer: e
Question (general): of the 180 people at a party , 70 were women , and 30 women tried the appetizer . if 50 people did not try the appetizer , what is the total number of men who tried the appetizer ?
Options: a ) 40 , b ) 50 , c ) 60 , d ) 70 , e ) 100
Rationale: "total people at party = 180 women = 70 so men 180 - 70 = 110 no . of pple who tried appetizer = 180 - 50 ( given info ) = 130 no of women who tried appetizer = 30 so remaining ppl ( men ) who tried the appetizer = 130 - 30 = 100 correct option e"
Answer: e
Question (physics): danny and steve are running towards each other , each one from his own house . danny can reach steve ' s house in 25 minutes of running , which is half the time it takes steve to reach danny ' s house . if the two started to run at the same time , how much time longer will it take steve to reach the halfway point between their houses than danny to reach the halfway point between their houses ?
Options: a ) 12.5 minutes . , b ) 25 minutes , c ) 35 minutes . , d ) 35 minutes , e ) 75 minutes
Rationale: "if the distance between the two houses is d . then speed of danny = ( d / 25 ) speed of steve = ( d / 50 ) [ steve takes 50 minutes to reach danny ' s house . double the time taken by danny ) obviously speed of danny is twice that of steve . now in order to cover distance ( d / 2 ) [ they meet in middle ] , steve will take : ( d / 2 ) / ( d / 50 ) = 25 minutes . distance is same and danny ' s speed is twice of steve . thus he will take 12.5 minutes to cover this same distance . steve take 25 - 12.5 = 12.5 minutes longer . a is the answer ."
Answer: a
Question (general): we run a business that rents out canoes and kayaks . a canoe rental costs $ 15 per day , and a kayak rental costs $ 18 dollars per day . one day , our business rents out 3 canoes for every 2 kayaks and receives a total of $ 405 in revenue . how many more canoes than kayaks were rented out ?
Options: a ) 5 , b ) 6 , c ) 7 , d ) 8 , e ) 9
Rationale: "let x be the number of canoes . then 2 x / 3 is the number of kayaks . 15 x + ( 2 x / 3 ) * 18 = 405 15 x + 12 x = 405 27 x = 405 x = 15 ( canoes ) 2 x / 3 = 10 ( kayaks ) there were 15 - 10 = 5 more canoes rented out . the answer is a ."
Answer: a
Question (general): how many positive integers between 1 and 200 are there such that they are multiples of 17 ?
Options: a ) 9 , b ) 11 , c ) 13 , d ) 10 , e ) 8
Rationale: "multiples of 17 = 17 , 34,51 , - - - - - 187 number of multiples of 17 = > 17 * 11 = 187 answer is b"
Answer: b
Question (general): in a company the manager wants to give some gifts to all of the workers . in each block there are about 100 workers are there . the total amount for giving the gifts for all the workers is $ 4000 . the worth of the gift is $ 4 . how many blocks are there in the company ?
Options: a ) 12 , b ) 10 , c ) 15 , d ) 17 , e ) 20
Rationale: each employee will get a gift worth of = $ 4 total employees = 4000 / 4 = 1000 total blocks = 1000 / 100 = 10 correct option is b
Answer: b
Question (physics): in what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way ?
Options: a ) 2 , b ) 7 , c ) 8 , d ) 6 , e ) 9
Rationale: "t = 60 / 36 * 18 / 5 = 6 sec answer : d"
Answer: d
Question (physics): three pipes a , b and c can fill a tank from empty to full in 30 minutes , 20 minutes and 10 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution p in the liquid in the tank after 3 minutes ?
Options: a ) 3 / 11 , b ) 2 / 11 , c ) 1 / 11 , d ) 4 / 11 , e ) 1 / 11
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 30 + 1 / 20 + 1 / 10 ) = 11 / 20 part filled by a in 3 minutes = 3 / 30 required ratio = 3 / 30 * 20 / 11 = 2 / 11 answer : b"
Answer: b