Cheukting/mathqa huggingface dataset:
Question (general): if a person walks at 12 km / hr instead of 10 km / hr , he would have walked 20 km more . the actual distance traveled by him is :
Options: a ) 50 km , b ) 100 km , c ) 60 km , d ) 70 km , e ) 80 km
Rationale: "let the actual distance travelled be x km . x / 10 = ( x + 20 ) / 12 12 x = 10 x + 200 2 x = 200 x = 100 km . answer : b"
Answer: b
Question (physics): cara leaves her home and walks toward don ' s house . two hours later , don leaves his home and walks toward cara ' s house . the distance between their homes is 45 kilometers , cara ' s walking speed is 6 km / h , and don ' s walking speed is 5 km / h . how many kilometers will cara walk before she meets don ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: cara walks 12 km in the first two hours so there are 33 km remaining . when don starts walking , they complete a total of 11 km per hour . they will meet three hours after don starts walking . since cara walks for 5 hours , she walks 30 km . the answer is e .
Answer: e
Question (probability): in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 3 / 4 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and curved
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 4 , d ) 3 / 4 , e ) 7 / 8
Rationale: good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 3 / 4 of the garden is green , so , since all the flowers must be either green or yellow , we know that 1 / 4 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( curved ) = 1 / 4 * 1 / 2 = 1 / 8 , or a .
Answer: a
Question (general): if n is a positive integer , what is the remainder when ( 7 ^ ( 3 n + 3 ) ) ( 6 ^ n ) is divided by 10 ?
Options: a ) 1 , b ) 2 , c ) 4 , d ) 6 , e ) 8
Rationale: "this one took me bout 3 1 / 2 min . just testin numbers and what not . first notice that n is positive . save time by noticing thati worked out one solution where n = 0 only to find that thats not an option : p . 1 - 7 stands for ^ 1 thru 7 1 : 7 * 1 = 7 2 : 7 * 7 = 9 3 : 7 * 9 = 3 4 : 7 * 3 = 1 5 : 7 * 1 = 7 6 : 7 * 7 = 9 7 : 7 * 9 = 3 pattern repeats every @ 5 . notice every ^ 4 or multiple of 4 is always going to be 1 . this is just for future notice for similar problems . so 7 ^ 4 n + 3 - - - > if n = 1 then its ( ( 7 ^ 7 ) * 6 ) ) / 10 which can say is going to be 3 * 8 - - > 18 / 10 - - > r = 8 now from here if id double check just to make sure . 7 ^ 4 ( 2 ) + 3 * 6 ^ 2 - - - > 7 ^ 11 * 36 or we can just say again 7 ^ 11 * 6 ( b / c we are only interested in the units digit ) . since ^ 12 is going to be 1 that means ^ 11 is going to be 3 ( as taken from our pattern ) so again 3 * 6 = 18 / 10 - - - > r = 6 . d or j in this problem ."
Answer: d
Question (general): 10 / 21 of 3 / 5 of a number is greater than 4 / 7 of 1 / 5 of the same number by 36 . what is half of that number ?
Options: a ) 105 , b ) 180 , c ) 210 , d ) 240 , e ) 315
Rationale: "let no . be x 10 / 21 * 3 / 5 * x - 4 / 7 * 1 / 5 * x = 8 by further solving 30 x / 105 - 4 x / 35 = 36 18 x / 105 = 36 x = 210 we have to find x / 2 = 210 / 2 = 105 answer : a"
Answer: a
Question (physics): the speed of a bus increases by 2 km after every one hour . if the distance travelling in the first one hour was 35 km . what was the total distance travelled in 12 hours ?
Options: a ) 233 , b ) 552 , c ) 376 , d ) 287 , e ) 166
Rationale: given that distance travelled in 1 st hour = 35 km and speed of the bus increases by 2 km after every one hour hence distance travelled in 2 nd hour = 37 km hence distance travelled in 3 rd hour = 39 km . . . total distance travelled = [ 35 + 37 + 39 + . . . ( 12 terms ) ] this is an arithmetic progression ( ap ) with first term , a = 35 , number of terms , n = 12 and common difference , d = 2 . the sequence a , ( a + d ) , ( a + 2 d ) , ( a + 3 d ) , ( a + 4 d ) , . . . is called an arithmetic progression ( ap ) where a is the first term and d is the common difference of the ap sum of the first n terms of an arithmetic progression ( ap ) , sn = n 2 [ 2 a + ( n − 1 ) d ] where n = number of terms hence , [ 35 + 37 + 39 + . . . ( 12 terms ) ] = s 12 = 122 [ 2 × 35 + ( 12 − 1 ) 2 ] = 6 [ 70 + 22 ] = 6 × 92 = 552 hence the total distance travelled = 552 km answer : b
Answer: b
Question (geometry): a tailor trims 11 feet from opposite edges of a square piece of cloth , and 7 feet from the other two edges . if 84 square feet of cloth remain , what was the length of a side of the original piece of cloth ?
Options: a ) 26 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: "let the original side of the square be x . ( x - 22 ) * ( x - 14 ) = 84 = 6 * 14 x = 28 the answer is c ."
Answer: c
Question (general): an order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth . what be the cost of a carpet whose length and breadth are 40 % more and 25 % more respectively than the first carpet . given that the ratio of carpet is rs . 45 per sq . m ?
Options: a ) rs . 4082.40 , b ) rs . 1024.21 , c ) rs . 2810.6 , d ) rs . 3214 , e ) none of these
Rationale: explanation : length of the first carpet = ( 1.44 ) ( 6 ) = 8.64 cm area of the second carpet = 8.64 ( 1 + 40 / 100 ) 6 ( 1 + 25 / 100 ) = 51.84 ( 1.4 ) ( 5 / 4 ) sq m = ( 12.96 ) ( 7 ) sq m cost of the second carpet = ( 45 ) ( 12.96 x 7 ) = 315 ( 13 - 0.04 ) = 4095 - 12.6 = rs . 4082.40 answer is a
Answer: a
Question (general): in a office work is distribute between p persons . if 1 / 7 members are absent then work increased for each person is ?
Options: a ) 13.67 % , b ) 14.67 % , c ) 15.67 % , d ) 16.67 % , e ) 17.67 %
Rationale: "let total % of work is 100 % total person = p 1 / 7 person are absent of total person . so absent person is 1 / 7 p ie p / 7 . left person is , p - p / 7 = 6 p / 7 . p person do the work 100 % 1 person do the work 100 * p % 6 p / 7 person do the work ( 100 * p * 7 ) / 6 p % = 116.67 % work increased for each person is = ( 116.67 - 100 ) % = 16.67 % answer : d"
Answer: d
Question (physics): a courtyard is 25 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm . the total number of bricks required is ?
Options: a ) 22877 , b ) 27778 , c ) 20000 , d ) 27999 , e ) 17799
Rationale: "number of bricks = courtyard area / 1 brick area = ( 2500 × 1600 / 20 × 10 ) = 20000 answer : c"
Answer: c
Question (gain): in a school of 700 boys , 44 % of muslims , 28 % hindus , 10 % sikhs and the remaining of other communities . how many belonged to the other communities ?
Options: a ) 173 , b ) 126 , c ) 153 , d ) 143 , e ) 133
Rationale: "44 + 28 + 10 = 82 % 100 – 82 = 18 % 700 * 18 / 100 = 126 answer : b"
Answer: b
Question (gain): a shop keeper marked 30 % above the cost price and offered 20 % discount then find it ' s net profit ?
Options: a ) 2 % , b ) 2.5 % , c ) 3.7 % , d ) 4.6 % , e ) 5 %
Rationale: "net profit = 30 - 20 + ( 30 * ( - 25 ) / 100 ) = 2.5 % answer is b"
Answer: b
Question (physics): the speed of a car is 100 km in the first hour and 80 km in the second hour . what is the average speed of the car ?
Options: a ) 12 , b ) 75 , c ) 88 , d ) 54 , e ) 90
Rationale: "s = ( 100 + 80 ) / 2 = 90 kmph answer : e"
Answer: e
Question (general): the average marks of 10 students in a class is 100 . but a student mark is wrongly noted as 60 instead of 10 then find the correct average marks ?
Options: a ) a ) 78 , b ) b ) 82 , c ) c ) 95 , d ) d ) 91 , e ) e ) 85
Rationale: "correct avg marks = 100 + ( 10 - 60 ) / 10 avg = 100 - 5 = 95 answer is c"
Answer: c
Question (gain): there are 300 seniors at morse high school , and 50 % of them have cars . of the remaining grades ( freshmen , sophomores , and juniors ) , only 10 % of them have cars . if 20 % of all the students at morse have cars , how many students are in the 3 lower grades ?
Options: a ) 600 , b ) 900 , c ) 1200 , d ) 1350 , e ) 1500
Rationale: let x be the number of students in the lower three grades . 0.1 x + 150 = 0.2 ( x + 300 ) 0.1 x = 900 x = 900 the answer is b .
Answer: b
Question (general): carrie likes to buy t - shirts at the local clothing store . they cost $ 9.95 each . one day , she bought 20 t - shirts . how much money did she spend ?
Options: a ) $ 150 , b ) $ 248.75 , c ) $ 199 , d ) $ 171.6 , e ) $ 190
Rationale: $ 9.95 * 20 = $ 199 . answer is c .
Answer: c
Question (physics): a train passes a station platform in 36 sec and a man standing on the platform in 20 sec . if the speed of the train is 90 km / hr . what is the length of the platform ?
Options: a ) 229 , b ) 240 , c ) 400 , d ) 277 , e ) 221
Rationale: "speed = 90 * 5 / 18 = 25 m / sec . length of the train = 25 * 20 = 500 m . let the length of the platform be x m . then , ( x + 500 ) / 36 = 25 = > x = 400 m . answer : c"
Answer: c
Question (general): in a mixed college 160 students are there in one class . out of this 160 students 5 / 8 students are girls . how many boys are there ?
Options: a ) a ) 40 , b ) b ) 60 , c ) c ) 80 , d ) d ) 120 , e ) e ) 140
Rationale: "total number of students : 160 total girls : 160 * 5 / 8 = 100 total boys : 160 - 100 = 60 answer is b"
Answer: b
Question (general): a ferry can transport 85 tons of vehicles . automobiles range in weight from 1,800 to 3,200 pounds . what is the greatest number of automobiles that can be loaded onto the ferry ?
Options: a ) 23 , b ) 41 , c ) 48 , d ) 90 , e ) 86
Rationale: "to get maximum vehicles we must take into consideration the minimum weight i . e 1800 pounds here since , 1 ton = 2000 pounds 85 tons will be 170,000 pounds from the answer choices : let max number of vehicles be 86 total weight will be = 90 * 1800 = 162000 pounds , which is lesser than the maximum weight allowed . ans : d"
Answer: d
Question (general): if 10 gallons of grape juice are added to 50 gallons of a mixture , which contains 10 percent grape juice then what percent of the resulting mixture is grape juice ?
Options: a ) 14 % , b ) 25 % , c ) 28 % , d ) 34 % , e ) 50 %
Rationale: "official solution : if we start with 40 gallons of a mixture that is 10 % grape juice , then we have : 50 × 0.10 = 5 gallons of grape juice . 50 × 0.90 = 45 gallons of other components . if we add 10 gallons of grape juice , we will end up with 15 gallons of grape juice and 45 gallons of other components , and we will have a total of 60 gallons of the mixture . so 15 / 60 of the new mixture is grape juice . now we convert this to a percent : percent grape juice = 25 / 100 = 25 % . the correct answer is choice ( b )"
Answer: b
Question (general): an artist who needs to buy only paint and canvas finds that the cost of canvas has decreased by 40 percent and the cost of paint has decreased by 60 percent . if paint previously accounted for 4 times as much of the expense of painting as did canvas , by what percent did the total cost for paint and canvas decrease ?
Options: a ) 40 % , b ) 44 % , c ) 50 % , d ) 56 % , e ) 60 %
Rationale: paint : canvas cost is 4 : 1 . so , paint accounts for 80 % of cost and canvas accounts for 20 % . canvas , after decrease by 40 % will be ( 100 - 40 ) % of 20 % = > 60 % of 20 % = > 12 % of original paint , after decrease by 60 % will be ( 100 - 60 ) % of 80 % = > 40 % of 80 % = > 32 % of original new cost as a % of old cost = 32 + 12 = 44 % of original . so , overall cost saving = 100 - 44 = 56 % therefore , ( d )
Answer: d
Question (physics): a man can row upstream at 55 kmph and downstream at 65 kmph , and then find the speed of the man in still water ?
Options: a ) 27 , b ) 70 , c ) 60 , d ) 80 , e ) 24
Rationale: "us = 55 ds = 65 m = ( 55 + 65 ) / 2 = 60 answer : c"
Answer: c
Question (physics): a rectangular grassy plot 110 m . by 65 m has a gravel path 2.5 m wide all round it on the inside . find the cost of gravelling the path at 60 paise per sq . metre
Options: a ) s 510 , b ) s 780 , c ) s 880 , d ) s 480 , e ) s 980
Rationale: "area of the plot = 110 m * 65 m = 7150 sq . m area of plot excluding gravel = 105 m * 60 m = 6300 sq . m area of gravel = 7150 sq . m - 6300 sq . m = 850 sq . m cost of building it = 850 sq . m * 60 = 51000 p in rs = 51000 / 100 = rs 510 answer : a"
Answer: a
Question (physics): a train is 360 meter long is running at a speed of 45 km / hour . in what time will it pass a bridge of 140 meter length
Options: a ) 20 seconds , b ) 30 seconds , c ) 40 seconds , d ) 50 seconds , e ) none of these
Rationale: "explanation : speed = 45 km / hr = 45 * ( 5 / 18 ) m / sec = 25 / 2 m / sec total distance = 360 + 140 = 500 meter time = distance / speed = 500 ∗ 2 / 25 = 40 seconds option c"
Answer: c
Question (gain): in some quantity of ghee , 60 % is pure ghee and 40 % is vanaspati . if 10 kg of pure ghee is added , then the strength of vanaspati ghee becomes 20 % . the original quantity was :
Options: a ) 10 , b ) 27 , c ) 87 , d ) 23 , e ) 93
Rationale: "explanation : let the original quantity be x kg . vanaspati ghee in x kg = ( 40 x / 100 ) kg = ( 2 x / 5 ) kg . now , ( 2 x / 5 ) / ( x + 10 ) = 20 / 100 < = > 2 x / ( 5 x + 50 ) = 1 / 5 < = > 5 x = 50 < = > x = 10 . answer : a ) 10 kg"
Answer: a
Question (general): evaluate 926 + 9.026 + 0.926 + 9.0026
Options: a ) 944.9755 , b ) 944.9655 , c ) 944.9565 , d ) 946.9565 , e ) 944.9546
Rationale: "926 + 9.026 + 0.926 + 9.0026 = 944.9546 option e"
Answer: e
Question (general): what is the units digit of the expression 17 ^ 7 - 2 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 7 , e ) 9
Rationale: "7 ^ 1 = 7 7 ^ 2 = 49 7 ^ 3 = 343 7 ^ 4 = 1 ( last digit ) 7 ^ 5 = 7 ( last digit ) and the cycle repeats after every 4 powers therefore , last digit of 17 ^ 7 = 3 3 - 2 = 1 answer a"
Answer: a
Question (general): if v is the product of the integers from 1 to 30 , inclusive , what is the greatest integer k for which 3 ^ k is a factor of v ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: v = 30 ! 8 v = 30 x 29 x 28 x 27 x 26 x 25 x 24 x 24 x 22 x 21 x 20 x 19 x 18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 09 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 out of these 30 , 27 , 24 , 21 , 18 , 15 , 12 , 09 , 06 , 3 are factors of 3 3 x 10 , 3 x 3 x 3 , 3 x 8 , 3 x 3 x 2 , 3 x 5 , 3 x 4 , 3 x 3 x 3 , 3 x 2 , 3 so we have a total of 14 three ' s . . . therefore the maximum value of k can be 14 ( c )
Answer: c
Question (physics): find the side of the largest possible square slabs which can be paved on the floor of a room 2 m 50 cm long and 1 m 50 cm broad . also find the number of such slabs to pave the floor .
Options: a ) 25 , 20 , b ) 30 , 15 , c ) 50 , 15 , d ) none of these , e ) 75,35
Rationale: explanation : hcf ( 250 , 150 ) = 50 cm the number slabs = 250 * 150 / 50 * 50 = 15 answer : c
Answer: c
Question (physics): a train speeds past a pole in 25 seconds and a platform 200 m long in 30 seconds . its length is :
Options: a ) 1200 m , b ) 2000 m , c ) 1500 m , d ) 1000 m , e ) 4000 m
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 25 = > y = x / 25 x + 200 / 30 = x / 25 x = 1000 m . answer : option d"
Answer: d
Question (geometry): two cubes have their volumes in the ratio 1 : 27 . find the ratio of their surface areas .
Options: a ) 1 : 9
b ) 2 : 9
c ) 3 : 9
d ) 5 : 9
e ) none of them
Rationale: let their edges be a and b . then , = a ^ 3 / b ^ 3 = 1 / 27 ( or ) ( a / b ) ^ 3 = ( 1 / 3 ) 3 ( or ) ( a / b ) = ( 1 / 3 ) . therefore , ratio of their surface area = 6 a ^ 2 / 6 b ^ 2 = a ^ 2 / b ^ 2 = ( a / b ) ^ 2 = 1 / 9 , i . e . 1 : 9 . answer is a .
Answer: a
Question (gain): one fourth of a solution that was 14 % salt by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight . the second solution was what percent salt by weight ?
Options: a ) 24 % , b ) 34 % , c ) 22 % , d ) 18 % , e ) 8.5 %
Rationale: "consider total solution to be 100 liters and in this case you ' ll have : 75 * 0.14 + 25 * x = 100 * 0.16 - - > x = 0.22 . answer : c ."
Answer: c
Question (other): a certain fraction has the same ratio to 1 / 18 , as 2 / 5 does to 2 / 9 . what is this certain fraction ?
Options: a ) 1 / 5 , b ) 1 / 7 , c ) 1 / 10 , d ) 1 / 12 , e ) 1 / 15
Rationale: "x / ( 1 / 18 ) = ( 2 / 5 ) / ( 2 / 9 ) x = 2 * 9 * 1 / 18 * 5 * 2 = 1 / 10 the answer is c ."
Answer: c
Question (geometry): how many odd numbers between 10 and 2000 are the squares of integers ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the numbers are the squares of 5 , 7 , 9 , . . . , 43 which includes 20 numbers . the answer is e ."
Answer: e
Question (general): for a certain exam , a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean . what was the mean score e for the exam ?
Options: a ) 74 , b ) 76 , c ) 78 , d ) 80 , e ) 82
Rationale: "a score of 58 was 2 standard deviations below the mean - - > 58 = mean - 2 d a score of 98 was 3 standard deviations above the mean - - > 98 = mean + 3 d solving above for mean e = 74 . answer : a ."
Answer: a
Question (physics): walking at the rate of 3 kmph a man cover certain distance in 3 hr 20 min . running at a speed of 9 kmph the man will cover the same distance in .
Options: a ) 45 min , b ) 50 min , c ) 40 min , d ) 48 min , e ) 54 min
Rationale: "distance = speed * time 3 * 10 / 3 = 10 km new speed = 9 kmph therefore time = d / s = 10 / 9 = 54 min answer : e ."
Answer: e
Question (gain): what percent is 25 gm of 1 kg ?
Options: a ) 0.5 % , b ) 1 % , c ) 1.5 % , d ) 2.5 % , e ) 3 %
Rationale: "1 kg = 1000 gm 25 / 1000 × 100 = 2500 / 1000 = 5 / 2 = 2.5 % d )"
Answer: d
Question (physics): an airplane covers 50 miles in 1 / 5 hours . how many miles can the airplane cover in 5 hours ?
Options: a ) 800 , b ) 600 , c ) 1250 , d ) 950 , e ) 1000
Rationale: divide 5 by 1 / 5 = 5 ÷ 1 / 5 = 5 / 1 ÷ 1 / 5 = 5 / 1 * 5 / 1 = 25 . then , multiply 50 by 25 to get 1250 in 5 hours , the airplane will cover 1250 miles answer is c .
Answer: c
Question (general): evaluate 35 / . 07
Options: a ) 400 , b ) 500 , c ) 505 , d ) none of these , e ) 506
Rationale: "explanation : 35 / . 07 = 3500 / 7 = 500 option b"
Answer: b
Question (gain): a shopkeeper sold an article offering a discount of 5 % and earned a profit of 19.7 % . what would have been the percentage of profit earned if no discount was offered ?
Options: a ) 60 % , b ) 26 % , c ) 30 % , d ) 56 % , e ) 73 %
Rationale: "let c . p . be rs . 100 . then , s . p . = rs . 19.70 let marked price be rs . x . then , 95 / 100 x = 119.70 x = 11970 / 95 = rs . 126 now , s . p . = rs . 126 , c . p . = rs . 100 profit % = 26 % . answer : b"
Answer: b
Question (general): 0.003 x 0.2 = ?
Options: a ) 0.0006 , b ) 0.006 , c ) 0.06 , d ) 0.6 , e ) 6.0
Rationale: "3 x 2 = 6 . sum of decimal places = 4 0.003 x 0.2 = 0.0006 answer : option a"
Answer: a
Question (gain): a candidate who gets 30 % of the marks fails by 60 marks . but another candidate who gets 45 % marks gets 30 marks more than necessary for passing . find the number of marks for passing ?
Options: a ) 100 marks , b ) 240 marks , c ) 280 marks , d ) 371 marks , e ) 827 marks
Rationale: "30 % - - - - - - - - - - - - 60 45 % - - - - - - - - - - - - 30 - - - - - - - - - - - - - - - - - - - - - - 15 % - - - - - - - - - - - - - 90 30 % - - - - - - - - - - - - - - 180 180 + 60 = 240 marks answer : b"
Answer: b
Question (geometry): in may , the groundskeeper at spring lake golf club built a circular green with an area of 80 π square feet . in august , the groundskeeper doubled the distance from the center of the green to the edge of the green . what is the total area of the renovated green ?
Options: a ) 160 π , b ) 320 π , c ) 400 π , d ) 540 π , e ) 640 π
Rationale: "area = π r ^ 2 , so doubling the radius results in an area that is 4 times the original area . 4 ( 80 π ) = 320 π the answer is b ."
Answer: b
Question (geometry): 80 pie square inches of material of negligible thickness are required to construct a 1 / 16 scale model of a cylindrical barrel . if the diameter of the base of the barrel is 160 inches , then what is the volume of the barrel , to the nearest cubic foot ?
Options: a ) 2 pie
b ) 11 pie
c ) 178 pie
d ) 711 pie
e ) 1280 pie
Rationale: radius of barrel , r = 80 radius of model , r = 80 / 16 = 5 surface area of the model = 2 ∗ pi ∗ r ( r + h ) = 80 ∗ pi which gives h = 3 and h = 3 ∗ 16 = 48 so , volume of the barrel = pi ∗ r 2 ∗ h = pi ∗ ( 80 ) 2 ∗ ( 48 ) in cubic inches converting in cubic ft results : volume = pi ∗ ( 80 ) 2 ∗ ( 48 ) / ( 12 ) 3 = 178 pi cubic ft approximately answer [ c ]
Answer: c
Question (general): the average weight of 20 girls increases by 2 kg when a new girl comes in place of one of them weighing 40 kg . what might be the weight of the new girl ?
Options: a ) 85 kg , b ) 90 kg , c ) 80 kg , d ) 75 kg , e ) 70 kg
Rationale: "total weight increased = 20 x 2 kg = 40 kg . weight of new person = 40 + 40 kg = 80 kg answer : c"
Answer: c
Question (general): a ( 5 , w ^ 3 ) is the ( x , y ) coordinate of point located on the parabola y = x ^ 2 + 2 . what is the value of w ?
Options: a ) 3 . , b ) 4 . , c ) 5 . , d ) 6 . , e ) 9
Rationale: "y = x ^ 2 + 2 x = 5 y = 5 ^ 2 + 2 = 27 y is in the form w ^ 3 w ^ 3 = 27 w = 3 answer : a"
Answer: a
Question (other): in a graduating class of 232 students , 144 took geometry and 119 took biology . what is the difference between the greatest possible number t and the smallest possible number of students that could have taken both geometry and biology ?
Options: a ) 144 , b ) 119 , c ) 113 , d ) 88 , e ) 31
Rationale: "official solution : first of all , notice that since 144 took geometry and 119 took biology , then the number of students who took both geometry and biology can not be greater than 119 . { total } = { geometry } + { biology } - { both } + { neither } ; 232 = 144 + 119 - { both } + { neither } ; { both } = 31 + { neither } . { both } is minimized when { neither } is 0 . in this case { both } = 31 . the greatest possible number t of students that could have taken both geometry and biology , is 119 . thus , the answer is 119 - 31 = 88 . answer : d ."
Answer: d
Question (other): a certain fruit stand sold apples for $ 0.80 each and bananas for $ 0.70 each . if a customer purchased both apples and bananas from the stand for a total of $ 6.50 , what total number of apples and bananas did the customer purchase ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 12
Rationale: let ' s start with 1 apple for $ 0.80 . let ' s subtract $ 0.80 from $ 6.50 until we get a multiple of $ 0.70 . $ 6.50 , $ 5.70 , $ 4.90 = 7 * $ 0.70 the customer purchased 7 bananas and 2 apples . the answer is b .
Answer: b
Question (general): what is the thousandths digit in the decimal equivalent of 62 / 5000 ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 5 , e ) 6
Rationale: "62 / 5000 = 62 / ( 5 * 10 ^ 3 ) = ( 62 / 5 ) * 10 ^ - 3 = 12.4 * 10 ^ - 3 = . 0124 thousandths digit = 2 answer c"
Answer: c
Question (physics): in how many seconds will a train 180 meters long pass an oak tree , if the speed of the train is 36 km / hr ?
Options: a ) 14 , b ) 16 , c ) 18 , d ) 20 , e ) 22
Rationale: "speed = 36 * 5 / 18 = 10 m / s time = 180 / 10 = 18 seconds the answer is c ."
Answer: c
Question (general): what number should replace the question mark ? 10 , 30 , 14 , 25 , 18 , 20 , - - - ?
Options: a ) 19 , b ) 21 , c ) 25 , d ) 22 , e ) 20
Rationale: "answer : d 10 , 30 , 14 , 25 , 18 , 20 , 22 ? there are two alternate sequences : + 4 and - 5 ."
Answer: d
Question (physics): a train of length 250 m crosses a bridge of length 180 m in 20 seconds . what is the speed of train ?
Options: a ) 33 , b ) 77.4 , c ) 25 , d ) 22 , e ) 72
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 180 ) = 20 x speed speed = 430 / 20 = 21.5 m / s = 77.4 km / h answer = b"
Answer: b