Cheukting/mathqa huggingface dataset:
Question (general): a sum of rs . 427 is to be divided among a , b and c in such a way that 3 times a ’ s share , 4 times b ’ s share and 7 times c ’ s share are all equal . the share of c is
Options: a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86
Rationale: "a + b + c = 427 3 a = 4 b = 7 c = > ( 7 c / 3 ) + ( 7 c / 4 ) + c = 427 = > c = 84 answer : c"
Answer: c
Question (general): find the average of first 4 multiples of 12 ?
Options: a ) 10 , b ) 12.6 , c ) 22.5 , d ) 30 , e ) 40.8
Rationale: "average = ( 12 + 24 + 36 + 48 ) / 4 = 30 answer is d"
Answer: d
Question (geometry): there is a rectangular prism made of 1 in cubes that has been covered in tin foil . there are exactly 128 cubes that are not touching any tin foil on any of their sides . if the width of the figure created by these 128 cubes is twice the length and twice the height , what is the p measure in inches of the width of the foil covered prism ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 10
Rationale: "if the width is w , then length and height would be w / 2 . so , w * w / 2 * w / 2 = 128 = > w ^ 3 = ( 2 ^ 3 ) * 64 = ( 2 ^ 3 ) * ( 4 ^ 3 ) = > w = 2 * 4 = 8 in . along the width of the cuboid , 8 cubes do n ' t touch the tin foil . so the actual width will be non - touching cubes + touching cubes = 8 + 2 = p = 10 ans e ."
Answer: e
Question (general): if 15 students in a class average 80 % on an english exam and 10 students average 90 % on the same exam , what is the average in percent for all 25 students ?
Options: a ) 83 % , b ) 83 1 ⁄ 2 % , c ) 84 % , d ) 85 % , e ) 86 2 ⁄ 3 %
Rationale: the average percentage = ( 15 x 80 % + 10 x 90 % ) / 25 = ( 15 x 80 % + 10 x 80 % + 10 x 10 % ) / 25 . . . . . . ( as 90 % = 10 % + 80 % ) = ( 25 x 80 % + 10 x 10 % ) / 25 = 80 % + 10 x 10 % / 25 = 80 % + 4 % = 84 % answer : c
Answer: c
Question (physics): a man sitting in a train which is traveling at 50 kmph observes that a goods train , traveling in opposite direction , takes 9 seconds to pass him . if the goods train is 280 m long , find its speed
Options: a ) 52 kmph , b ) 56 kmph , c ) 58 kmph , d ) 62 kmph , e ) 72 kmph
Rationale: "explanation : relative speed = 280 / 9 m / sec = ( ( 280 / 9 ) × ( 18 / 5 ) ) kmph = 112 kmph . speed of goods train = ( 112 - 50 ) kmph = 62 kmph answer : option d"
Answer: d
Question (other): how many positive factors do 160 and 96 have in common ?
Options: a ) 6 , b ) 12 , c ) 16 , d ) 18 , e ) 24
Rationale: "the number of common factors will be same as number of factors of the highest common factor ( hcf ) hcf of 160 and 96 is 32 number of factors of 32 = 6 answer : a"
Answer: a
Question (general): how many odd prime numbers are there less than 50 ?
Options: a ) 15 , b ) 1 , c ) 2 , d ) 14 , e ) 17
Rationale: "odd prime number less than 50 : 3 , 5 , 7 , 11 , 13 , 17 , 19 , 23 , 29 , 31 , 37 , 41 , 43 , 47 there is 14 the odd prime number answer is d"
Answer: d
Question (gain): at a local appliance manufacturing facility , the workers received a 15 % hourly pay raise due to extraordinary performance . if one worker decided to reduce the number of hours that he worked so that his overall pay would remain unchanged , by approximately what percent would he reduce the number of hours that he worked ?
Options: a ) 13 % , b ) 80 % , c ) 20 % , d ) 17 % , e ) 12 %
Rationale: "let ' s say he works usually 10 hours and earns 100 per hour . 10 * 100 = 1000 10 * 115 = 1150 ( this are the new earnings after the raise ) to figure out how much he needs to work with the new salary in order to earn the original 1000 : 1000 / 115 = 8.7 so he can reduce his work by 1.3 hours . which is > 13 % . answer a"
Answer: a
Question (gain): if the simple interest on $ 2000 increase by $ 40 , when the time increase by 4 years . find the rate percent per annum .
Options: a ) 1.2 % , b ) 0.5 % , c ) 0.7 % , d ) 0.9 % , e ) 0.3 %
Rationale: "applying the above formula , we have 40 = 2000 * r * 4 / 100 r = 40 * 100 / 2000 * 4 = 0.5 % . answer is b"
Answer: b
Question (general): in a room filled with 7 people , 4 people have exactly 1 sibling in the room and 3 people have exactly 2 siblings in the room . if two individuals are selected from the room at random , what is the probability that those two individuals are not siblings ?
Options: a ) 5 / 21 , b ) 3 / 7 , c ) 4 / 7 , d ) 5 / 7 , e ) 16 / 21
Rationale: "# of selections of 2 out of 7 - c 27 = 21 c 72 = 21 ; # of selections of 2 people which are not siblings - c 12 ∗ c 12 c 21 ∗ c 21 ( one from first pair of siblings * one from second pair of siblings ) + c 12 ∗ c 13 c 21 ∗ c 31 ( one from first pair of siblings * one from triple ) + c 1 ^ _ 2 * c ^ 1 _ 3 ( one from second pair of siblings * one from triple ) = 4 + 6 + 6 = 16 = 4 + 6 + 6 = 16 . p = 16 / 21 answer : e"
Answer: e
Question (physics): working at their respective constant rates , machine a makes 100 copies in 12 minutes and machine b makes 150 copies in 15 minutes . if these machines work simultaneously at their respective rates for 30 minutes , what is the total number of copies that they will produce ?
Options: a ) 250 , b ) 425 , c ) 550 , d ) 700 , e ) 750
Rationale: machine a can produce 100 * 30 / 12 = 250 copies and , machine b can produce 150 * 30 / 15 = 300 copies total producing 550 copies . c is the answer
Answer: c
Question (general): which number can we add to 897326 to get a number exactly divisible by 456 ?
Options: a ) 58 , b ) 66 , c ) 74 , d ) 82 , e ) 90
Rationale: 897326 / 456 = 1967 with a remainder of 374 . we need to add 456 - 374 = 82 the answer is d .
Answer: d
Question (probability): when two dice are rolled , what is the probability that the sum is either 7 or 11 ?
Options: a ) 1 / 4 , b ) 1 / 9 , c ) 4 / 3 , d ) 3 / 9 , e ) 2 / 9
Rationale: total number of outcomes possible = 36 probability of getting sum of 7 = 6 / 36 probability of getting sum of 11 = 2 / 36 probability that the sum is either 7 or 11 = 6 / 36 + 2 / 36 = 2 / 9 answer : e
Answer: e
Question (physics): the radius of a wheel is 24.2 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 708 m , b ) 704 m , c ) 774 m , d ) 760.57 m , e ) 744 m
Rationale: "in one resolution , the distance covered by the wheel is its own circumference . distance covered in 500 resolutions . = 500 * 2 * 22 / 7 * 24.2 = 76057 cm = 760.57 m answer : d"
Answer: d
Question (general): after spending rs . 5000 on rent , rs . 1500 on milk , rs . 4500 on groceries , rs . 2500 on childrens education rs . 2000 on petrol and rs . 3940 on miscellaneous expenses , mr . kishore saved 10 % of his monthly salary . how much did he save in rs . ?
Options: a ) 2160 , b ) 2350 , c ) 2000 , d ) 2300 , e ) none of these
Rationale: "explanation : total exp = 5000 + 1500 + 4500 + 2500 + 2000 + 3940 = 19440 exp in % = 100 - 10 = 90 % , 19440 = 90 % saving = 10 % = 19440 x 10 / 90 = rs . 2160 answer : a"
Answer: a
Question (general): the standard deviation of a normal distribution of data is 2 , and 3 standard deviations below the mean is greater than 44 . what is a possible value for the mean of the distribution ?
Options: a ) 46 , b ) 47 , c ) 48 , d ) 49 , e ) 51
Rationale: "the standard deviation ( { sd } ) = 2 ; 3 standard deviations below the mean is greater than 44 : { mean } - 3 * { sd } > 44 ; { mean } - 6 > 44 ; { mean } > 50 . answer : e ."
Answer: e
Question (general): the set x = { 78 , 910 } . the set y = { 23 , 45 } . we will randomly choose one element x from set x and one element y from set y . what is the probability that x / y will be an integer ?
Options: a ) 7 / 16 , b ) 5 / 16 , c ) 3 / 16 , d ) 7 / 8 , e ) 5 / 8
Rationale: the total number of x and y pairs is 4 * 4 = 16 . there are five pairs such that x / y is an integer . the probability that x / y is an integer is 5 / 16 . the answer is b .
Answer: b
Question (general): what is the value of 4 ^ 5 + 4 ^ 8 ?
Options: a ) 4 ^ 12 , b ) 4 ^ 35 , c ) 17 ( 4 ^ 5 ) , d ) 8 ^ 12 , e ) 65 ( 4 ^ 5 )
Rationale: "4 ^ 5 + 4 ^ 8 = 4 ^ 5 ( 1 + 4 ^ 3 ) = 4 ^ 5 * 65 answer e"
Answer: e
Question (general): john bought a total of 12 mangoes and oranges . each mango costs 80 cents and each orange costs 50 cents . if the average price of the 12 mangoes and oranges that john originally purchased was 65 cents , then how many oranges needs to return to raise the average price of his purchase to 72 cents ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let number of mangoes be x , number of oranges be 12 - x 0.80 x + ( 12 - x ) 0.50 / 12 = 0.65 solving for x , we get x = 6 - - > mangoes 6 , oranges 6 now , number of oranges to be returned be y [ 0.80 * 6 + ( 6 - y ) * 0.50 ] / 12 - y = 0.72 solving for y , y = 4 ans : a"
Answer: a
Question (other): two vessels contains equal number of mixtures milk and water in the ratio 4 : 2 and 5 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 3 : 1 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 15 : 4
Rationale: "the ratio of milk and water in the new vessel is = ( 4 / 6 + 5 / 6 ) : ( 2 / 6 + 1 / 6 ) = 9 / 6 : 3 / 6 = 3 : 1 answer is a"
Answer: a
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the even integers between 99 and 201 ?
Options: a ) 7650 , b ) 9250 , c ) 12,650 , d ) 14,250 , e ) 15,150
Rationale: "100 + 102 + . . . + 200 = 100 * 51 + ( 2 + 4 + . . . + 100 ) = 100 * 51 + 2 * ( 1 + 2 + . . . + 50 ) = 100 * 51 + 2 ( 50 ) ( 51 ) / 2 = 100 * 51 + 50 * 51 = 150 ( 51 ) = 7650 the answer is a ."
Answer: a
Question (physics): in what time will a train 90 m long cross an electric pole , it its speed be 72 km / hr ?
Options: a ) 1.5 , b ) 2.5 , c ) 3.5 , d ) 4.5 , e ) 5.5
Rationale: "speed = 72 * 5 / 18 = 20 m / sec time taken = 90 / 20 = 4.5 sec . answer : d"
Answer: d
Question (physics): a can give b 200 meters start and c 400 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 250 , c ) 111.64 , d ) 111.11 , e ) 101.12
Rationale: "a runs 1000 m while b runs 800 m and c runs 600 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 600 ) / 800 = 750 m . b can give c = 1000 - 750 = 250 m . answer : b"
Answer: b
Question (gain): a reduction of 40 % in the price of bananas would enable a man to obtain 65 more for rs . 40 , what is reduced price per dozen ?
Options: a ) 1.95 , b ) 2.95 , c ) 4.95 , d ) 3.95 , e ) 5.95
Rationale: "40 * ( 40 / 100 ) = 16 - - - 65 ? - - - 12 = > rs . 2.95 answer : b"
Answer: b
Question (gain): a shop owner professes to sell his articles at certain cost price but he uses false weights with which he cheats by 20 % while buying and by 10 % while selling . what is his percentage profit ?
Options: a ) 10.22 % , b ) 20.22 % , c ) 21.22 % , d ) 20 % , e ) ca n ' t be calculated
Rationale: "the owner buys 100 kg but actually gets 120 kg ; the owner sells 100 kg but actually gives 90 kg ; profit : ( 120 - 90 ) / 90 * 100 = 20 % answer : d ."
Answer: d
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 50 units . if today ' s production of 115 units raises the average to 55 units per day , what is the value of n ?
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: the daily production was raised by 5 units for n days , which has a weighting of 5 n . 5 n = 115 - 55 = 60 n = 12 the answer is c .
Answer: c
Question (physics): the h . c . f . of two numbers is 11 and their l . c . m . is 7700 . if one of the numbers is 275 , then the other is :
Options: a ) 279 , b ) 283 , c ) 308 , d ) 318 , e ) 338
Rationale: other number = ( 11 x 7700 ) / 275 = 308 . answer : c
Answer: c
Question (physics): excluding stoppages , the speed of a bus is 54 kmph and including stoppages , it is 41 kmph . for how many minutes does the bus stop per hour ?
Options: a ) 7 min , b ) 8 min , c ) 14.4 min , d ) 10 min , e ) 11 min
Rationale: due to stoppages , it covers 13 km less . time taken to cover 13 km = ( 13 / 54 ) x 60 = 14.4 min answer : c
Answer: c
Question (physics): a train length 100 m going with speed 10 m / sec another train 150 m long going with speed 15 m / sec . the distance between two train is 50 m . then how much time second train will take to cross the first train ?
Options: a ) 60 sec , b ) 40 sec , c ) 30 sec , d ) 45 sec , e ) 1 min 10 sec
Rationale: net speed = 15 - 10 = 5 m / sec net distance = 100 + 150 + 50 = 300 total time = 300 / 5 = 60 sec answer a
Answer: a
Question (physics): one copy machine can make 15 copies a minute , and a second copy machine makes 10 copies a minute . if the two copiers work together , how long would it take them to make 1,000 copies ?
Options: a ) 20 minutes , b ) 30 minutes , c ) 40 minutes , d ) 50 minutes , e ) 60 minutes
Rationale: total work done by both machines in a minute = 15 + 10 = 25 copies total number of copies required = 1000 time = 1000 / 25 = 40 mins answer c
Answer: c
Question (physics): a and b start walking towards each other at 6 pm at speed of 6 kmph and 4 kmph . they were initially 50 km apart . at what time do they meet ?
Options: a ) 8 pm , b ) 6 pm , c ) 11 pm , d ) 10 pm , e ) 5 pm
Rationale: "time of meeting = distance / relative speed = 50 / 4 + 6 = 50 / 10 = 5 hrs after 6 pm = 11 pm answer is c"
Answer: c
Question (general): what is the units digit of 33 ^ 2 * 17 ^ 3 * 49 ^ 3 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "the units digit of 33 ^ 2 is the units digit of 3 * 3 = 9 which is 9 . the units digit of 17 ^ 3 is the units digit of 7 * 7 * 7 = 343 which is 3 . the units digit of 49 ^ 3 is the units digit of 9 * 9 * 9 = 729 which is 9 . the units digit of 9 * 3 * 9 = 243 is 3 . the answer is b ."
Answer: b
Question (gain): solution y is 30 percent liquid x and 70 percent water . if 2 kilograms of water evaporate from 10 kilograms of solution y and 2 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 34 , b ) 35 , c ) 36 , d ) 37 1 / 25 , e ) 40
Rationale: "in 8 kilograms of solution y there are 0.3 * 10 = 3 kilograms of solution x ; after 2 kilograms of water are replaced by 2 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 2 = 0.6 kilograms of solution x are added , so in the new solution of 8 kilograms there are 3 + 0.6 = 3.6 kilograms of solution x , which is 3.6 / 10 * 100 = 36 % of this new solution . answer : c ."
Answer: c
Question (physics): water is poured into a tank so that the tank is being filled at the rate of 4 cubic feet per hour . if the empty rectangular tank is 6 feet long , 4 feet wide , and 3 feet deep , approximately how many hours does it take to fill the tank ?
Options: a ) 16 , b ) 18 , c ) 20 , d ) 22 , e ) 24
Rationale: "the volume the tank is : length * width * depth = 6 * 4 * 3 = 72 cubic feet . 72 cubic feet / 4 cubic feet per hour = 18 hours . it will take 18 hours to fill the tank . the answer is b ."
Answer: b
Question (gain): two pipes a and b can separately fill a cistern in 60 min and 75 min respectively . there is a third pipe in the bottom of the cistern to empty it . if all the 3 pipes are simultaneously opened , then the cistern is full in 50 min . in how much time , the third pipe alone can empty the cistern ?
Options: a ) 197 min , b ) 100 min , c ) 177 min , d ) 176 min , e ) 186 min
Rationale: work done by the third pipe in 1 min = 1 / 50 - ( 1 / 60 + 1 / 75 ) = - 1 / 100 . [ - ve sign means emptying ] the third pipe alone can empty the cistern in 100 min . answer : b
Answer: b
Question (physics): a and b undertake to do a piece of work for rs . 1200 . a alone can do it in 6 days while b alone can do it in 8 days . with the help of c , they finish it in 3 days . find the share of b .
Options: a ) 250 , b ) 450 , c ) 750 , d ) 800 , e ) none of them
Rationale: "c ' s 1 day ' s work = 1 / 3 - ( 1 / 6 + 1 / 8 ) = 24 a : b : c = ratio of their 1 day ' s work = 1 / 6 : 1 / 8 : 1 / 24 = 4 : 3 : 1 . a ’ s share = rs . ( 1200 * 4 / 8 ) = rs . 600 , b ' s share = rs . ( 1200 * 3 / 8 ) = rs . 450 c ' s share = rs . [ 1200 - ( 300 + 225 » ) = rs . 150 . answer is b"
Answer: b
Question (physics): a trader sells 92 meters of cloth for rs . 9890 at the profit of rs . 24 per metre of cloth . what is the cost price of one metre of cloth ?
Options: a ) 22 , b ) 89.5 , c ) 76.9 , d ) 83.5 , e ) 11
Rationale: "sp of 1 m of cloth = 9890 / 92 = rs . 107.5 cp of 1 m of cloth = sp of 1 m of cloth - profit on 1 m of cloth = rs . 107.5 - rs . 24 = rs . 83.5 answer : d"
Answer: d
Question (general): what is the least value of x . so that 21 x 57 is divisible by 3 .
Options: a ) 2 , b ) 0 , c ) 1 , d ) 3 , e ) 4
Rationale: "explanation : the sum of the digits of the number is divisible by 3 , then the number is divisible by 3 . 2 + 1 + x + 5 + 7 = 15 + x least value of x may be 0 therefore 15 + 0 = 15 is divisible by 3 . answer : option b"
Answer: b
Question (other): the ratio of numbers is 3 : 4 and their h . c . f is 3 . their l . c . m is :
Options: a ) 12 , b ) 16 , c ) 36 , d ) 48 , e ) 98
Rationale: "let the numbers be 3 x and 4 x . then their h . c . f = x . so , x = 3 . so , the numbers are 9 and 12 . l . c . m of 9 and 12 = 36 . answer : c"
Answer: c
Question (general): the average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg . what is the correct weight ?
Options: a ) 67.4 kg , b ) 57.75 kg , c ) 58.85 kg , d ) 49.4 kg , e ) none of these
Rationale: "actual total weight is ( 20 ã — 58.4 - 56 + 65 ) = 1177 kgs actual average weight is 1177 / 20 = 58.85 kgs answer is c"
Answer: c
Question (gain): the sale price sarees listed for rs . 400 after successive discount is 30 % and 20 % is ?
Options: a ) 297 , b ) 879 , c ) 342 , d ) 762 , e ) 224
Rationale: "400 * ( 70 / 100 ) * ( 80 / 100 ) = 224 answer : e"
Answer: e
Question (physics): a runs 1 ¾ times as fast as b . if a gives b a start of 84 m , bow far must winning post be so that a and b might reach it at the same time ?
Options: a ) 196 m , b ) 194 m , c ) 186 m , d ) 296 m , e ) 106 m
Rationale: . ratio of the rates of a and b = 7 / 4 : 1 = 7 : 4 . so , in a race of 7 m , a gains 3 m over b . : . 3 m are gained by a in a race of 7 m . : . 84 m are gained by a in a race of ( 7 / 3 x 84 ) m = 196 m . : . winning post must be 196 m away from the starting point . answer is a .
Answer: a
Question (general): a box contains 13 apples , 12 of which are red . an apple is drawn from the box and its color is noted before it is eaten . this is done a total of n times , and the probability that a red apple is drawn each time is less than 0.5 . what is the smallest possible value of n ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "p ( choosing a red apple 7 times in a row ) = 12 / 13 * 11 / 12 * 10 / 11 * 9 / 10 * 8 / 9 * 7 / 8 * 6 / 7 = 6 / 13 < 0.5 the answer is e ."
Answer: e
Question (general): a soccer store typically sells replica jerseys at a discount of 30 percent to 50 percent off list price . during the annual summer sale , everything in the store is an additional 40 percent off the original list price . if a replica jersey ' s list price is $ 80 , approximately what percent of the list price is the lowest possible sale price ?
Options: a ) 20 , b ) 25 , c ) 30 , d ) 40 , e ) 50
Rationale: "let the list price be 2 x for min sale price , the first discount given should be 50 % , 2 x becomes x here now , during summer sale additional 20 % off is given ie sale price becomes 0.8 x it is given lise price is $ 80 = > 2 x = 80 = > x = 20 and 0.8 x = 32 so lowest sale price is 32 , which is 40 % of 80 hence , a is the answer"
Answer: a
Question (general): a = { 2 , 3 , 5 , 7 , 11 } b = { 2 , 4 , 6 , 19 } two integers will be randomly selected from sets a and b , one integer from set a and one from set b , and then multiplied together . how many different products can be obtained ?
Options: a ) 15 , b ) 16 , c ) 19 , d ) 24 , e ) 36
Rationale: step 1 : find out the number of products you get . 5 distinct numbers in set a and 4 distinct in set b so number of products = 5 * 4 = 20 step 2 : remove the products that appear more than once . notice that 5 , 7 , 11 and 13 are primes and none of their multiples are in either set . so ignore them . we just need to focus on 2 and 3 of set a and 2 , 4 and 6 of set b . 2 , 3 2 , 4 , 6 the only product repeated when you take a number from each set is 12 . ( 3 * 4 and 2 * 6 ) rest all are distinct . answer = 20 - 1 = 24 note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets . d
Answer: d
Question (general): if one - seventh of a number exceeds its eleventh part by 100 then the number is …
Options: a ) 770 , b ) 870 , c ) 1825 , d ) 1925 , e ) 925
Rationale: let no be : x 1 / 7 x - 1 / 11 x = 100 4 x / 77 = 100 x = 7700 / 4 = 1925 answer : d
Answer: d
Question (geometry): a regular 10 sided area is inscribed in a circle . if a and b are adjacent vertices of the pentagon and o is the center of the circle , what is the value of ∠ oab ?
Options: a ) 48 degrees
b ) 54 degrees
c ) 72 degrees
d ) 84 degrees
e ) 72 degrees
Rationale: its a regular 10 sided so divide the globe by 10 . = 360 / 10 = 36 36 would be the angle at o . angles at a and b are equivalent , so 36 + 2 x = 180 2 x = 144 x = 72 angles oab and oba will be 72 degrees each . e
Answer: e
Question (general): a rower whose speed is 6 km / hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 3 km / hr . what is the rower ' s average speed ( in km / hr ) for the total journey ?
Options: a ) 3.9 , b ) 4.2 , c ) 4.5 , d ) 4.8 , e ) 5.1
Rationale: "time upstream = d / 3 time downstream = d / 9 total time = d / 3 + d / 9 = 4 d / 9 average speed = 2 d / ( 4 d / 9 ) = 4.5 km / hr the answer is c ."
Answer: c
Question (general): list i : 3 , 4 , 8 , 19 list ii : x , 3 , 4 , 8 , 19
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: we start by calculating the median of the numbers of list i : 3 , 4 , 8 , 19 . we see that the numbers in the list are in order already and , since we have an even number of numbers , the median is the average of the two middle numbers . median = ( 4 + 8 ) / 2 median = 12 / 2 median = 6 the median of list i is 6 . looking at list ii : x , 3 , 4 , 8 , 19 , we see that we have an odd number of terms . thus , when the list is ordered from least to greatest the median must be the middle term . since the medians of the two lists must be equal , we know that the median of list ii must be 6 and therefore x is 6 . the answer is a .
Answer: a
Question (general): there are 4 more women than there are men on a local co - ed softball team . if there are a total of 20 players on the team , what is the ratio of men to women ?
Options: a ) 8 / 12 , b ) 6 / 16 , c ) 4 / 16 , d ) 6 / 10 , e ) 4 / 10
Rationale: "w = m + 4 w + m = 20 m + 4 + m = 20 2 m = 16 m = 8 w = 12 ratio : 8 : 12 ans : a"
Answer: a
Question (physics): it is currently 9 : 53 pm . what time was it in the morning exactly 149,061 minutes ago ?
Options: a ) 9 : 12 , b ) 9 : 18 , c ) 9 : 26 , d ) 9 : 32 , e ) 9 : 38
Rationale: divide by 60 to convert 149,061 minutes to hours : 149,061 / 60 = 2,484 r 21 . that is 2,484 hours and 21 minutes . all of the answers are in the 9 am hour before : 53 , thus we can assume 2,484 previous must be 9 : 53 am . 21 minutes before that is 9 : 32 am . d
Answer: d
Question (gain): a man can row his boat with the stream at 20 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 7 kmph , c ) 98 kmph , d ) 6 kmph , e ) 8 kmph
Rationale: "ds = 20 us = 4 s = ? s = ( 20 - 4 ) / 2 = 8 kmph answer : e"
Answer: e