Cheukting/mathqa huggingface dataset:
Question (physics): a train 360 m long runs with a speed of 45 km / hr . what time will it take to pass a platform of 150 m long ?
Options: a ) 38 sec , b ) 35 sec , c ) 44 sec , d ) 40.8 sec , e ) none of these
Rationale: "speed = 45 km / hr = 45 ã — ( 5 / 18 ) m / s = 150 / 12 = 50 / 4 = 25 / 2 m / s total distance = length of the train + length of the platform = 360 + 150 = 510 meter time taken to cross the platform = 510 / ( 25 / 2 ) = 510 ã — 2 / 25 = 40.8 seconds answer : d"
Answer: d
Question (general): the mean proportional between 4 and 16 is ?
Options: a ) 12 , b ) 13 , c ) 14 , d ) 15 , e ) 16
Rationale: "root of ( 4 * 16 ) = 2 * 4 = 16 answer : e"
Answer: e
Question (general): two brother x and y appeared for an exam . the probability of selection of x is 1 / 3 and that of b is 2 / 7 . find the probability that both of them are selected .
Options: a ) 2 / 69 , b ) 2 / 21 , c ) 2 / 23 , d ) 2 / 29 , e ) 2 / 10
Rationale: explanation : let a be the event that x is selected and b is the event that y is selected . p ( a ) = 1 / 3 , p ( b ) = 2 / 7 . let c be the event that both are selected . p ( c ) = p ( a ) ã — p ( b ) as a and b are independent events : = ( 1 / 3 ) ã — ( 2 / 7 ) = 2 / 21 answer : b ) 2 / 21
Answer: b
Question (gain): if a speaks the truth 60 % of the times , b speaks the truth 50 % of the times . what is the probability that at least one will tell the truth
Options: a ) 0.8 , b ) 0.9 , c ) 1.0 , d ) 1.2 , e ) 1.3
Rationale: "probability of a speaks truth p ( a ) = 6 / 10 ; false = 4 / 10 probability of b speaks truth p ( b ) = 5 / 10 ; false = 5 / 10 . for given qtn ans = 1 - ( neither of them tell truth ) . because a & b are independent events = 1 - [ ( 4 / 10 ) * ( 5 / 10 ) ] = 4 / 5 = 0.8 answer : a"
Answer: a
Question (general): meena wrote all the numbers from 1 to 29,999 inclusive . how many digits did she write in total ?
Options: a ) 118,889 , b ) 138,889 , c ) 159,889 , d ) 188,789 , e ) 188,989
Rationale: "1 - 9 = > 1 * 9 digits 10 - 99 = > 2 * 90 = 180 ( numbers between 10 - 99 is 90 where each has 2 digits ) 100 - 999 = > 3 * 900 = 2700 1000 - 9999 = > 4 * 9000 = 36,000 10000 - 29999 = > 5 * 20,000 = 100,000 the answer is 138,889 the answer is b ."
Answer: b
Question (probability): a box contains 22 electric bulbs , out of which 4 are defective . two bulbs are chosen at random from this box . the probability that at least one of these is defective is
Options: a ) 4 / 19 , b ) 7 / 19 , c ) 12 / 19 , d ) 21 / 99 , e ) 26 / 77
Rationale: "solution p ( none is defective ) = 18 c 2 / 22 c 2 = 51 / 77 p ( at least one is defective ) = ( 1 - 51 / 77 ) = 26 / 77 . answer e"
Answer: e
Question (general): the events a and b are independent , the probability that event a occurs is greater than 0 , and the probability that event a occurs is twice the probability that event b occurs . the probability that at least one of events a and b occurs is 8 times the probability that both events a and b occur . what is the probability that event a occurs ?
Options: a ) 1 / 12 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 3 , e ) 2 / 3
Rationale: "let us say probability of a occurring is a . let us say probability of b occurring is b . a = 2 b probability ( either a or b or both ) = 8 times probability ( a and b ) a * ( 1 - b ) + b * ( 1 - a ) + ab = 8 * ab substituting a = 2 b in the second equation : 2 b * ( 1 - b ) + b * ( 1 - 2 b ) + 2 b * b = 8 * 2 b * b 3 b - 2 b ^ 2 = 16 b ^ 2 3 b = 18 b ^ 2 b = 3 / 18 = 1 / 6 so , a = 2 b = 1 / 3 answer : d"
Answer: d
Question (general): if - 2 and - 3 are negative integers , then - 2 * - 3 + 2 is
Options: a ) - 5 , b ) 8 , c ) - 6 , d ) - 3 , e ) - 8
Rationale: answer : b
Answer: b
Question (physics): a can give b 50 meters start and c 100 meters start in a kilometer race . how much start can b give c in a kilometer race ?
Options: a ) 111.12 , b ) 111.67 , c ) 111.64 , d ) 52.63 , e ) 101.12
Rationale: "a runs 1000 m while b runs 950 m and c runs 900 m . the number of meters that c runs when b runs 1000 m , = ( 1000 * 900 ) / 950 = 947.37 m . b can give c = 1000 - 947.37 = 52.63 m . answer : d"
Answer: d
Question (physics): a train covers a distance of 100 km in 1 hour . if its speed is decreased by 10 km / hr , the time taken by the car to cover the same distance will be ?
Options: a ) 1 hr , b ) 1 hr 6 min , c ) 50 min , d ) 1 hr 30 min , e ) 1 hr 45 min
Rationale: "speed = 100 / 1 = 100 km / hr new speed = 100 - 10 = 90 km / hr time taken = 100 / 90 = 1 hr 6 min answer is b"
Answer: b
Question (general): if s = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x is between
Options: a ) 0 and 3 , b ) 3 and 6 , c ) 6 and 9 , d ) 9 and 12 , e ) 12 and 15
Rationale: my attempt : if s = x ^ 4 + y ^ 4 = 100 , then the greatest possible value of x would be when y is minimum . let y ^ 4 be 0 . now x ^ 4 = 100 . x should be definitely greater than 3 but less than 4 . the only option that fits this range is b hence answer is - - b ) 3 and 6 .
Answer: b
Question (general): a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by b are ?
Options: a ) 24 , b ) 18 , c ) 13 , d ) 17 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 6 / 25 * 100 = 24 answer : a"
Answer: a
Question (physics): a train 100 m long crosses a platform 125 m long in 1 sec ; find the speed of the train ?
Options: a ) 810 , b ) 700 , c ) 930 , d ) 100 , e ) 200
Rationale: "d = 100 + 125 = 225 t = 15 s = 225 / 1 * 18 / 5 = 810 kmph answer : a"
Answer: a
Question (general): if [ x ] is the greatest integer less than or equal to x , what is the value of [ - 2.6 ] + [ 1.4 ] + [ 2.7 ] ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 6 , e ) 7
Rationale: you are asked what the closest lesser integer value to [ x ] is . [ - 2.6 ] = - 3.0 [ 1.4 ] = 1.0 [ 2.7 ] = 2.0 therefore , answer is : - 3.0 + 1.0 + 2.0 = 0.0 option a .
Answer: a
Question (general): if i equals the sum of the even integers from 2 to 200 , inclusive , and k equals the sum of the even integers from 20 to 200 , inclusive , what is the value of i - k ?
Options: a ) 10 , b ) 99 , c ) 9 , d ) 88 , e ) 90
Rationale: "use following formulae for such problems : sum of evenly spaced integers = ( # of integers ) * ( mean of integers ) # of integers = [ ( last - first ) / 2 ] + 1 mean of integers = ( last + first ) / 2 in above problem : # of integers = [ ( 200 - 2 ) / 2 ] + 1 = 100 and [ ( 200 - 20 ) / 2 ] + 1 = 91 mean of integers = ( 200 + 2 ) / 2 = 101 and ( 200 + 20 ) / 2 = 110 sum of integers = ( 100 * 101 ) = 10100 and ( 91 * 110 ) = 10010 thus their difference i - k = 10100 - 10010 = 90 answer : e"
Answer: e
Question (gain): by selling 32 pencils for a rupee a man loses 60 % . how many for a rupee should he sell in order to gain 60 % ?
Options: a ) 10 , b ) 9 , c ) 8 , d ) 6 , e ) 4
Rationale: "40 % - - - 40 160 % - - - ? 40 / 160 * 40 = 10 answer : a"
Answer: a
Question (physics): how many seconds will a 800 meter long train moving with a speed of 63 km / hr take to cross a man walking with a speed of 3 km / hr in the direction of the train ?
Options: a ) 48 , b ) 52 , c ) 38 , d ) 42 , e ) 45
Rationale: "explanation : here distance d = 800 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = 800 x 18 / 60 x 5 = 48 sec . answer is a"
Answer: a
Question (general): if a - b = 8 and a ^ 2 + b ^ 2 = 164 , find the value of ab
Options: a ) 10 , b ) 12 , c ) 50 , d ) 18 , e ) 19
Rationale: 2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 164 - 64 = 100 = > ab = 50 answer : c
Answer: c
Question (gain): a sum fetched a total simple interest of rs . 929.20 at the rate of 8 p . c . p . a . in 5 years . what is the sum ?
Options: a ) 2323 , b ) 1223 , c ) 2563 , d ) 1853 , e ) 2353
Rationale: "explanation : si = rs . 929.20 p = ? t = 5 years r = 8 % p = 100 × si / rt = 100 × 929.20 / 8 × 5 = rs . 2323 answer : option a"
Answer: a
Question (gain): ? % of 360 = 151.2
Options: a ) 42 , b ) 36 , c ) 64 , d ) 72 , e ) none of these
Rationale: "? % of 360 = 151.2 or , ? = 151.2 × 100 / 360 = 42 answer a"
Answer: a
Question (physics): the radius of a wheel is 22.5 cm . what is the distance covered by the wheel in making 500 resolutions ?
Options: a ) 708 m , b ) 707.14 m , c ) 774 m , d ) 714 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 * 22.5 = 70714 cm = 707.14 m answer : b"
Answer: b
Question (physics): jane makes toy bears . when she works with an assistant , she makes 89 percent more bears per week and works 10 percent fewer hours each week . having an assistant increases jane ’ s output of toy bears per hour by what percent ?
Options: a ) 20 % , b ) 80 % , c ) 110 % , d ) 180 % , e ) 200 %
Rationale: "let ' s assume just jane 40 bears per 40 / hrs a week , so that is 1 bear / hr . with an assistant she makes 75.6 bears per 36 hours a week or 2.1 bears / hr ( [ 40 bears * 1.89 ] / [ 40 hrs * . 90 ] ) . [ ( 2.1 - 1 ) / 1 ] * 100 % = 110 % answer : c"
Answer: c
Question (physics): how many cubes of 10 cm edge can be put in a cubical box of 1 m edge ?
Options: a ) 1 , b ) 10 , c ) 100 , d ) 1000 , e ) none
Rationale: "sol . number of cubes = [ 100 * 100 * 100 / 10 * 10 * 10 ] = 1000 . answer d"
Answer: d
Question (physics): 12 men work 8 hours per day to complete the work in 10 days . to complete the same work in 8 days , working 15 hours a day , the number of men required ?
Options: a ) 8 days , b ) 9 days , c ) 11 days , d ) 13 days , e ) 15 days
Rationale: "that is , 1 work done = 12 × 8 × 10 then , 12 8 × 10 = ? × 15 × 8 ? ( i . e . no . of men required ) = 12 × 8 × 10 / 15 × 10 = 8 days . a )"
Answer: a
Question (gain): if a man lost 10 % by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44 % ?
Options: a ) 6.5 , b ) 7.5 , c ) 7 , d ) 8 , e ) 2
Rationale: 90 % - - - - 12 144 % - - - - ? 90 / 144 * 12 = 7.50 answer : b
Answer: b
Question (other): jo ' s collection contains us , indian and british stamps . if the ratio of us to indian stamps is 5 to 2 and the ratio of indian to british stamps is 5 to 1 , what is the ratio of us to british stamps ?
Options: a ) 10 : 5 , b ) 15 : 2 , c ) 20 : 2 , d ) 25 : 2 , e ) none of these
Rationale: "explanation : indian stamps are common to both ratios . multiply both ratios by factors such that the indian stamps are represented by the same number . us : indian = 5 : 2 , and indian : british = 5 : 1 . multiply the first by 5 , and the second by 2 . hence the two ratios can be combined and us : british = 25 : 2 now us : indian = 25 : 10 , and indian : british = 10 : 2 answer : d"
Answer: d
Question (physics): a canteen requires 13 dozen bananas per day . how many bananas will it require for 9 weeks ?
Options: a ) 728 , b ) 9828 , c ) 1404 , d ) 9882 , e ) none
Rationale: requirement of bananas for 1 day in the canteen = 13 dozens ∴ requirement of bananas for 9 weeks i . e . 63 days = 63 × 13 dozens = 63 × 13 × 12 = 9828 . answer d
Answer: d
Question (other): an amount of money is to be distributed among faruk , vasim and ranjith in the ratio 3 : 5 : 11 . if vasims share is rs . 1500 , what is the difference between faruk ' s and ranjith ' s shares ?
Options: a ) s 1200 , b ) s 1500 , c ) s 1600 , d ) s 1900 , e ) s 2400
Rationale: "explanation : let p = faruk , q = vasim , r = ranjith let p = 3 x , q = 5 x and r = 11 x . then , 5 x = 1500 ? x = 300 . p = 900 , q = 1500 and r = 3300 . hence , ( r - p ) = ( 3300 - 900 ) = 2400 answer : e"
Answer: e
Question (geometry): the perimeter of a rectangular yard is completely surrounded by a fence that measures 36 meters . what is the length of the yard if the area of the yard is 40 meters squared ?
Options: a ) 12 , b ) 10 , c ) 8 , d ) 14 , e ) 16
Rationale: "perimeter of rectangular yard = 2 ( l + b ) = 36 - - > l + b = 18 area = l * b = 40 b = 18 - l l ( 18 - l ) = 40 18 l - l ^ 2 = 40 l ^ 2 - 18 l + 40 = 0 upon simplifying we get l = 5 or 8 . only 8 is there in the answer choice . answer : c"
Answer: c
Question (other): a shipment of 230 smartphones contains 84 that are defective . if a customer buys two smartphones at random from the shipment , what is the approximate probability that both phones are defective ?
Options: a ) 1 / 250 , b ) 1 / 84 , c ) 1 / 11 , d ) 9 / 68 , e ) 1 / 3
Rationale: "probability of chosing one defective phone from a lot of 230 which ontains 84 defective phones is = ( 84 / 230 ) probability of chosing one defective phone from a lot of 229 ( we already picked one ) which ontains 83 ( we already picked one ) defective phones is = ( 83 / 229 ) combined probability of series of events = product of the probabilities = ( 84 / 230 ) * ( 83 / 229 ) 84 / 230 is close to ( 23 / 63 ) and ( 83 / 229 ) = ( 29 / 80 ) so answer is ( 23 / 63 ) * ( 29 / 80 ) = ( 9 / 68 ) so , answer will be d"
Answer: d
Question (general): a large box contains 20 small boxes and each small box contains 32 chocolate bars . how many chocolate bars are in the large box ?
Options: a ) a ) 220 , b ) b ) 490 , c ) c ) 380 , d ) d ) 450 , e ) e ) 640
Rationale: "the only thing you have to do is a simple multiply we have : 20 * 32 = 640 correct answer is : e ) 640"
Answer: e
Question (general): how many digits are in ( 8 × 10 ^ 12 ) ( 10 × 10 ^ 9 ) ?
Options: a ) 20 , b ) 23 , c ) 26 , d ) 27 , e ) 28
Rationale: "the question simplfies to ( 8 × 10 ^ 12 ) ( 10 ^ 10 ) = > 8 * 10 ^ 22 = > will contain 22 zeros + 1 digit 8 = > 23 ans b"
Answer: b
Question (physics): pipe a fills a swimming pool in 4 hours . pipe b empties the pool in 6 hours . if pipe a was opened at 6 : 00 am and pipe b at 7 : 00 am , at what time will the pool be full ?
Options: a ) 14 : 00 , b ) 15 : 00 , c ) 13 : 00 , d ) 16 : 00 , e ) 17 : 00
Rationale: "pipe a fills the pool in 4 hrs . 1 hour ' s work : 1 / 4 pipe b empties the pool in 6 hrs . 1 hour ' s work : 1 / 6 together if they work , 1 hour ' s work = 1 / 4 - 1 / 6 = 1 / 12 given : pipe a started at 6 : 00 a . m and pipe b at 7 : 00 a . m pool filled after 1 hour by pipe a : 1 / 4 or 3 / 12 after 7 : 00 a . m pool filled after 1 hour with both the pipes on : 1 / 12 pool filled after 9 hours with both pipes on : 9 / 12 pool filled in 1 hour + pool filled in 9 hours = 3 / 12 + 9 / 12 = 1 therefore , it takes 10 hrs to fill the pool as pipe a started at 6 : 00 a . m , pool is full at 16 : 00 hrs answer : d"
Answer: d
Question (general): in a mayoral election , candidate x received 1 / 2 more votes than candidate y , and candidate y received 2 / 5 fewer votes than z . if z received 25000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22500 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: z = 25 - - > y received 2 / 5 fewer votes than z - - > y = z - 2 / 5 * z = 15 ; x received 1 / 2 more votes than y - - > x = y + 1 / 2 * y = 22,5 . answer : b .
Answer: b
Question (physics): a train 800 m long can cross a pole in 10 sec and then find the speed of the train ?
Options: a ) 280 , b ) 282 , c ) 284 , d ) 286 , e ) 288
Rationale: "length = speed * time speed = l / t s = 800 / 10 s = 80 m / sec speed = 80 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 288 kmph answer : e"
Answer: e
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 two 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 ) 18 : 8
Rationale: water : soap = 3 : 2 soap : salt = 6 : 2 = > for 6 soap , salt = 2 = > for 2 soap , salt = ( 2 / 6 ) * 2 = 2 / 3 so , water : soap : salt = 3 : 2 : 2 / 3 = 18 : 12 : 4 after open container , water : soap : salt = 9 : 18 : 4 so , water : salt = 9 : 4 = 18 : 8 e
Answer: e
Question (other): irin , ingrid and nell bake chocolate chip cookies in the ratio of 9.18 : 5.17 : 2.05 . if altogether they baked a batch of 150 cookies , what percent of the cookies did nell bake ?
Options: a ) 0.125 % , b ) 1.25 % , c ) 12.6 % , d ) 125 % , e ) 0.152 %
Rationale: "9.18 x + 5.17 x + 2.05 x = 16.4 x = 150 cookies x = 150 / 16.4 = 9.1 ( approx ) so , nell baked 9.1 * 2.05 cookies or 19 cookies ( approx ) % share = 19 / 150 = 12.6 approx hence , answer is c ."
Answer: c
Question (general): if the average ( arithmetic mean ) of a and b is 45 and the average of b and c is 80 , what is the value of c − a ?
Options: a ) 25 , b ) 60 , c ) 90 , d ) 140 , e ) it can not be determined from the information given .
Rationale: "- ( a + b = 90 ) b + c = 160 c - a = 60 b . 60"
Answer: b
Question (probability): a string of 30 light bulbs is wired in such a way that if any individual light bulb fails , the entire string fails . if for each individual light bulb the probability of failing during time period t is 0.1 , what is the probability that the string of light bulbs will fail during the time period t ?
Options: a ) 0.1 , b ) ( 0.1 ) ^ 30 , c ) 1 - ( 0.1 ) ^ 30 , d ) ( 0.93 ) ^ 30 , e ) 1 - ( 0.90 ) ^ 30
Rationale: "the string of light bulbs will fail if at least one light bulb fails . so , let ' s find the probability of the opposite event and subtract that value from 1 . the opposite event is when none of the 30 light bulbs fails , since the probability of each light bulb not to fail is 1 - 0.1 = 0.90 the the probability that none of the 30 light bulbs fails is 0.90 ^ 30 . hence , the probability that at least one light bulb fails is 1 - 0.90 ^ 30 . answer : e . now , you should have spotted that your reasoning was not right because of one simple thing , consider the case when we have 100 light bulbs instead of 30 , then according to your logic the probability that the string of light bulbs will fail would be 100 * 0.1 = 10 , which is not possible since the probability of an event can not be more than 1 ( 100 % ) ."
Answer: e
Question (general): the “ length of integer x ” refers to the number of prime factors , not necessarily distinct , that x has . ( if x = 60 , the length of x would be 4 because 60 = 2 × 2 × 3 × 5 . ) what is the greatest possible length of integer z if z < 800 ?
Options: a ) 13 , b ) 10 , c ) 9 , d ) 7 , e ) 6
Rationale: "to maximize the length of z , we should minimize its prime base . the smallest prime is 2 and since 2 ^ 9 = 512 < 800 , then the greatest possible length of integer z is 9 . the answer is c ."
Answer: c
Question (gain): an association of mathematics teachers has 1,260 members . only 560 of these members cast votes in the election for president of the association . what percent of the total membership voted for the winning candidate if the winning candidate received 60 percent of the votes cast ?
Options: a ) 75 % , b ) 26.67 % , c ) 42 % , d ) 34 % , e ) 25 %
Rationale: "total number of members = 1260 number of members that cast votes = 560 since , winning candidate received 60 percent of the votes cast number of votes for winning candidate = ( 60 / 100 ) * 560 = 336 percent of total membership that voted for winning candidate = ( 336 / 1260 ) * 100 = 26.67 % answer b"
Answer: b
Question (physics): the circumference of the front wheel of a cart is 30 ft long and that of the back wheel is 32 ft long . what is the distance traveled by the cart , when the front wheel has done five more revolutions than the rear wheel ?
Options: a ) 20 ft , b ) 25 ft , c ) 750 ft , d ) 900 ft , e ) 2400 ft
Rationale: "point to note : both the wheels would have traveled the same distance . now consider , no . of revolutions made by back wheel as x , which implies that the number of revolutions made by the front wheel is ( x + 5 ) . equating the distance traveled by front wheel to back wheel : ( x + 5 ) * 30 = x * 32 . ( formula for calculating the distance traveled by each wheel is : # of revolutions * circumference . ) solving this eqn . gives x = 75 . sub x = 75 either in ( x + 5 ) * 30 or in x * 32 to get the distance , which is 2400 . so the correct choice is e ."
Answer: e
Question (general): for a certain art exhibit , a museum sold admission tickets to a group of 30 people every 5 minutes from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive . the price of a regular admission ticket was $ 10 and the price of a student ticket was $ 6 . if on one day 3 times as many regular admission tickets were sold as student tickets , what was the total revenue from ticket sales that day ?
Options: a ) $ 24960 , b ) $ 25920 , c ) $ 28080 , d ) $ 28500 , e ) $ 29160
Rationale: from 9 : 00 in the morning to 4 : 55 in the afternoon , inclusive there are 8 * 12 = 96 five - minute intervals , thus total of 96 * 30 tickets were sold . say x student and 3 x regular tickets were sold , then x + 3 x = 96 * 30 - - > x = 24 * 30 and 3 x = 3 * ( 24 * 30 ) = 24 * 90 . therefore , the total revenue from ticket sales that day was 24 * 30 * 6 + 24 * 90 * 10 = $ 25,920 . answer : b .
Answer: b
Question (physics): during a car trip , maria stopped to rest after she traveled 1 / 2 of the total distance to her destination . she stopped again after she traveled 1 / 4 of the distance remaining between her first stop and her destination , and then she drove the remaining 105 miles to her detination . what was the total distance , in miles from maria ' s starting point to her destination ?
Options: a ) 280 , b ) 320 , c ) 360 , d ) 420 , e ) 480
Rationale: "easy 280 is the answer . 3 / 4 ( x / 2 ) = 105 x = 105 * 8 / 3 = 280 . answer a"
Answer: a
Question (physics): a can do a job in 20 days and b can do it in 30 days . a and b working together will finish thrice the amount of work in - - - - - - - days ?
Options: a ) 22 days , b ) 22 days , c ) 36 days , d ) 72 days , e ) 24 days
Rationale: "1 / 20 + 1 / 30 = 5 / 60 = 1 / 12 12 / 1 = 12 * 3 = 36 days answer : c"
Answer: c
Question (physics): if 2 / 3 rd of the contents of a container evaporated on the 1 st day . and 1 / 4 th of the remaining evaporated on the second day . what part of the contents of the container is left at the end of the second day ?
Options: a ) 1 / 4 , b ) 1 / 12 , c ) 1 / 18 , d ) 1 / 6 , e ) 1 / 2
Rationale: after first day , 1 / 3 of the contents remain . after second day , ( 1 / 3 ) - ( 1 / 4 ( 2 / 3 ) ) = ( 1 / 3 ) - ( 1 / 6 ) = 1 / 6 of the contents remain answer : d
Answer: d
Question (general): the average of first 7 prime numbers is ?
Options: a ) 10.11 , b ) 11.11 , c ) 8.29 , d ) 13.11 , e ) 14.11
Rationale: "sum of 7 prime no . = 58 average = 58 / 7 = 8.29 answer : c"
Answer: c
Question (other): in a group of 28 junior high school students , 5 take french , 10 take spanish , and 4 take both languages . the students taking both french and spanish are not counted with the 7 taking french or the 10 taking spanish . how many students are not taking either french or spanish ?
Options: a ) 7 , b ) 13 , c ) 9 , d ) 12 , e ) 10
Rationale: b 13 add 1 + 10 + 4 to get 15 . then subtract 21 from the total students ⇒ 28 – 15 = 13 . answer is b
Answer: b
Question (general): if pintu is coded as 79523 in a certain code language , how would you code dumbo in the same language ?
Options: a ) 43426 , b ) 14236 , c ) 13436 , d ) 14263 , e ) 15263
Rationale: "1 2 3 4 5 6 7 8 9 a b c d e f g h i j k l m n o p q r s t u v w x y z sooo . . . dumbo is 43426 . . . answer : a"
Answer: a
Question (physics): a , b , c can complete a piece of work in 3,9 and 15 days respectively . working together , they will complete the same work in how many days ?
Options: a ) 45 / 23 , b ) 55 / 23 , c ) 61 / 57 , d ) 12 / 13 , e ) 22 / 23
Rationale: ( a + b + c ) ' s 1 day work = ( 1 / 3 ) + ( 1 / 9 ) + ( 1 / 115 ) = 23 / 45 a , b , c together will complete the work in 45 / 23 days answer is a
Answer: a