Cheukting/mathqa huggingface dataset:
Question (general): a combustion reaction forms carbon dioxide . a carbon dioxide molecule contains one carbon and two oxygen atoms . if , over a period of 10 minutes , a combustion reaction creates 10,000 molecules of carbon dioxide then approximately how many more atoms of oxygen than carbon are created on average per minute ?
Options: a ) 1,000 , b ) 500 , c ) 250 , d ) 50 , e ) 0
Rationale: solution : 10,000 carbon dioxide molecules are created over a period of 10 minutes . therefore 10,000 / 10 = 1,000 carbon dioxide molecules are created on average per minute each carbon dioxide molecule contains one carbon atom and two oxygen atoms . so 1,000 carbon dioxide molecules contain 1 × 1,000 = 1,000 carbon atoms and 2 × 1,000 = 2,000 oxygen atoms . the difference is 2,000 – 1,000 = 1,000 . the correct answer is a .
Answer: a
Question (general): find the average of all the numbers between 6 and 34 which is divisible by 5
Options: a ) 15 , b ) 18 , c ) 13 , d ) 19 , e ) 20
Rationale: "avg = ( 10 + 15 + 20 + 25 + 30 ) / 5 = 100 / 5 = > 20 answer e"
Answer: e
Question (general): . 3 + 33 + 333 + 3.33 = ?
Options: a ) 369.63 , b ) 372.33 , c ) 702.33 , d ) 702 , e ) none of them
Rationale: . 3 33 333 3.33 - - - - - - - - - - 369.63 - - - - - - - - - - answer is a
Answer: a
Question (physics): an woman swims downstream 45 km and upstream 25 km taking 5 hours each time ; what is the speed of the current ?
Options: a ) 2 , b ) 1 , c ) 3 , d ) 4 , e ) 2.1
Rationale: "45 - - - 5 ds = 9 ? - - - - 1 25 - - - - 5 us = 5 ? - - - - 1 s = ? s = ( 9 - 5 ) / 2 = 2 answer : a"
Answer: a
Question (general): find a sum for first 6 prime number ' ss ?
Options: a ) 25 , b ) 28 , c ) 30 , d ) 35 , e ) 41
Rationale: required sum = ( 2 + 3 + 5 + 7 + 11 + 13 ) = 41 note : 1 is not a prime number option e
Answer: e
Question (physics): a computer factory produces 8400 computers per month at a constant rate , how many computers are built every 30 minutes assuming that there are 28 days in one month ?
Options: a ) 2.25 . , b ) 3.125 . , c ) 4.5 . , d ) 5.225 . , e ) 6.25 .
Rationale: "number of hours in 28 days = 28 * 24 number of 30 mins in 28 days = 28 * 24 * 2 number of computers built every 30 mins = 8400 / ( 28 * 24 * 2 ) = 6.25 answer e"
Answer: e
Question (general): what least number should be subtracted from 3,381 so that the remainder when divided by 9 , 11 , and 17 will leave in each case the same remainder 8 ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 12 , e ) 15
Rationale: "the lcm of 9 , 11 and 17 is 1,683 . the next multiple is 2 * 1,683 = 3,366 . 3,366 + { remainder } = 3,366 + 8 = 3,374 , which is 7 less than 3,381 . answer : b ."
Answer: b
Question (gain): a trader marked the selling price of an article at 40 % above the cost price . at the time of selling , he allows certain discount and suffers a loss of 1 % . he allowed a discount of :
Options: a ) 10 % , b ) 7.8 % , c ) 11 % , d ) 12.5 % , e ) none
Rationale: sol . let c . p . = rs . 100 . then , marked price = rs . 140 , s . p . = rs . 99 . ∴ discount % = [ 11 / 140 * 100 ] % = 7.8 % answer b
Answer: b
Question (general): diana is painting statues . she has 7 / 16 of a gallon of paint remaining . each statue requires 1 / 16 gallon of paint . how many statues can she paint ?
Options: a ) 7 , b ) 20 , c ) 28 , d ) 14 , e ) 19
Rationale: "number of statues = all the paint ÷ amount used per statue = 7 / 16 ÷ 1 / 16 = 7 / 16 * 16 / 1 = 7 / 1 = 7 answer is a ."
Answer: a
Question (gain): in an election a candidate who gets 60 % of the votes is elected by a majority of 1300 votes . what is the total number of votes polled ?
Options: a ) a ) 4500 , b ) b ) 5200 , c ) c ) 6900 , d ) d ) 7520 , e ) e ) 6500
Rationale: "let the total number of votes polled be x then , votes polled by other candidate = ( 100 - 60 ) % of x = 40 % of x 60 % of x - 40 % of x = 1300 20 x / 100 = 1300 x = 1300 * 100 / 20 = 6500 answer is e"
Answer: e
Question (gain): fresh grapes contain 60 % by weight while dried grapes contain 20 % water by weight . what is the weight of dry grapes available from 30 kg of fresh grapes ?
Options: a ) 10 kg , b ) 15 kg , c ) 20 kg , d ) 25 kg , e ) 40 kg
Rationale: "from the question we know : 30 kg * 60 % = 18 kg of water in the fresh grapes 30 kg - 18 kg of water = 12 kg of non - water mass we are looking for the weight of the dry grapes ( x ) . since the question tells us that 20 % of the weight of the dry graps is water and we know that 12 kg is non - water mass we can set up the following equation : x = 1 / 5 ( x ) + 12 kg 4 / 5 ( x ) = 12 kg x = 15 kg answer - b"
Answer: b
Question (physics): without stoppages , a train travels certain distance with an average speed of 80 km / h , and with stoppages , it covers the same distance with an average speed of 60 km / h . how many minutes per hour the train stops ?
Options: a ) 15 , b ) 18 , c ) 10 , d ) 16 , e ) none of these
Rationale: "due to stoppages , it covers 20 km less . time taken to cover 20 km = 20 ⁄ 80 h = 1 ⁄ 4 h = 1 ⁄ 4 × 60 min = 15 min answer a"
Answer: a
Question (general): if 5 / ( 4 + 1 / x ) = 1 , then x =
Options: a ) 3 , b ) 1 , c ) 1 / 3 , d ) - 1 / 3 , e ) - 3
Rationale: "the expression 5 / ( 4 + 1 / x ) = 1 should have been equal to something . if 5 / ( 4 + 1 / x ) = 1 = > 5 x / ( 4 x + 1 ) = 1 = > 5 x = 4 x + 1 = > x = 1 correct option : b"
Answer: b
Question (general): the average age of a class of 22 students is 21 years . the average increased by 1 when the teacher ' s age also included . what is the age of the teacher ?
Options: a ) 44 , b ) 48 , c ) 45 , d ) 43 , e ) 50
Rationale: "total age = 22 * 21 tot age of all stu + age of the teacher = 23 * 22 age of the teacher = 23 * 22 - 22 * 21 = 44 answer a"
Answer: a
Question (gain): by selling 88 pens , a trader gains the cost of 22 pens . find his gain percentage ?
Options: a ) 25 % , b ) 26 % , c ) 27 % , d ) 28 % , e ) 29 %
Rationale: let the cp of each pen be rs . 1 . cp of 88 pens = rs . 88 profit = cost of 22 pens = rs . 22 profit % = 22 / 88 * 100 = 25 % answer : a
Answer: a
Question (physics): the population of a bacteria colony doubles every day . if it was started 9 days ago with 2 bacteria and each bacteria lives for 13 days , how large is the colony today ?
Options: a ) 512 , b ) 1024 , c ) 768 , d ) 2048 , e ) 4096
Rationale: "9 days ago - 2 8 days ago - 4 7 days ago - 8 6 days ago - 16 5 days ago - 32 4 days ago - 64 3 days ago - 128 2 days ago - 256 yesterday - 512 today - 1024 ans : b"
Answer: b
Question (physics): due to construction , the speed limit along an 9 - mile section of highway is reduced from 55 miles per hour to 35 miles per hour . approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
Options: a ) 5 , b ) 7 , c ) 10 , d ) 15 , e ) 24
Rationale: "9 / 35 - 9 / 55 = 9 / 5 * ( 11 - 7 ) / 77 = 9 / 5 * 4 / 77 * 60 min = 9 * 12 * 4 / 77 = 432 / 77 ~ 5.6 answer - b"
Answer: b
Question (general): if k is a non - negative integer and 18 ^ k is a divisor of 624,938 then 6 ^ k - k ^ 6 =
Options: a ) 0 , b ) 1 , c ) 36 , d ) 118 , e ) 420
Rationale: "6 + 2 + 4 + 9 + 3 + 8 = 32 , so this number is not divisible by 3 and thus not divisible by 18 . therefore , k = 0 6 ^ k - k ^ 6 = 1 - 0 = 1 the answer is b ."
Answer: b
Question (general): in the first m games of a team ' s season , the ratio of the team ' s wins to its losses was 1 : 3 . in the subsequent n games , the ratio of the team ´ s wins to losses was 2 : 3 . if m : n = 4 : 5 , what was the ratio of the team ' s wins to its losses for all m + n games ?
Options: a ) 7 : 18 , b ) 3 : 7 , c ) 1 : 2 , d ) 2 : 5 , e ) 4 : 9
Rationale: m = 4 / 9 of total games n = 5 / 9 of total games wins = 1 / 4 * 4 / 9 + 2 / 5 * 5 / 9 = 1 / 9 + 2 / 9 = 1 / 3 losses = 1 - 1 / 3 = 2 / 3 the ratio of wins to losses is 1 : 2 . the answer is c .
Answer: c
Question (general): two trains start at same time from two stations and proceed towards each other at the rate of 20 km / hr and 25 km / hr respectively . when they meet , it is found that one train has traveled 55 km more than the other . what is the distance between the two stations ?
Options: a ) 540 km , b ) 495 km , c ) 276 km , d ) 178 km , e ) 176 km
Rationale: "explanation : let us assume that trains meet after ' x ' hours distance = speed * time distance traveled by two trains = 20 x km and 25 x km resp . as one train travels 55 km more than the other , 25 x â € “ 20 x = 55 5 x = 55 x = 11 hours as the two trains are moving towards each other , relative speed = 20 + 25 = 45 km / hr therefore , total distance = 45 * 11 = 495 km . answer : b"
Answer: b
Question (other): the compound ratio of 5 : 6 , 3 : 2 and 4 : 5 ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 2 , d ) 1 : 1 , e ) 1 : 7
Rationale: "5 / 6 * 3 / 2 * 4 / 5 = 1 / 1 1 : 1 answer : d"
Answer: d
Question (general): in a division sum , the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 17 to the thrice of the remainder . the dividend is
Options: a ) 74 , b ) 146 , c ) 86 , d ) 92 , e ) 98
Rationale: "divisor = ( 6 * 3 ) + 17 = 35 5 * quotient = 35 quotient = 7 . dividend = ( divisor * quotient ) + remainder dividend = ( 20 * 7 ) + 6 = 146 . b )"
Answer: b
Question (gain): if albert ’ s monthly earnings rise by 36 % , he would earn $ 495 . if , instead , his earnings rise by only 25 % , how much ( in $ ) would he earn this month ?
Options: a ) 643 , b ) 652 , c ) 454 , d ) 460 , e ) 490
Rationale: "= 495 / 1.36 ∗ 1.25 = 454 = 454 answer is c"
Answer: c
Question (general): lilly has 10 fish and rosy has 9 fish . in total , how many fish do they have in all ?
Options: a ) 16 , b ) 17 , c ) 18 , d ) 19 , e ) 20
Rationale: "10 + 9 = 19 the answer is d ."
Answer: d
Question (gain): after giving a discount of rs . 100 the shopkeeper still gets a profit of 30 % , if the cost price is rs . 1000 . find the markup % ?
Options: a ) . 50 , b ) . 45 , c ) . 40 , d ) . 48 , e ) . 52
Rationale: "cost price = 1000 s . p = 1000 * 130 / 100 = 1300 disc = 100 so . . . mark price = 1300 + 100 = 1400 . . . . . . mark up % = 1400 - 1000 / 1000 = 400 / 1000 = . 40 ( or ) 40 % answer : c"
Answer: c
Question (general): of the goose eggs laid at a certain pond , 1 / 3 hatched and 4 / 5 of the geese that hatched from those eggs survived the first month . of the geese that survived the first month , 3 / 5 did not survive the first year . if 120 geese survived the first year and if no more than one goose hatched from each egg , how many goose eggs were laid at the pond ?
Options: a ) 1025 , b ) 1075 , c ) 1125 , d ) 1175 , e ) 1225
Rationale: "let x be the number of eggs that were laid . ( 2 / 5 ) ( 4 / 5 ) ( 1 / 3 ) x = 120 ( 8 / 75 ) x = 120 x = 1125 the answer is c ."
Answer: c
Question (general): a certain car traveled twice as many miles from town a to town b as it did from town b to town c . from town a to town b , the car averaged 20 miles per gallon , and from town b to town c , the car averaged 24 miles per gallon . what is the average miles per gallon that the car achieved on its trip from town a through town b to town c ?
Options: a ) 40 , b ) 30 , c ) 42 , d ) 33 , e ) 35
Rationale: "step 1 ) took lcm of 20 and 24 . . came as 120 . step 2 ) 120 distance between b to c . . . do 120 / 24 hence 5 gallons used step 3 ) twice distance . . hence 120 * 2 = 240 . . . do as above . . 240 / 20 = 7 gallons used step 4 ) total gallons . . 5 + 7 = 12 gallons step ) total miles = 120 + 240 = 360 miles hence . . average of whole journey = 360 / 12 which comes to 30 answer : b"
Answer: b
Question (gain): a bowl of fruit contains 10 apples and 23 oranges . how many oranges must be removed so that 50 % of the pieces of fruit in the bowl will be apples ?
Options: a ) 3 , b ) 13 , c ) 14 , d ) 17 , e ) 20
Rationale: "number of apples = 10 number of oranges = 23 let number of oranges that must be removed so that 50 % of pieces of fruit in bowl will be apples = x total number of fruits after x oranges are removed = 10 + ( 23 - x ) = 33 - x 10 / ( 33 - x ) = 5 / 10 = > 20 = 33 - x = > x = 13 answer b"
Answer: b
Question (general): given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 5 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 11
Rationale: "p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p + 5 is 6 + 5 = 11 . answer : e ."
Answer: e
Question (general): if a / x = 1 / 3 and a / y = 1 / 4 , then ( x + y ) =
Options: a ) 2 a , b ) a / 2 , c ) 6 a , d ) 7 a , e ) 9 a
Rationale: ratio 1 : 3 a = x ratio 2 : 4 a = y x + y = 7 a answer is d
Answer: d
Question (general): for the past n days , the average ( arithmetic mean ) daily production at a company was 70 units . if today ' s production of 90 units raises the average to 75 units per day , what is the value of n ?
Options: a ) 30 , b ) 18 , c ) 10 , d ) 9 , e ) 3
Rationale: "( average production for n days ) * n = ( total production for n days ) - - > 70 n = ( total production for n days ) ; ( total production for n days ) + 90 = ( average production for n + 1 days ) * ( n + 1 ) - - > 70 n + 90 = 75 * ( n + 1 ) - - > n = 3 . answer : e ."
Answer: e
Question (physics): a is twice as good a work man as b and together they finish the work in 6 days . in how many days a alone can finish the work ?
Options: a ) 3 , b ) 9 , c ) 7 , d ) 2 , e ) 6
Rationale: "wc = 2 : 1 2 x + x = 1 / 6 = > x = 1 / 18 2 x = 1 / 9 a can do the work in 9 days . answer : b"
Answer: b
Question (physics): three cubes of metal whose edges are 9 , 12 and 21 cm respectively , are melted and one new cube is made . find the edge of the new cube ?
Options: a ) 28 , b ) 22.7 , c ) 66 , d ) 18 , e ) 99
Rationale: "93 + 123 + 213 = a 3 = > a = 22.7 answer : b"
Answer: b
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 five 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 ) 45 : 8
Rationale: "water : soap = 3 : 2 soap : salt = 15 : 2 = > for 15 soap , salt = 2 = > for 2 soap , salt = ( 2 / 15 ) * 2 = 4 / 15 so , water : soap : salt = 3 : 2 : 4 / 15 = 45 : 30 : 4 after open container , water : soap : salt = 22.5 : 30 : 4 so , water : salt = 22.5 : 4 = 45 : 8 e"
Answer: e
Question (general): if a @ b = a * b ^ ( 1 / 2 ) then 4 @ 9 = ? self made
Options: a ) 2 , b ) 12 , c ) 3 , d ) 8 , e ) 4
Rationale: 4 * ( 9 ) ^ 1 / 2 = 4 * 3 = 12 b is the answer
Answer: b
Question (gain): population of a city in 20004 was 1000000 . if in 2005 there isan increment of 25 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 979923 , c ) 980241 , d ) 1178125 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 25 / 100 ) ( 1 - 35 / 100 ) ( 1 + 45 / 100 ) = 1178125 d"
Answer: d
Question (gain): the difference between simple interest and compound interest of a certain sum of money at 20 % per annum for 2 years is $ 48 . then the sum is
Options: a ) $ 600 , b ) $ 1000 , c ) $ 1200 , d ) $ 1500 , e ) $ 2000
Rationale: "20 % of ( year 1 interest ) = 20 % of ( 20 % of principal ) = 48 principal = $ 1200 answer ( c )"
Answer: c
Question (general): the equal amounts of money are deposited in two banks each at 15 % per annum for 3.5 years and 5 years respectively . if the difference between their interests is rs . 144 , find the each sum ?
Options: a ) 640 , b ) 500 , c ) 3000 , d ) 1000 , e ) 2000
Rationale: ( p * 5 * 15 ) / 100 - ( p * 3.5 * 15 ) / 100 = 144 75 p / 100 â € “ 52.5 p / 100 = 144 22.5 p = 144 * 100 = > p = rs . 640 answer a
Answer: a
Question (other): the number of stamps that p and q had were in the ratio of 5 : 3 respectively . after p gave q 10 stamps , the ratio of the number of p ' s stamps to the number of q ' s stamps was 9 : 7 . as a result of the gift , p had how many more stamps than q ?
Options: a ) 20 , b ) 30 , c ) 40 , d ) 60 , e ) 90
Rationale: "p started with 5 k stamps and q started with 3 k stamps . ( 5 k - 10 ) / ( 3 k + 10 ) = 9 / 7 35 k - 27 k = 160 k = 20 p has 5 ( 20 ) - 10 = 90 stamps and q has 3 ( 20 ) + 10 = 70 stamps . the answer is a ."
Answer: a
Question (geometry): if y is the smallest positive integer such that 31,360 multiplied by y is the square of an integer , then y must be
Options: a ) 21 , b ) 10 , c ) 61 , d ) 72 , e ) 14
Rationale: "31360 = 8 * 8 * 7 * 7 * 5 * 2 , so we need one 5 and one 2 to make it a square of a number . so 5 * 2 = 10 ans : b"
Answer: b
Question (gain): solution y is 30 percent liquid x and 70 percent water . if 3 kilograms of water evaporate from 8 kilograms of solution y and 3 kilograms of solution y are added to the remaining 6 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 35 % , b ) 37 % , c ) 41.3 % , d ) 42 % , e ) 45 %
Rationale: in 8 kilograms of solution y there are 0.3 * 8 = 2.4 kilograms of solution x ; after 3 kilograms of water are replaced by 3 kilograms of solution y , to the existing 2.4 kilograms of solution x , 0.3 * 3 = 0.9 kilograms of solution x are added , so in the new solution of 8 kilograms there are 2.4 + 0.9 = 3.3 kilograms of solution x , which is 3.3 / 8 * 100 = 41.3 % of this new solution . answer : c .
Answer: c
Question (physics): a train 480 m in length crosses a telegraph post in 16 seconds . the speed of the train is ?
Options: a ) 22 kmph , b ) 108 kmph , c ) 54 kmph , d ) 71 kmph , e ) 88 kmph
Rationale: "s = 480 / 16 * 18 / 5 = 108 kmph answer : b"
Answer: b
Question (physics): a boat can travel with a speed of 13 km / hr in still water . if the speed of the stream is 4 km / hr . find the time taken by the boat to go 80 km downstream ?
Options: a ) 2 hours , b ) 3 hours , c ) 4 hours , d ) 5 hours , e ) none
Rationale: "solution speed downstream = ( 13 + 4 ) km / hr = 17 km / hr . time taken to travel 80 km downstream = ( 80 / 17 ) hrs = 4 hrs 42 minutes . answer e"
Answer: e
Question (general): a library has an average of 510 visitors on sunday and 240 on other days . the average number of visitors per day in a month of 30 days beginning with a sunday is ?
Options: a ) 187 , b ) 279 , c ) 280 , d ) 285 , e ) 262
Rationale: "since the month begins with a sunday , so there will be five sundays in the month . required average = [ ( 510 * 5 ) + ( 240 * 25 ) ] / 30 = 8550 / 30 = 285 . answer : d"
Answer: d
Question (general): the sum of present age of abe and the age before 7 years is 35 . find the present age of abe . what will be his age after 7 years ?
Options: a ) 25 , b ) 26 , c ) 27 , d ) 28 , e ) 29
Rationale: present age = x before 7 yrs , y = x - 7 after 7 yrs , z = x + 7 by the qn , x + ( x - 7 ) = 35 2 x - 7 = 35 2 x = 35 + 7 x = 42 / 2 x = 21 z = x + 7 = 21 + 7 = 28 answer : d
Answer: d
Question (general): the two lines y = x and x = - 6 intersect on the coordinate plane . what is the value of the area of the figure formed by the intersecting lines and the x - axis ?
Options: a ) 12 , b ) 14 , c ) 16 , d ) 18 , e ) 20
Rationale: "the point of intersection is ( - 6 , - 6 ) . the triangle has a base of length 6 and a height of 6 . area = ( 1 / 2 ) * base * height = ( 1 / 2 ) * 6 * 6 = 18 the answer is d ."
Answer: d
Question (physics): what distance will be covered by a bus moving at 36 kmph in 30 seconds ?
Options: a ) 287 , b ) 600 , c ) 289 , d ) 300 , e ) 207
Rationale: "36 kmph = 36 * 5 / 18 = 10 mps d = speed * time = 10 * 30 = 300 m . answer : d"
Answer: d
Question (other): if 2.5 of a number is equal to 0.75 of another number , the ratio of the numbers is :
Options: a ) 2 : 3 , b ) 3 : 4 , c ) 3 : 10 , d ) 20 : 3 , e ) 30 : 7
Rationale: "2.5 a = 0.75 b - > a / b = 0.75 / 2.5 = 75 / 250 = 3 / 10 : . a : b = 3 : 10 answer : c"
Answer: c
Question (general): the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.5 kg . the weight of the new student is
Options: a ) 22 kg , b ) 21.6 kg , c ) 22.4 kg , d ) 13 kg , e ) none of these
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.5 weight of the new student = ( 30 * 27.5 – 29 * 28 ) = 825 - 812 = 13 answer : d"
Answer: d
Question (other): if 4 tic equals 3 tacs and 6 tacs equal 4 tocs , what is the ratio of one tic to one toc ?
Options: a ) 15 / 2 , b ) 6 / 5 , c ) 5 / 6 , d ) 3 / 10 , e ) 2 / 1
Rationale: "4 tic = 3 * tac and 6 * tac = 4 * toc ; 24 * tic = 18 * tac and 18 * tac = 12 * toc - - > 24 * tic = 12 * toc - - > tic / toc = 24 / 12 = 2 / 1 . answer : e ."
Answer: e
Question (physics): the speed of a boat in still water is 30 kmph . what is the speed of the stream if the boat can cover 80 km downstream or 40 km upstream in the same time ?
Options: a ) 11 kmph , b ) 10 kmph , c ) 12 kmph , d ) 16 kmph , e ) 15 kmph
Rationale: x = the speed of the stream ( 30 + x ) / ( 30 - x ) = 2 / 1 30 + x = 60 - 2 x 3 x = 30 x = 10 km / hour if the speed of the stream is 10 km / hour , then the ' downstream ' speed of the boat is 30 + 10 = 40 km / hour and the ' upstream ' speed of the boat is 30 - 10 = 20 km / hour . in that way , if the boat traveled for 2 hours , it would travel 2 x 40 = 80 km downstream and 2 x 20 = 40 km / hour upstream . answer : b
Answer: b
Question (gain): after getting 2 successive discounts , a shirt with a list price of rs 150 is available at rs 105 . if the second discount is 12.55 , find the first discount .
Options: a ) 22 % , b ) 18 % , c ) 24 % , d ) 17 % , e ) 20 %
Rationale: "let the first discount be x % then , 87.5 % of ( 100 - x ) % of 150 = 105 = 87.5 / 100 * ( 100 - x ) / 100 * 450 = 150 = > 105 = > 100 - x = ( 105 * 100 * 100 ) / ( 150 * 87.5 ) = 80 x = ( 100 - 80 ) = 20 first discount = 20 % answer is e ."
Answer: e
Question (physics): a rectangular plot measuring 60 meters by 50 meters is to be enclosed by wire fencing . if the poles of the fence are kept 5 meters apart . how many poles will be needed ?
Options: a ) 44 m
b ) 66 m
c ) 26 m
d ) 56 m
e ) 25 m
Rationale: perimeter of the plot = 2 ( 60 + 50 ) = 220 m no of poles = 220 / 5 = 44 m answer : a
Answer: a
Question (general): the arithmetic mean and standard deviation of a certain normal distribution are 15 and 1.5 , respectively . what value is exactly 2 standard deviations less than the mean ?
Options: a ) 10.5 , b ) 11 , c ) 11.5 , d ) 12 , e ) 12.5
Rationale: the value which isexactlytwo sd less than the mean is : mean - 2 * sd = 15 - 2 * 1.5 = 12 . answer : d .
Answer: d
Question (gain): in how many years will a sum of money doubles itself at 12 % per annum on simple interest ?
Options: a ) 15 % , b ) 20 % , c ) 10 % , d ) 8 % , e ) 22 %
Rationale: "p = ( p * 12 * r ) / 100 r = 8 % answer : d"
Answer: d
Question (gain): 20 % of a number is more than 20 % of 650 by 190 . find the number ?
Options: a ) 288 , b ) 278 , c ) 800 , d ) 1600 , e ) 121
Rationale: "( 20 / 100 ) * x â € “ ( 20 / 100 ) * 650 = 190 1 / 5 x = 320 x = 1600 answer : d"
Answer: d
Question (physics): it will take 18 days for cameron to complete a certain task alone . he worked for 9 days before she was joined by sandra . both of them completed the remaining task in 3 and half days . how many days will it take both of them to complete the entire job ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 9
Rationale: explanation : cameron and sandra completed half work in 3.5 days = > they can complete whole work in 7 days answer : option b
Answer: b