Cheukting/mathqa huggingface dataset:
Question (general): if a wholesaler distributes items to several outlets ( a , b , c and d ) in the ratio of 1 / 2 : 1 / 11 : 1 / 12 : 1 / 13 then find the total number of items the wholesaler distributes ?
Options: a ) 289 , b ) 1289 , c ) 1389 , d ) 1281 , e ) 128
Rationale: "here , a : b : c : d = 1 / 2 : 1 / 11 : 1 / 12 : 1 / 13 1 ) l . c . m of 2 : 11 : 12 : 13 is 1716 2 ) find the number of books each friend received - - - - - - - - - ( to find no . of books each friend has , multiply the ratio with the l . c . m . calculated ) a = ( 1 / 2 ) x 1716 = 858 b = ( 1 / 11 ) x 1716 = 156 c = ( 1 / 12 ) x 1716 = 143 d = ( 1 / 13 ) x 1716 = 132 3 ) total number of toys = ( 858 x + 156 x + 143 x + 132 x ) = 1289 x minimum number of pens ( x ) = 1 therefore , total number of items = 1289 items . correct option : b"
Answer: b
Question (general): the sum of ages of 5 children born 3 years different each is 60 yrs . what is the age of the elder child ?
Options: a ) 17 , b ) 19 , c ) 16 , d ) 18 , e ) 21
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 60 5 x = 30 x = 6 . x + 12 = 6 + 12 = 18 d"
Answer: d
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 - 3 ?
Options: a ) 10 , b ) 8 , c ) 7 , d ) 3 , 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 - 3 is 6 - 3 = 3 . answer : d ."
Answer: d
Question (physics): a 240 meter long train crosses a man standing on the platform in 6 sec . what is the speed of the train ?
Options: a ) 229 , b ) 144 , c ) 278 , d ) 126 , e ) 112
Rationale: "s = 240 / 6 * 18 / 5 = 144 kmph answer : b"
Answer: b
Question (physics): a person travels equal distances with speeds of 2 km / hr , 6 km / hr , 6 km / hr . and takes a total time of 11 minutes . find the total distance ?
Options: a ) 1 km , b ) 500 mts , c ) 660 mts , d ) 2 km , e ) 250 mts
Rationale: "let the each distance be x km total distance = 3 x then total time , ( x / 2 ) + ( x / 6 ) + ( x / 6 ) = 11 / 60 x = 0.22 total distance = 3 * 0.22 = 0.66 km = 660 meters correct option is c"
Answer: c
Question (physics): natasha climbs up a hill , and descends along the same way she went up . it takes her 4 hours to reach the top and 2 hours to come back down . if her average speed along the whole journey is 3 kilometers per hour , what was her average speed ( in kilometers per hour ) while climbing to the top ?
Options: a ) 1.75 , b ) 2.25 , c ) 2.5 , d ) 2.75 , e ) 3.25
Rationale: let the distance to the top be x , so the total distance traveled by natasha is 2 x . the total time is 4 + 2 = 6 hours the average speed = total distance / total time taken = 2 x / 6 = x / 3 the average speed of the complete journey is 3 km / hour x / 3 = 3 x = 9 km the average speed while climbing = distance / time = 9 / 4 = 2.25 km / h the answer is b .
Answer: b
Question (physics): mike drives his new corvette from san francisco to las vegas , a journey of 640 miles . he drives the first half of the trip at an average rate of 80 miles per hour , but has to slow down for the second half of his journey . if the second half of the trip takes him 200 percent longer than the first half , what is his average rate p in miles per hour for the entire trip ?
Options: a ) p = 26.7 , b ) p = 30.0 , c ) p = 40.0 , d ) p = 53.3 , e ) p = 60.0
Rationale: "veritas prepofficial solution correct answer : c using the formula : time = distance / rate , we find that mike takes 4 hours to cover the first 320 miles of his trip . since the 2 nd 320 miles take 200 % longer than the first , it takes mike 8 hours longer , or 12 hours . ( note : 200 % longer than the first half is not 200 % of the first half . ) the overall time is 4 hours + 12 hours or 16 hours . since the definition of average rate = total distance traveled / total time of travel , mike ' s average rate = 640 / 16 or 40 miles per hour . answer choice c is correct ."
Answer: c
Question (general): a group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 1 students left over . what is the sum of the two smallest possible values of n ?
Options: a ) 33 , b ) 62 , c ) 49 , d ) 53 , e ) 86
Rationale: "4 x + 1 = 5 y + 1 . . . . . . . . . . . ie : 4 x - 5 y = 2 x , y must be > 1 and y is even ie ( 2 , 4,6 , . . etc ) if y = 2 thus x = fraction ( not possible ) if y = 4 thus x = 5 n = 21 if y = 6 thus x = not possible fraction if y = 8 thus x = 10 n = 41 21 + 41 = 62 . . . . . b"
Answer: b
Question (gain): the annual interest rate earned by an investment increased by 10 percent from last year to this year . if the annual interest rate earned by the investment this year was 12 percent , what was the annual interest rate last year ?
Options: a ) 1 % , b ) 1.1 % , c ) 9.1 % , d ) 10 % , e ) 10.9 %
Rationale: "12 = 1.1 * x x = 10.90 % answer e )"
Answer: e
Question (general): if a - b = 6 and a ^ 2 + b ^ 2 = 100 , find the value of ab
Options: a ) 10 , b ) 32 , c ) 15 , d ) 18 , e ) 19
Rationale: "2 ab = ( a ^ 2 + b ^ 2 ) - ( a - b ) ^ 2 = 100 - 36 = 64 = > ab = 32 answer : b"
Answer: b
Question (general): the average amount with a group of 7 numbers is rs . 20 . if the newly joined member has rs . 56 with him , what was the average amount with the group before his joining the group ?
Options: a ) s . 13 , b ) s . 12 , c ) s . 15 , d ) s . 22 , e ) s . 14
Rationale: total members in the group = 7 average amount = rs . 20 total amount with them = 7 * 20 = rs . 140 one number has rs . 56 . so , the amount with remaining 6 people = 140 - 56 = rs . 84 the average amount with them = 84 / 6 = rs . 14 . answer : e
Answer: e
Question (gain): find the missing figures : ? % of 50 = 2.125
Options: a ) 8.55 , b ) 6.55 , c ) 8.75 , d ) 7.75 , e ) 4.25
Rationale: ( i ) let x % of 50 = 2.125 . then , ( x / 100 ) * 50 = 2.125 x = ( 2.125 * 2 ) = 4.25 answer is e .
Answer: e
Question (gain): a person borrows rs . 5000 for 2 years at 4 % p . a . simple interest . he immediately lends it to another person at 8 % p . a for 2 years . find his gain in the transaction per year .
Options: a ) 167.5 , b ) 150 , c ) 200 , d ) 112.5 , e ) 212.5
Rationale: explanation : the person borrows rs . 5000 for 2 years at 4 % p . a . simple interest simple interest that he needs to pay = prt / 100 = 5000 × 4 × 2 / 100 = 400 he also lends it at 8 % p . a for 2 years simple interest that he gets = prt / 100 = 5000 × 8 × 2 / 100 = 800 his overall gain in 2 years = rs . 800 - rs . 400 = rs . 400 his overall gain in 1 year = 400 / 2 = rs . 200 answer : option c
Answer: c
Question (geometry): the volume of a certain substance is always directly proportional to its weight . if 48 cubic inches of the substance weigh 114 ounces , what is the volume , in cubic inches , of 63 ounces of this substance ?
Options: a ) 27 , b ) 26 , c ) 42 , d ) 64 , e ) 147
Rationale: "112 ounces of a substance has a volume of 48 cubic inches 63 ounces of a substance has a volume of ( 48 / 114 ) * 63 = 26 cubic inches answer b"
Answer: b
Question (geometry): the side of a square is increased by 5 % then how much % does its area increases ?
Options: a ) 15.00 % , b ) 10.25 % , c ) 10.00 % , d ) 12.25 % , e ) 12.50 %
Rationale: "a = 100 a 2 = 10000 a = 105 a 2 = 11025 - - - - - - - - - - - - - - - - 10000 - - - - - - - - - 1025 100 - - - - - - - ? = > 10.25 % answer : b"
Answer: b
Question (geometry): a circular mat with radius 10 inches is placed on a square tabletop , each of whose sides is 24 inches long . which of the following is closest to the fraction of the tabletop covered by the mat ?
Options: a ) 5 / 12
b ) 2 / 5
c ) 0.5451
d ) 3 / 4
e ) 5 / 6
Rationale: c . it is a circle inscribed in a square . square side = 24 - - - > square ( table ) area = 24 ^ 2 circle diameter = 20 - - - > circle area = pir ^ 2 = 100 pi ( where pi = ~ 3.14 ) covered fraction = 100 * 3.14 / 24 * 24 = ~ 314 / 24 * 24 = 0.5451 c
Answer: c
Question (gain): money invested at x % , compounded annually , triples in value in approximately every 112 / x years . if $ 1500 is invested at a rate of 8 % , compounded annually , what will be its approximate worth in 28 years ?
Options: a ) $ 3,750 , b ) $ 5,600 , c ) $ 13,500 , d ) $ 15,000 , e ) $ 22,500
Rationale: "x = 8 % 112 / x years = 112 / 8 = 14 years now , money triples every 14 years therefore , in 14 yrs , if $ 1500 triples to $ 4500 , in 28 years , it will again triple to $ 4500 * 3 = $ 13,500 answer c"
Answer: c
Question (general): the sum of ages of 5 children born 3 years different each is 75 yrs . what is the age of the elder child ?
Options: a ) 7 , b ) 9 , c ) 16 , d ) 18 , e ) 21
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 75 5 x = 45 x = 9 . x + 12 = 9 + 12 = 21 e"
Answer: e
Question (general): in how many ways can a teacher write an answer key for a mini - quiz that contains 3 true - false questions followed by 2 multiples - choice questions with 4 answer choices each , if the correct answers to all true - false questions can not be the same ?
Options: a ) 88 , b ) 90 , c ) 96 , d ) 98 , e ) 102
Rationale: 2 multiples - choice questions can be answered in = 4 x 4 = 16 ways 3 true - false questions can be answered in = 2 x 2 x 2 = 8 ways but out of the 8 ways , 2 ways [ ( true - true - true ) ( false - false - false ) ] will contain same answers thus 3 true - false questions can be answered in = 2 x 2 x 2 = 6 ways total ways to answer the quiz = 16 x 6 = 96 answer c
Answer: c
Question (general): a 50 - liter solution of alcohol and water is 5 percent alcohol . if 1.5 liters of alcohol and 8.5 liters of water are added to this solution , what percent of the solution produced is alcohol ?
Options: a ) 5.5 % , b ) 6 % , c ) 6 1 / 3 % , d ) 6 2 / 3 % , e ) 7 %
Rationale: "50 l * . 05 = 2.5 l of alc , 50 l - 2.5 l = 47.5 l of water 2.5 + 1.5 = 4 l of alcohol in new solution 47.5 l + 8.5 l = 56 l of water 4 l / 56 l = 1 / 14 this is ~ 7 % answer : e"
Answer: e
Question (general): there are 3 departments having students 72 , 5824 . in an exam they have to be seated in rooms such that each room has equal number of students and each room has students of one type only ( no mixing of departments ) . find the minimum number of rooms required ?
Options: a ) 73 , b ) 74 , c ) 75 , d ) 76 , e ) 77
Rationale: we need to take gcd which is 2 thus all the rooms will have 2 students of the same dept 1 ) 72 / 2 = 36 2 ) 58 / 2 = 29 3 ) 24 / 2 = 12 total no . of min rooms reqd = 36 + 12 + 29 = 77 answer : e
Answer: e
Question (physics): a car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 120 kilometers per hour . at what speed , in kilometers per hour , is the car traveling ?
Options: a ) 121.5 , b ) 122 , c ) 122.5 , d ) 113 , e ) 112.5
Rationale: "e 120 * t = 1 km = > t = 1 / 120 km / h v * ( t + 2 / 3600 ) = 1 v ( 1 / 120 + 2 / 3600 ) = 1 = > v = 112.5 km / h"
Answer: e
Question (gain): an article is bought for rs . 765 and sold for rs . 1000 , find the gain percent ?
Options: a ) 30.6 % , b ) 30.5 % , c ) 30.7 % , d ) 30.8 % , e ) 30.9 %
Rationale: "765 - - - - 235 100 - - - - ? = > 30.7 % answer : c"
Answer: c
Question (general): the price of a cycle is reduced by 25 per cent . the new price is reduced by a further 70 per cent . the two reductions together are equal to a single reduction of
Options: a ) 45 % , b ) 40 % , c ) 35 % , d ) 77.5 % , e ) 30 %
Rationale: "price = p initially price reduced by 25 % which means new price is 3 / 4 p now on this new price further 70 percent is reduced which means the new price is merely 30 percent of 3 / 4 p = = > ( 3 / 4 ) x ( 3 / 10 ) p = 9 / 40 p is the new price after both deduction which is 22.5 percent of the original value p . this implies this entire series of deduction is worth having discounted 77.5 % of p . so answer is d = 77.5 %"
Answer: d
Question (gain): the percentage profit earned by selling an article for rs . 1920 is equal to the percentage loss incurred by selling the same article for rs . 1280 . at what price should the article be sold to make 35 % profit ?
Options: a ) 2080 , b ) 2778 , c ) 2299 , d ) 2778 , e ) 2771
Rationale: let c . p . be rs . x . then , ( 1920 - x ) / x * 100 = ( x - 1280 ) / x * 100 1920 - x = x - 1280 2 x = 3200 = > x = 1600 required s . p . = 130 % of rs . 1600 = 130 / 100 * 1600 = rs . 2080 . answer : a
Answer: a
Question (gain): running at the same constant rate , 6 identical machines can produce a total of 270 bottles per minute . at this rate , how many bottles could 10 such machines produce in 4 minutes ?
Options: a ) 648 , b ) 1800 , c ) 2700 , d ) 10800 , e ) none
Rationale: "let the number of required bottles be x machine 6 : 10 time 1 : 4 = : : 270 : x therefore 6 x 1 x x = 10 x 4 x 270 = > x = ( 10 x 4 x 270 ) / ( 6 ) = > x = 1800 answer : option b"
Answer: b
Question (gain): thirty percent of the members of a swim club have passed the lifesaving test . among the members who havenotpassed the test , 40 have taken the preparatory course and 30 have not taken the course . how many members are there in the swim club ?
Options: a ) 60 , b ) 80 , c ) 100 , d ) 120 , e ) 140
Rationale: "30 % of the members have passed the test , thus 70 % have not passed the test . we also know that 30 + 40 = 70 members have not passed the test , thus 0.7 * total = 70 - - > total = 100 . answer : c ."
Answer: c
Question (general): what is the smallest number which when diminished by 8 , is divisible by 9 , 6 , 12 and 18 ?
Options: a ) 50 , b ) 45 , c ) 44 , d ) 60 , e ) 65
Rationale: "explanation : required number = lcm of ( 9 , 6 , 12 and 18 ) + 8 = 36 + 8 = 44 answer : option c"
Answer: c
Question (other): the ratio of two quantities is 1 to 2 . if each of the quantities is increased by 15 , what is the ratio of these 2 new quantities ?
Options: a ) 5 : 6 , b ) 25 : 27 , c ) 15 : 16 , d ) 20 : 21 , e ) it can not be determined from the information given
Rationale: "the ratio can not be straight way added any quantity . . . 1 : 2 means 1 x : 2 x . . . so when you add a quantity , it becomes 1 x + 15 : 2 x + 15 . . so value of x is must . . ans e"
Answer: e
Question (general): on a partly cloudy day , derek decides to walk back from work . when it is sunny , he walks at a speed of s miles / hr ( s is an integer ) and when it gets rain cloud , he increases his speed to ( s + 1 ) miles / hr . if his average speed for the entire distance is 2.8 miles / hr , what fraction of the total distance did he cover while the sun was shining on him ?
Options: a ) 1 / 8 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 5 , e ) 1 / 4
Rationale: if s is an integer and we know that the average speed is 2.8 , s must be = 2 . that meanss + 1 = 3 . this implies that the ratio of time for s = 2 is 1 / 4 of the total time . the formula for distance / rate is d = rt . . . so the distance travelled when s = 2 is 2 t . the distance travelled for s + 1 = 3 is 3 * 4 t or 12 t . therefore , total distance covered while the sun was shining over him is 2 / 14 = 1 / 7 . answer : c
Answer: c
Question (geometry): two tracks are parallel . the first track has 6 checkpoints and the second one has 10 checkpoints . in how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle ?
Options: a ) 120
b ) 150
c ) 200
d ) 270
e ) 420
Rationale: to make a triangle , you need 2 checkpoints from one track and 1 from the other . you can not have all 3 from the same track since then the points will be in a line ( assuming straight line of track ) you select 2 checkpoints from the first track and one from the second or two from the second track and one from the first . 6 c 2 * 10 c 1 + 10 c 2 * 6 c 1 = 150 + 270 = 420 answer ( e )
Answer: e
Question (physics): an engineer undertakes a project to build a road 15 km long in 300 days and employs 55 men for the purpose . after 100 days , he finds only 2.5 km of the road has been completed . find the ( approximate ) number of extra men he must employ to finish the work in time .
Options: a ) a . 43 , b ) b . 45 , c ) c . 55 , d ) d . 68 , e ) e . 83
Rationale: "55 workers working already let x be the total men required to finish the task in next 200 days 2.5 km done hence remaining is 12.5 km also , work has to be completed in next 200 days ( 300 - 100 = 200 ) we know that , proportion of men to distance is direct proportion and , proportion of men to days is inverse proportion hence , x = ( 55 * 12.5 * 100 ) / ( 2.5 * 200 ) thus , x = 137.5 that is approximately 138 thus , more men needed to finish the task = 138 - 55 = 83 hence answer is e"
Answer: e
Question (general): bob invested $ 2000 in fund a and $ 1000 in fund b . over the next two years , the money in fund a earned a total interest of 12 percent for the two years combined and the money in fund b earned 30 percent annual interest compounded annually . two years after bob made these investments . bob ' s investment in fund a was worth how much more than his investment in fund b ?
Options: a ) $ 500 , b ) $ 550 , c ) $ 600 , d ) $ 650 , e ) $ 700
Rationale: bob earned 2000 * ( 1 + 0.12 ) in total by fund a and earned 1000 * ( 1 + 0.3 ) ^ 2 in total by fund b . so 2000 * ( 1.12 ) - 1000 * ( 1.69 ) = 550 . the answer is , therefore , ( b ) .
Answer: b
Question (other): the ratio between the sale price and the cost price of an article is 6 : 5 . what is the ratio between the profit and the cost price of that article ?
Options: a ) 2 : 9 , b ) 1 : 5 , c ) 3 : 6 , d ) 2 : 0 , e ) 2 : 1
Rationale: let c . p . = rs . 5 x and s . p . = rs . 6 x . then , gain = rs . x required ratio = x : 5 x = 1 : 5 answer : b
Answer: b
Question (general): how many digits 2 ^ 1000 has ?
Options: a ) 31 , b ) 35 , c ) 50 , d ) 99 , e ) 310
Rationale: "2 ^ 10 = 1.024 * 10 ^ 3 = > 2 ^ 1000 = ( 1.024 ) ^ 100 * 10 ^ 300 therefore 310 digits would be my best guess e"
Answer: e
Question (probability): a father purchased dress for his 3 daughters . the dresses are of same color but diff size and they are kept in dark room . what is probability that all the 3 will not choose their own dress ?
Options: a ) 22 , b ) 87 , c ) 29 , d ) 26 , e ) 191
Rationale: answer : b
Answer: b
Question (physics): if the population of a certain country increases at the rate of two person every 60 seconds , by how many persons does the population increase in 100 minutes ?
Options: a ) 120 , b ) 150 , c ) 240 , d ) 220 , e ) 200
Rationale: "answer = 2 * 100 = 200 answer = e"
Answer: e
Question (general): a salt manufacturing company produced a total of 2500 tonnes of salt in january of a particular year . starting from february its production increased by 100 tonnes every month over the previous months until the end of the year . find its ave 66 rage daily production for that year ?
Options: a ) 100 , b ) 105 , c ) 109 , d ) 120 , e ) 90
Rationale: "total production of salt by the company in that year = 2500 + 2600 + 2700 + . . . . + 3600 = 36600 . average monthly production of salt for that year = 36600 / 365 â ‰ ˆ 100 answer : a"
Answer: a
Question (physics): 1200 men have provisions for 18 days . if 450 more men join them , for how many days will the provisions last now ?
Options: a ) 12.9 , b ) 12.0 , c ) 12.5 , d ) 12.2 , e ) 13.1
Rationale: "1200 * 18 = 1650 * x x = 13.1 answer : e"
Answer: e
Question (physics): when a train travels at a speed of 90 kmph , it reaches the destination on time . when the same train travels at a speed of 50 kmph , it reaches its destination 15 min late . what is the length of journey ?
Options: a ) 18.75 km , b ) 50 km , c ) 60 km , d ) 85 km , e ) 95 km
Rationale: "let x be the time reached with the speed 90 km / h 50 km / h - - - - > x + 15 distance is equal so 90 ( km / h ) × xhr = 50 ( km / h ) × ( x + 15 ) hr so 90 x = 50 x + 750 so the would be in km and x = 18.75 answer : a"
Answer: a
Question (gain): a student needs 60 % of the marks on a test to pass the test . if the student gets 80 marks and fails the test by 40 marks , find the maximum marks set for the test .
Options: a ) 180 , b ) 200 , c ) 220 , d ) 240 , e ) 260
Rationale: "60 % = 120 marks 1 % = 2 marks 100 % = 200 marks the answer is b ."
Answer: b
Question (general): what is the sum of all even numbers from 1 to 401 ?
Options: a ) 122821 , b ) 281228 , c ) 281199 , d ) 122850 , e ) 40200
Rationale: "explanation : 400 / 2 = 200 200 * 201 = 40200 answer : e"
Answer: e
Question (geometry): the size of a flat - screen television is given as the length of the screen ’ s diagonal . how many square inches greater is the screen of a square 21 - inch flat - screen television than a square 19 - inch flat - screen television ?
Options: a ) 42 , b ) 40 , c ) 38 , d ) 36 , e ) 48
Rationale: "if we take a square with side length x and draw a diagonal , we get two isosceles right triangles . if we focus on one such right triangle , we see that the legs have length x . square 21 - inch flat - screen television the diagonal ( hypotenuse ) = 21 so , we can apply the pythagorean theorem to get x ² + x ² = 21 ² simplify : 2 x ² = 21 ² divide both sides by 2 to get : x ² = 21 ² / 2 since the area of the square = x ² , we can see that the area of this square is 21 ² / 2 square 19 - inch flat - screen television the diagonal ( hypotenuse ) = 19 so , we can apply the pythagorean theorem to get x ² + x ² = 19 ² simplify : 2 x ² = 19 ² divide both sides by 2 to get : x ² = 19 ² / 2 since the area of the square = x ² , we can see that the area of this square is 19 ² / 2 difference in areas = 21 ² / 2 - 19 ² / 2 = ( 21 + 19 ) ( 21 - 19 ) / 2 = 40 b"
Answer: b
Question (general): the proportion of copper and zinc in the brass is 13 : 7 . how much zinc will there be in 100 kg of brass ?
Options: a ) 37 kg , b ) 35 kg , c ) 85 kg , d ) 45 kg , e ) 25 kg
Rationale: 7 / 20 * 100 = 35 answer : b
Answer: b
Question (gain): if a man lost 8 % by selling oranges at the rate of 18 a rupee at how many a rupee must he sell them to gain 45 % ?
Options: a ) 33.56 , b ) 23.68 , c ) 11.42 , d ) 9.56 , e ) 23.55
Rationale: "92 % - - - - 18 145 % - - - - ? 92 / 145 * 18 = 11.42 answer : c"
Answer: c
Question (physics): the time it took car p to travel 150 miles was 2 hours less than the time it took car r to travel the same distance . if car p ’ s average speed was 10 miles per hour greater than that of car r , what was car r ’ s average speed , in miles per hour ?
Options: a ) 23 , b ) 50 , c ) 60 , d ) 70 , e ) 80
Rationale: "let speed of car r be = x then speed of car p = x + 10 a / q , ( 150 / x ) - ( 150 / ( x + 10 ) ) = 2 solving for x = 23 miles \ hr . a"
Answer: a
Question (general): subtracting 2 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.98 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: answer let a - 2 % of a = ab . ⇒ ( 98 x a ) / 100 = ab ∴ b = 0.98 correct option : a
Answer: a
Question (physics): a cistern 5 m long and 2 m wide contains water up to a breadth of 1 m 10 cm . find the total area of the wet surface .
Options: a ) 42 m sqaure , b ) 49 m sqaure , c ) 25 m sqaure , d ) 28 m sqaure , e ) none of these
Rationale: "explanation : area of the wet surface = 2 [ lb + bh + hl ] - lb = 2 [ bh + hl ] + lb = 2 [ ( 2 * 1.1 + 5 * 1.1 ) ] + 5 * 2 = 25 m square option c"
Answer: c
Question (other): right now , the ratio between the ages of sandy and molly is 4 : 3 . after 6 years , sandy ’ s age will be 42 years . what is molly ' s age right now ?
Options: a ) 24 , b ) 27 , c ) 30 , d ) 33 , e ) 36
Rationale: "now , sandy is 42 - 6 = 36 molly ' s age is ( 3 / 4 ) * 36 = 27 the answer is b ."
Answer: b