Cheukting/mathqa huggingface dataset:
Question (gain): the banker ' s gain of a certain sum due 3 years hence at 10 % per annum is rs . 36 . what is the present worth ?
Options: a ) rs . 400 , b ) rs . 300 , c ) rs . 500 , d ) rs . 350 , e ) none of these
Rationale: "explanation : t = 3 years r = 10 % td = ( bg × 100 ) / tr = ( 36 × 100 ) / ( 3 × 10 ) = 12 × 10 = rs . 120 td = ( pw × tr ) / 100 ⇒ 120 = ( pw × 3 × 10 ) / 100 ⇒ 1200 = pw × 3 pw = 1200 / 3 = rs . 400 answer : option a"
Answer: a
Question (general): average age of students of an adult school is 40 years . 120 new students whose average age is 32 years joined the school . as a result the average age is decreased by 4 years . find the number of students of the school after joining of the new students .
Options: a ) 1200 , b ) 120 , c ) 360 , d ) 240 , e ) none of these
Rationale: "explanation : let the original no . of students be x . according to situation , 40 x + 120 * 32 = ( x + 120 ) 36 ⇒ x = 120 so , required no . of students after joining the new students = x + 120 = 240 . answer : d"
Answer: d
Question (general): sophia finished 2 / 3 of a book . she calculated that she finished 90 more pages than she has yet to read . how long is her book ?
Options: a ) 229 , b ) 270 , c ) 877 , d ) 266 , e ) 281
Rationale: let xx be the total number of pages in the book , then she finished 23 ⋅ x 23 ⋅ x pages . then she has x − 23 ⋅ x = 13 ⋅ xx − 23 ⋅ x = 13 ⋅ x pages left . 23 ⋅ x − 13 ⋅ x = 9023 ⋅ x − 13 ⋅ x = 90 13 ⋅ x = 9013 ⋅ x = 90 x = 270 x = 270 so the book is 270 pages long . answer : b
Answer: b
Question (gain): 120 is what percent of 50 ?
Options: a ) 5 % , b ) 240 % , c ) 50 % , d ) 2 % , e ) 500 %
Rationale: "50 * x = 120 - - > x = 2.4 - - > 2.4 expressed as percent is 240 % . answer : b ."
Answer: b
Question (other): there are 10 girls and 20 boys in a classroom . what is the ratio of girls to boys ?
Options: a ) 1 / 2 , b ) 1 / 3 , c ) 1 / 5 , d ) 10 / 30 , e ) 2 / 5
Rationale: if girls is 10 and boys is 20 , then 10 / 20 . so ratio of girls to boys is = 10 / 20 = 1 / 2 answer : a
Answer: a
Question (gain): an empty fuel tank with a capacity of 218 gallons was filled partially with fuel a and then to capacity with fuel b . fuel a contains 12 % ethanol by volume and fuel b contains 16 % ethanol by volume . if the full fuel tank contains 30 gallons of ethanol , how many gallons of fuel a were added ?
Options: a ) 122 , b ) 150 , c ) 100 , d ) 80 , e ) 50
Rationale: "say there are a gallons of fuel a in the tank , then there would be 218 - a gallons of fuel b . the amount of ethanol in a gallons of fuel a is 0.12 a ; the amount of ethanol in 218 - a gallons of fuel b is 0.16 ( 218 - a ) ; since the total amount of ethanol is 30 gallons then 0.12 a + 0.16 ( 218 - a ) = 30 - - > a = 122 . answer : a ."
Answer: a
Question (gain): an article is bought for rs . 823 and sold for rs . 1000 , find the gain percent ?
Options: a ) 21.4 % , b ) 21.5 % , c ) 21.6 % , d ) 21.7 % , e ) 21.8 %
Rationale: "823 - - - - 177 100 - - - - ? = > 21.5 % answer : b"
Answer: b
Question (physics): 6 workers should finish a job in 8 days . after 3 days came 4 workers join them . how many days m do they need to finish the same job ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let rate of one worker be r = > ( 6 * r ) * 8 = 1 ( rate * time = work ) = > r = 1 / 48 = > work remaining after 3 days 1 - ( 3 * 6 ) / 48 = 30 / 48 after 4 ppl joined in ( ( 6 + 4 ) * time ) / 48 = 30 / 48 time m = 3 days to finish the task imo a"
Answer: a
Question (gain): j is 25 % less than p and 20 % less than t . t is q % less than p . what is the value of q ?
Options: a ) 93.5 , b ) 90 , c ) 6.75 , d ) 6.25 , e ) 2
Rationale: "usually we can solve every question of this type by choosing appropriate value of the variable and deriving the value of other related variables . let , p = 400 then j = ( 75 / 100 ) * 400 = 300 also j = ( 80 / 100 ) * t i . e . t = 300 * 100 / 80 = 375 and t = [ 1 - ( q / 100 ) ] * p i . e . 100 - q = 100 * t / p = 100 * 375 / 400 = 93.75 i . e . q = 6.25 answer : option d"
Answer: d
Question (general): a student was asked to find 4 / 5 of a number . but the student divided the number by 4 / 5 , thus the student got 36 more than the correct answer . find the number .
Options: a ) 60 , b ) 70 , c ) 80 , d ) 90 , e ) 100
Rationale: "let the number be x . ( 5 / 4 ) * x = ( 4 / 5 ) * x + 36 25 x = 16 x + 720 9 x = 720 x = 80 the answer is c ."
Answer: c
Question (general): the average weight of 8 person ' s increases by 1.5 kg when a new person comes in place of one of them weighing 75 kg . what might be the weight of the new person ?
Options: a ) 81 kg , b ) 85 kg , c ) 90 kg , d ) 100 kg , e ) 110 kg
Rationale: "total weight increased = ( 8 x 1.5 ) kg = 6 kg . weight of new person = ( 75 + 6 ) kg = 81 kg . answer : a"
Answer: a
Question (physics): a train 125 m long passes a man , running at 15 km / hr in the same direction in which the train is going , in 10 seconds . the speed of the train is ?
Options: a ) 60 , b ) 50 , c ) 28 , d ) 26 , e ) 29
Rationale: "speed of the train relative to man = ( 125 / 10 ) m / sec = ( 25 / 2 ) m / sec . [ ( 25 / 2 ) * ( 18 / 5 ) ] km / hr = 45 km / hr . let the speed of the train be x km / hr . then , relative speed = ( x - 15 ) km / hr . x - 15 = 45 = = > x = 60 km / hr answer : a"
Answer: a
Question (general): the average of 15 result is 60 . average of the first 10 of them is 10 and that of the last 10 is 80 . find the 8 th result ?
Options: a ) 35 , b ) 200 , c ) 150 , d ) 250 , e ) 300
Rationale: "sum of all the 13 results = 15 * 60 = 900 sum of the first 7 of them = 10 * 10 = 100 sum of the last 7 of them = 10 * 80 = 800 so , the 8 th number = 900 + 100 - 800 = 200 . b"
Answer: b
Question (general): a salesman â € ™ s terms were changed from a flat commission of 5 % on all his sales to a fixed salary of rs . 1000 plus 2.5 % commission on all sales exceeding rs . 4,000 . if his remuneration as per new scheme was rs . 500 more than that by the previous schema , his sales were worth ?
Options: a ) s . 14,000 , b ) s . 12,000 , c ) s . 16,000 , d ) s . 40,000 , e ) s . 50,000
Rationale: "[ 1000 + ( x - 4000 ) * ( 2.5 / 100 ) ] - x * ( 5 / 100 ) = 600 x = 16000 answer : c"
Answer: c
Question (geometry): a rectangular floor that measures 15 meters by 18 meters is to be covered with carpet squares that each measure 3 meters by 3 meters . if the carpet squares cost $ 12 apiece , what is the total cost for the number of carpet squares needed to cover the floor ?
Options: a ) $ 200 , b ) $ 240 , c ) $ 360 , d ) $ 960 , e ) $ 1,920
Rationale: "the width of the rectangular floor ( 15 m ) is a multiple of one side of the square ( 3 m ) , and the length of the floor ( 18 m ) is also a multiple of the side of the square . so the number of carpets to cover the floor is ( 15 / 3 ) * ( 18 / 3 ) = 30 . the total cost is 30 * 12 = $ 360 . the answer is , therefore , c ."
Answer: c
Question (general): a vessel of capacity 2 litre has 30 % of alcohol and another vessel of capacity 6 litre had 40 % alcohol . the total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water . what is the new concentration of mixture ?
Options: a ) 30 % . , b ) 71 % . , c ) 49 % . , d ) 29 % . , e ) 51 % .
Rationale: "30 % of 2 litres = 0.6 litres 40 % of 6 litres = 2.4 litres therefore , total quantity of alcohol is 3.0 litres . this mixture is in a 10 litre vessel . hence , the concentration of alcohol in this 10 litre vessel is 30 % answer : a"
Answer: a
Question (general): the total of 324 of 20 paise and 25 paise make a sum of rs . 70 . the no of 20 paise coins is
Options: a ) 238 , b ) 277 , c ) 220 , d ) 200 , e ) 288
Rationale: "explanation : let the number of 20 paise coins be x . then the no of 25 paise coins = ( 324 - x ) . 0.20 * ( x ) + 0.25 ( 324 - x ) = 70 = > x = 220 . . answer : c ) 220"
Answer: c
Question (general): in 1970 there were 8,902 women stockbrokers in the united states . by 1978 the number had increased to 18,947 . approximately what was the percent increase ?
Options: a ) 45 % , b ) 113 % , c ) 145 % , d ) 150 % , e ) 225 %
Rationale: "the percent increase is ( 18947 - 8902 ) / 8902 = 10045 / 8902 = 1.13 so the approximate answer is b"
Answer: b
Question (other): what is the number of integers from 1 to 1100 ( inclusive ) that are divisible by neither 11 nor by 35 ?
Options: a ) 884 , b ) 890 , c ) 892 , d ) 910 , e ) 945
Rationale: "normally , i would use the method used by bunuel . it ' s the most accurate . but if you are looking for a speedy solution , you can use another method which will sometimes give you an estimate . looking at the options ( most of them are spread out ) , i wont mind trying it . ( mind you , the method is accurate here since the numbers start from 1 . ) in 1000 consecutive numbers , number of multiples of 11 = 1000 / 11 = 90 ( ignore decimals ) in 1000 consecutive numbers , number of multiples of 35 = 1000 / 35 = 28 number of multiples of 11 * 35 i . e . 385 = 1000 / 385 = 2 number of integers from 1 to 1000 that are divisible by neither 11 nor by 35 = 1000 - ( 90 + 28 - 2 ) { using the concept of sets here ) = 945 think : why did i say the method is approximate in some cases ? think what happens if the given range is 11 to 1010 both inclusive ( again 1000 numbers ) what is the number of multiples in this case ? e"
Answer: e
Question (gain): arun makes a popular brand of ice cream in a rectangular shaped bar 6 cm long , 5 cm wide and 2 cm thick . to cut costs , the company had decided to reduce the volume of the bar by 19 % . the thickness will remain same , but the length and width will be decreased by some percentage . the new width will be ,
Options: a ) 33 , b ) 87 , c ) 99 , d ) 367 , e ) 72
Rationale: answer : a
Answer: a
Question (physics): kim finds a 5 - meter tree branch and marks it off in thirds and fifths . she then breaks the branch along all the markings and removes one piece of every distinct length . what fraction of the original branch remains ?
Options: a ) 8 / 15 , b ) 1 / 2 , c ) 7 / 5 , d ) 3 / 5 , e ) 7 / 5
Rationale: "3 pieces of 1 / 5 length and two piece each of 1 / 15 and 2 / 15 lengths . removing one piece each from pieces of each kind of lengths the all that will remain will be 2 pieces of 1 / 5 i . e 2 / 5 , 1 piece of 1 / 15 , and 1 piece of 2 / 15 which gives us 2 / 5 + 1 / 15 + 2 / 15 - - - - - > 3 / 5 answer is d"
Answer: d
Question (general): mark bought a set of 6 flower pots of different sizes at a total cost of $ 8.25 . each pot cost 0.1 more than the next one below it in size . what was the cost , in dollars , of the largest pot ?
Options: a ) $ 1.62 , b ) $ 1.85 , c ) $ 2.00 , d ) $ 2.15 , e ) $ 2.30
Rationale: "this question can be solved with a handful of different algebra approaches ( as has been shown in the various posts ) . since the question asks for the price of the largest pot , and the answers are prices , we can test the answers . we ' re told that there are 6 pots and that each pot costs 25 cents more than the next . the total price of the pots is $ 8.25 . we ' re asked for the price of the largest ( most expensive ) pot . since the total price is $ 8.25 ( a 10 - cent increment ) and the the difference in sequential prices of the pots is 10 cents , the largest pot probably has a price that is a 10 - cent increment . from the answer choices , i would then test answer a first if . . . . the largest pot = $ 1.625 1.125 1.225 1.325 1.425 1.525 1.625 total = $ 8.25 so this must be the answer . a"
Answer: a
Question (general): in the above number , a and b represent the tens and units digits , respectively . if the above number is divisible by 45 , what is the greatest possible value of b x a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 20
Rationale: "i also was confused when i was looking forabove number : d as far as i understood , 45 is a factor of ab . in other words , the values of b ( units digits can be 5 or 0 . better to have option for 5 in this case to havebigger result ) . now let ' s try 45 x 1 ( a = 4 , b = 5 respectively we have = 20 ) . this is the greatest possible value of b x a . imo e ."
Answer: e
Question (gain): the profit obtained by selling an article for rs . 57 is the same as the loss obtained by selling it for rs . 43 . what is the cost price of the article ?
Options: a ) rs . 40 , b ) rs . 50 , c ) rs . 49 , d ) rs . 59 , e ) none of these
Rationale: "s . p 1 - c . p = c . p – s . p 2 57 - c . p = c . p - 43 2 c . p = 57 + 43 ; c . p = 100 / 2 = 50 answer : b"
Answer: b
Question (gain): in 2008 , the profits of company n were 8 percent of revenues . in 2009 , the revenues of company n fell by 20 percent , but profits were 15 percent of revenues . the profits in 2009 were what percent of the profits in 2008 ?
Options: a ) 150 % , b ) 105 % , c ) 120 % , d ) 124.2 % , e ) 138 %
Rationale: "the profit 0 f 2009 interms of 2008 = 0.8 * 15 / 8 * 100 = 150 % a"
Answer: a
Question (physics): a garrison of 2000 men has provisions for 54 days . at the end of 15 days , a reinforcement arrives , and it is now found that the provisions will last only for 20 days more . what is the reinforcement ?
Options: a ) 1778 , b ) 1682 , c ) 9178 , d ) 1900 , e ) 1782
Rationale: "2000 - - - - 54 2000 - - - - 39 x - - - - - 20 x * 20 = 2000 * 39 x = 3900 2000 - - - - - - - 1900 answer : d"
Answer: d
Question (general): if a bicyclist in motion increases his speed by 30 percent and then increases this speed by 10 percent , what percent of the original speed is the total increase in speed ?
Options: a ) 10 % , b ) 40 % , c ) 43 % , d ) 64 % , e ) 140 %
Rationale: let the sped be 100 an increase of 30 % the speed now is 130 a further increase of 10 % on 130 = 13 total increase = 43 on 100 = 43 % c
Answer: c
Question (general): what is the greatest number that divides 263 , 935 and 1383 leaving a remainder of 7 in each case ?
Options: a ) 30 , b ) 31 , c ) 32 , d ) 35 , e ) 37
Rationale: answer the required greatest number is the hcf of 263 - 7 , 935 - 7 , 1383 - 7 i . e . 256 , 928 and 1376 hcf = 32 correct option : c
Answer: c
Question (physics): how many seconds will a 900 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 ) 36 , c ) 54 , d ) 11 , e ) 18
Rationale: "explanation : here distance d = 900 mts speed s = 63 - 3 = 60 kmph = 60 x 5 / 18 m / s time t = = 54 sec . answer : c"
Answer: c
Question (general): find the average of all the numbers between 6 and 38 which are divisible by 4 .
Options: a ) 18 , b ) 22 , c ) 20 , d ) 30 , e ) 28
Rationale: "solution average = ( ( 8 + 12 + 16 + 20 + 24 + 28 + 32 + 36 ) / 8 ) = 186 / 7 = 22 answer b"
Answer: b
Question (gain): if the cost price is 96 % of sp then what is the profit %
Options: a ) 4.07 % , b ) 4 % , c ) 4.7 % , d ) 4.17 % , e ) 4.27 %
Rationale: "sol . sp = rs 100 : then cp = rs 96 : profit = rs 4 . profit = { ( 4 / 96 ) * 100 } % = 4.17 % answer is d ."
Answer: d
Question (physics): a car gets 27 miles to the gallon . if it is modified to use a solar panel , it will use only 75 percent as much fuel as it does now . if the fuel tank holds 14 gallons , how many more miles will the car be able to travel , per full tank of fuel , after it has been modified ?
Options: a ) 120 , b ) 126 , c ) 132 , d ) 138 , e ) 144
Rationale: "originally , the distance the car could go on a full tank was 14 * 27 = 378 miles . after it has been modified , the car can go 27 / 0.75 = 36 miles per gallon . on a full tank , the car can go 14 * 36 = 504 miles , thus 126 miles more . the answer is b ."
Answer: b
Question (physics): a fort had provision of food for 150 men for 45 days . after 10 days , 25 men left the fort . the number of days for which the remaining food will last , is :
Options: a ) 34 , b ) 387 , c ) 42 , d ) 28 , e ) 71
Rationale: "explanation : after 10 days : 150 men had food for 35 days . suppose 125 men had food for x days . now , less men , more days ( indirect proportion ) { \ color { blue } \ therefore } 125 : 150 : : 35 : x { \ color { blue } \ rightarrow } 125 x x = 150 x 35 { \ color { blue } \ rightarrow x = \ frac { 150 \ times 35 } { 125 } } { \ color { blue } \ rightarrow } x = 42 . answer : c ) 42"
Answer: c
Question (gain): a person lent a certain sum of money at 4 % per annum at simple interest and in 8 years the interest amounted to rs . 306 less than the sum lent . what was the sum lent ?
Options: a ) 228 , b ) 278 , c ) 289 , d ) 500 , e ) 450
Rationale: "p - 306 = ( p * 4 * 8 ) / 100 p = 450 answer : e"
Answer: e
Question (general): a man has some hens and cows . if the number of heads be 50 and the number of feet equals 144 , then the number of hens will be
Options: a ) 22 , b ) 24 , c ) 26 , d ) 20 , e ) 28
Rationale: "explanation : let number of hens = h and number of cows = c number of heads = 50 = > h + c = 48 - - - ( equation 1 ) number of feet = 144 = > 2 h + 4 c = 144 = > h + 2 c = 72 - - - ( equation 2 ) ( equation 2 ) - ( equation 1 ) gives 2 c - c = 72 - 50 = > c = 22 substituting the value of c in equation 1 , we get h + 22 = 50 = > h = 50 - 22 = 28 i . e . , number of hens = 28 answer : e"
Answer: e
Question (gain): because he ’ s taxed by his home planet , mork pays a tax rate of 40 % on his income , while mindy pays a rate of only 30 % on hers . if mindy earned 3 times as much as mork did , what was their combined tax rate ?
Options: a ) 32.5 % , b ) 34 % , c ) 35 % , d ) 36 % , e ) 37.5 %
Rationale: "say morks income is - 100 so tax paid will be 40 say mindy ' s income is 3 * 100 = 300 so tax paid is 30 % * 300 = 90 total tax paid = 40 + 90 = 130 . combined tax % will be 130 / 100 + 300 = 32.5 % answer : a"
Answer: a
Question (gain): a watch was sold at a loss of 5 % . if it was sold for rs . 500 more , there would have been a gain of 5 % . what is the cost price ?
Options: a ) 1000 , b ) 2998 , c ) 2778 , d ) 2788 , e ) 2991
Rationale: "95 % 105 % - - - - - - - - 10 % - - - - 500 100 % - - - - ? = > rs . 5000 answer : d"
Answer: d
Question (physics): a car travels at a speed of 65 miles per hour . how far will it travel in 6 hours ?
Options: a ) 125 miles , b ) 225 miles , c ) 390 miles , d ) 425 miles , e ) 525 miles
Rationale: "during each hour , the car travels 65 miles . for 6 hours it will travel 65 + 65 + 65 + 65 + 65 + 65 = 6 × 65 = 390 miles correct answer is c ) 390 miles"
Answer: c
Question (other): in a family 13 people eat only vegetarian , 7 people eat only non veg . , 8 people eat both veg and non veg . . how many people eat veg in the family ?
Options: a ) 20 , b ) 11 , c ) 9 , d ) 31 , e ) 21
Rationale: "total people eat veg = only veg + both veg and non veg total = 13 + 8 = 21 answer = e"
Answer: e
Question (general): if p / q = 4 / 5 , then the value of 11 / 7 + { ( 2 q - p ) / ( 2 q + p ) } is ?
Options: a ) 3 / 7 , b ) 34 , c ) 1 , d ) 2 , e ) 3
Rationale: answer given exp . = 11 / 7 + { ( 2 q - p ) / ( 2 q + p ) } dividing numerator as well as denominator by q , exp = 11 / 7 + { 2 - p / q ) / ( 2 + p / q ) } = 11 / 7 + { ( 2 - 4 / 5 ) / ( 2 + 4 / 5 ) } = 11 / 7 + 6 / 14 = 11 / 7 + 3 / 7 = 14 / 7 = 2 correct option : d
Answer: d
Question (general): if x ^ 2 + y ^ 2 = 13 and xy = 3 , then ( x − y ) ^ 2 =
Options: a ) 7 , b ) 11 , c ) 14 , d ) 17 , e ) 20
Rationale: "but you can not take xy + 3 to mean xy = - 3 . . only if xy + 3 = 0 , it will mean xy = - 3 . . rest your solution is perfect and you will get your correct answer as 13 - 2 * 3 = 7 . . answer a"
Answer: a
Question (general): a big container is 40 % full with water . if 14 liters of water is added , the container becomes 3 / 4 full . what is the capacity of the big container in liters ?
Options: a ) 32 , b ) 36 , c ) 40 , d ) 44 , e ) 48
Rationale: 14 liters is 35 % of the capacity c . 14 = 0.35 c c = 14 / 0.35 = 40 liters . the answer is c .
Answer: c
Question (other): the ratio of the arithmetic mean of two numbers to one of the numbers is 5 : 8 . what is the ratio of the smaller number to the larger number ?
Options: a ) 1 : 8 , b ) 1 : 6 , c ) 1 : 5 , d ) 1 : 4 , e ) 1 : 3
Rationale: "for two numbers , the arithmetic mean is the middle of the two numbers . the ratio of the mean to the larger number is 5 : 8 , thus the smaller number must have a ratio of 2 . the ratio of the smaller number to the larger number is 2 : 8 = 1 : 4 . the answer is d ."
Answer: d
Question (other): the salaries of a , b , and c are in the ratio of 1 : 2 : 3 . the salary of b and c together is rs . 6000 . by what percent is the salary of c more than that of a ?
Options: a ) 209 % , b ) 200 % , c ) 290 % , d ) 600 % , e ) 100 %
Rationale: explanation : let the salaries of a , b , c be x , 2 x and 3 x respectively . then , 2 x + 3 x = 6000 = > x = 1200 . a ' s salary = rs . 1200 , b ' s salary = rs . 2400 , and cs salary rs . 3600 . excess of c ' s salary over a ' s = [ ( 2400 / 1200 ) x 100 ] = 200 % . answer : b ) 200 %
Answer: b
Question (physics): a man swims downstream 96 km and upstream 40 km taking 8 hours each time ; what is the speed of the current ?
Options: a ) 3.5 kmph , b ) 1.5 kmph , c ) 13 kmph , d ) 6.5 kmph , e ) 7 : 3 kmph
Rationale: "explanation : 96 - - - 8 ds = 12 ? - - - - 1 40 - - - - 8 us = 5 ? - - - - 1 s = ? s = ( 12 - 5 ) / 2 = 3.5 answer : option a"
Answer: a
Question (physics): vinoth can complete a painting work in 20 days . prakash can do the same work in 25 days . they start the work together but vinoth quit after 3 days of work . how many days are required to complete the remaining painting work by prakash .
Options: a ) 15.25 days , b ) 16.25 days , c ) 17.25 days , d ) 18.25 days , e ) 19.25 days
Rationale: vinoth can complete the painting work in one day is 1 / 20 prakash can complete the same work in one day is 1 / 25 both of them can complete the work in 1 / 20 + days = 9 / 100 ( 1 / 20 + 1 / 25 ) they must have completed in three days = 9 / 100 * 3 = 27 / 100 remaining work to be done is by prakash = 1 - 27 / 100 = 73 / 100 for one work , prakash can do in 25 days for 73 / 100 work , he can do in 73 / 100 * 25 = 73 / 4 days or 18.25 days answer : d
Answer: d
Question (general): the total cost of a vacation was divided among 3 people . if the total cost of the vacation had been divided equally among 5 people , the cost per person would have been $ 50 less . what was the total cost cost of the vacation ?
Options: a ) $ 200 , b ) $ 375 , c ) $ 400 , d ) $ 500 , e ) $ 600
Rationale: c for cost . p price per person . c = 3 * p c = 5 * p - 250 substituting the value of p from the first equation onto the second we get p = 125 . plugging in the value of p in the first equation , we get c = 375 . which leads us to answer choice b
Answer: b
Question (gain): how many ounces of a 60 % salt solution must be added to 30 ounces of a 20 percent salt solution so that the resulting mixture is 40 % salt ?
Options: a ) 16.67 , b ) 30 , c ) 50 , d ) 60.33 , e ) 70
Rationale: "let x = ounces of 60 % salt solution to be added . 2 * 30 + . 6 x = . 4 ( 30 + x ) x = 30 answer b"
Answer: b
Question (gain): if 20 % of a is the same as 30 % of b , then a : b is :
Options: a ) 5 : 4 , b ) 5 : 3 , c ) 4 : 3 , d ) 3 : 2 , e ) 1 : 3
Rationale: "expl : 20 % of a i = 30 % of b = 20 a / 100 = 30 b / 100 = 3 / 2 = 3 : 2 answer : d"
Answer: d
Question (geometry): d and e are two points respectively on sides ab and ac of triangle abc such that de is parallel to bc . if the ratio of area of triangle ade to that of the trapezium decb is 144 : 25 and bc = 13 cm , then find the length of de .
Options: a ) 12 , b ) 13 , c ) 14 , d ) 11 , e ) 15
Rationale: "abc and ade are similar triangles . so ( side of abc / side of ade ) ^ 2 = 25 / 169 side of abc / side of ade = 5 / 13 so the length of de = 5 answer - c"
Answer: c