Cheukting/mathqa huggingface dataset:
Question (physics): a can complete a project in 20 days and b can complete the same project in 40 days . if a and b start working on the project together and a quits 10 days before the project is completed , in how many days will the project be completed ?
Options: a ) 18 days , b ) 20 days , c ) 26.67 days , d ) 16 days , e ) 12 days
Rationale: "let x = the number of days taken to complete the project . the amount of work done by a is ( x - 10 ) * ( 1 / 20 ) . the amount of work done by b is ( x ) * ( 1 / 40 ) . ( 1 / 20 ) * ( x - 10 ) + ( 1 / 40 ) * ( x ) = 1 ( x / 20 ) + ( x / 40 ) - ( 10 / 20 ) = 1 3 x / 40 = 3 / 2 x = 20 therefore , the answer is b : 20 ."
Answer: b
Question (general): . 005 / ? = . 01
Options: a ) . 5 , b ) . 05 , c ) . 005 , d ) . 0005 , e ) none of them
Rationale: "let . 005 / x = . 01 ; then x = . 005 / . 01 = . 5 / 1 = . 5 answer is a"
Answer: a
Question (physics): the sum of two consecutive integers is 51 . find the numbers .
Options: a ) 17 , 18 , b ) 7 , 8 , c ) 5 , 6 , d ) 1 , 2 , e ) 25,26
Rationale: "n + ( n + 1 ) = 51 2 n + 1 = 51 2 n = 50 n = 25 answer : e"
Answer: e
Question (physics): a can finish a work in 12 days and b can do same work in half the time taken by a . then working together , what part of same work they can finish in a day ?
Options: a ) 1 / 4 , b ) 1 / 6 , c ) 1 / 7 , d ) 1 / 8 , e ) none of these
Rationale: "explanation : please note in this question , we need to answer part of work for a day rather than complete work . it was worth mentioning here because many do mistake at this point in hurry to solve the question so lets solve now , a ' s 1 day work = 1 / 12 b ' s 1 day work = 1 / 6 [ because b take half the time than a ] ( a + b ) ' s one day work = ( 1 / 12 + 1 / 6 ) = 1 / 4 so in one day 1 / 4 work will be done answer : a"
Answer: a
Question (physics): a train speeds past a pole in 25 seconds and a platform 150 m long in 30 seconds . its length is ?
Options: a ) 23 , b ) 22 , c ) 21 , d ) 30 , e ) 19
Rationale: "let the length of the train be x meters and its speed be y m / sec . they , x / y = 25 = > y = x / 25 ( x + 150 ) / 30 = x / 25 x = 30 m . answer : d"
Answer: d
Question (general): the sum of all the digits of the integers from 18 to 21 inclusive is 24 ( 1 + 8 + 1 + 9 + 2 + 0 + 2 + 1 = 24 ) . what is the sum e of all the digits of the integers from 0 to 99 inclusive ?
Options: a ) 450 , b ) 810 , c ) 900 , d ) 1000 , e ) 1100
Rationale: we want the sum of the digits from 0 to 99 , so i approximated : 0 - 9 - > 45 - > ( 9 + 0 ) * 10 / 2 40 - 49 - > 85 ( 13 + 4 ) * 10 / 2 90 - 99 - > 135 ( 18 + 9 ) * 10 / 2 we can see at a glance that theweightgoes up as the numbers go up ( meaning the difference between 85 and 45 is 40 , while 135 - 85 is 50 , this means that the second part of this sequence carries more weight for our result ) , so we know that the final answer has to be more than 850 ( 85 * 10 ) but close to it , and that ' s just e = 900 : the answer is c .
Answer: c
Question (general): if m is the average ( arithmetic mean ) of the first 10 positive multiples of 3 and if m is the median of the first 10 positive multiples of 3 , what is the value of m – m ?
Options: a ) – 5 , b ) 5 , c ) 0 , d ) 25 , e ) 27.5
Rationale: the first 10 positive multiples of 3 is an evenly spaced set . one of the most important properties of evenly spaced set ( aka arithmetic progression ) is : in any evenly spaced set the arithmetic mean ( average ) is equal to the median . hence m = m - - > m - m = 0 . answer : c .
Answer: c
Question (general): subtracting 3 % of a from a is equivalent to multiplying a by how much ?
Options: a ) 0.97 , b ) 9.4 , c ) 0.094 , d ) 94 , e ) none
Rationale: "answer let a - 3 % of a = ab . ⇒ ( 97 x a ) / 100 = ab ∴ b = 0.97 correct option : a"
Answer: a
Question (other): sachin is older than rahul by 7 years . if the ratio of their ages is 11 : 9 , find the age of sachin
Options: a ) 24.5 , b ) 24.8 , c ) 38.5 , d ) 24.88 , e ) 24.19
Rationale: explanation : if rahul age is x , then sachin age is x + 7 , so , 9 x + 63 = 11 x 2 x = 63 x = 31.5 so sachin age is 31.5 + 7 = 38.5 answer : c ) 38.5
Answer: c
Question (general): when a certain number x is divided by 61 , the remainder is 24 . what is the remainder when x is divided by 5 ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "when a certain number x is divided by 61 , the remainder is 24 . what is the remainder when x is divided by 5 ? putting a value say x = 24 we get remainder as 24 when divided by 61 . when 24 divided by 5 we get 4 as remainder . c is the answer ."
Answer: c
Question (general): solve below question 2 x + 1 = - 19
Options: a ) - 8 , b ) - 9 , c ) 9 , d ) 8 , e ) - 10
Rationale: "2 x + 1 = - 19 x = - 10 e"
Answer: e
Question (physics): a train 150 m long can cross an electric pole in 3 sec and then find the speed of the train ?
Options: a ) 180 , b ) 120 , c ) 72 , d ) 27 , e ) 28
Rationale: "length = speed * time speed = l / t s = 150 / 3 s = 50 m / sec speed = 50 * 18 / 5 ( to convert m / sec in to kmph multiply by 18 / 5 ) speed = 180 kmph answer : a"
Answer: a
Question (general): approximately how many revolutions will be made by a car tire with a 10 - inch diameter if the car travels 1 ⁄ 2 mile ?
Options: a ) 120 , b ) 180 , c ) 1003 , d ) 1000 , e ) 1,440
Rationale: "diameter of car tire = 10 inches radius of car tire = 5 inches = 5 * 2.54 cm = 12.7 cm circumference of the car tire = 2 * pi * 12.7 = 2 * 3.14 * 12.7 = 79.76 cm distance traveled by car = . 5 mile = . 5 * 1.6 km = . 8 km = 800 m = 8 * 10 ^ 4 cm number of revolutions = distance traveled / circumference of tire = 8 * 10 ^ 4 / 79.76 = 1003 since the answer choices are far apart we should use estimation in this question . ideally , in the gmat the conversion between units would be provided . answer c"
Answer: c
Question (general): calculate the share of z , if rs . 3720 is divided among x , y and z in the ratio 7 : 8 : 11 ?
Options: a ) 1564.1 , b ) 1214.1 , c ) 1574.1 , d ) 1271.1 , e ) 1044.1
Rationale: 7 + 8 + 11 = 26 3720 / 26 = 143.1 so z ' s share = 11 * 143.1 answer : c
Answer: c
Question (geometry): the area of a triangle is with base 18 m and height 6 m ?
Options: a ) 88 m 2 , b ) 10 m 2 , c ) 66 m 2 , d ) 54 m 2 , e ) 31 m 2
Rationale: "1 / 2 * 18 * 6 = 54 m 2 answer : d"
Answer: d
Question (gain): if a population of women in a town is 50 % of men . what is the population of men as a % of population of women ?
Options: a ) 200 % , b ) 100 % , c ) 50 % , d ) 65 % , e ) 110 %
Rationale: "we ' re told that the number of women in a town is equal to 50 % of the number of men in that town . if . . . . men = 10 women = 5 we ' re asked for the number of men , as a percentage of the number of women . m / w = 10 / 5 = 2 = 200 % answer is a"
Answer: a
Question (physics): 225 mtrs long yard , 26 trees are palnted at equal distances , one tree being at each end of the yard . what is the distance between 2 consecutive trees ?
Options: a ) 10 , b ) 12 , c ) 14 , d ) 16 , e ) 18
Rationale: 26 trees have 25 gaps between them , required distance ( 225 / 25 ) = 10 a
Answer: a
Question (other): in a circuit board factory , all circuit boards that pass a verification process are certified . every board that fails the verification process is indeed faulty , but 1 / 8 of those that pass are also faulty . approximately how many faulty circuit boards exist in a group of 3,200 circuit boards where 64 fail inspection ?
Options: a ) 72 , b ) 192 , c ) 456 , d ) 256 , e ) 264
Rationale: total of 3,200 boards . all that fail verification are indeed faulty . so the 64 are indeed faulty . 1 / 8 those that pass are also faulty . from the 3,200 we know 64 fail . so 3,136 must pass . of these 1 / 8 are faulty . 3,136 divided by 8 gives you 392 . what one must do now is to add to the 392 which were not detected the actually detected faulty ones , namely the 64 . total faulty : 456 . answer : c
Answer: c
Question (physics): the rate of spin of a certain gyroscope doubled every 15 seconds from the moment a particular stopwatch started . if after a minute and a half the gyroscope reached a speed of 400 meters per second , what was the speed , in meters per second , when the stopwatch was started ?
Options: a ) 25 / 2 , b ) 25 / 4 , c ) 25 / 8 , d ) 25 / 16 , e ) 25 / 32
Rationale: "let x be the original speed when the stopwatch was started . in 90 seconds , the speed doubled 6 times . 2 ^ 6 * x = 400 x = ( 2 ^ 4 * 25 ) / 2 ^ 6 = 25 / 4 the answer is b ."
Answer: b
Question (geometry): the area of a parallelogram is 288 sq m and its altitude is twice the corresponding base . then the length of the base is ?
Options: a ) 12 , b ) 9 , c ) 7 , d ) 6 , e ) 5
Rationale: "2 x * x = 288 = > x = 12 answer : a"
Answer: a
Question (general): robert ' s salary was increased by 50 % and subsequently decreased by 10 % . how much percentage does he gain ?
Options: a ) 15 % , b ) 20 % , c ) 10 % , d ) 25 % , e ) 30 %
Rationale: let original salary be $ 100 increased salary = 10 % of ( 150 % of $ 100 ) = ( 10 / 100 ) * ( 150 / 100 ) * 100 = $ 15 increase = 15 % correct option is a
Answer: a
Question (general): the average ( arithmetic mean ) of 7 , 8 , 10 and 11 equals the average of 2 , 9 , 13 , and
Options: a ) 7 , b ) 9 , c ) 10 , d ) 12 , e ) 13
Rationale: "7 + 8 + 10 + 11 = 2 + 9 + 13 + x 36 = 24 + x or , x = 12 hence , answer will be ( d ) 12"
Answer: d
Question (general): a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 29.16 , the number of the member is the group is :
Options: a ) 57 , b ) 54 , c ) 77 , d ) 87 , e ) 97
Rationale: money collected = ( 29.16 x 100 ) paise = 29.16 paise numbers of members = 2916 squareroot = 54 answer b
Answer: b
Question (gain): a dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg , what is his percent ?
Options: a ) 25 % , b ) 25 % , c ) 29 % , d ) 55 % , e ) 45 %
Rationale: "800 - - - 200 100 - - - ? = > 25 % answer : b"
Answer: b
Question (general): the average weight of 8 person ' s increases by 2.5 kg when a new person comes in place of one of them weighing 66 kg . what might be the weight of the new person ?
Options: a ) 56 kg , b ) 90 kg , c ) 86 kg , d ) data inadequate , e ) none of these
Rationale: "c 86 kg total weight increased = ( 8 x 2.5 ) kg = 20 kg . weight of new person = ( 66 + 20 ) kg = 86 kg ."
Answer: c
Question (general): if ( 5 ^ 9 ) ( 9 ^ 5 ) = 3 ( 15 ^ x ) , what is the value of x ?
Options: a ) 7 , b ) 9 , c ) 11 , d ) 13 , e ) 15
Rationale: "( 5 ^ 9 ) ( 9 ^ 5 ) = 3 ( 15 ^ x ) = > 5 ^ 9 * 3 ^ 10 = 3 * 3 ^ x * 5 ^ x = > 5 ^ 9 * 3 ^ 10 = 3 ^ ( x + 1 ) * 5 ^ x value of x = 9 answer b"
Answer: b
Question (physics): a boat having a length 8 m and breadth 2 m is floating on a lake . the boat sinks by 1 cm when a man gets on it . the mass of the man is :
Options: a ) 12 kg , b ) 60 kg , c ) 72 kg , d ) 160 kg , e ) none of these
Rationale: "explanation : volume of water displaced = ( 8 x 2 x 0.01 ) m 3 = 0.16 m 3 . ∴ mass of man = volume of water displaced x density of water = ( 0.16 x 1000 ) kg = 160 kg . answer : d"
Answer: d
Question (general): what is the sum between the place values of two 3 ' s in the numeral 63130
Options: a ) 3111 , b ) 300 , c ) 3029 , d ) 3030 , e ) 3003
Rationale: required sum = 3000 + 30 = 3030 answer is d
Answer: d
Question (physics): lloyd normally works 7.5 hours per day and earns $ 4.00 per hour . for each hour he works in excess of 7.5 hours on a given day , he is paid 1.5 times his regular rate . if lloyd works 10.5 hours on a given day , how much does he earn for that day ?
Options: a ) $ 33.75 , b ) $ 48.00 , c ) $ 51.75 , d ) $ 54.00 , e ) $ 70.00
Rationale: "daily working hour * regular rate + overtime * increased rate 7.5 * 4.0 + 3 * 4.0 * 1.5 = 48 answer b"
Answer: b
Question (general): the average weight of 20 boys in a class is 50.25 kg and that of the remaining 8 boys is 45.15 kg . find the average weights of all the boys in the class .
Options: a ) 48.79286 , b ) 42.25 , c ) 50.87364 , d ) 51.25 , e ) 52.25474
Rationale: "explanation : average weight of 20 boys = 50.25 total weight of 20 boys = 50.25 × 20 average weight of remaining 8 boys = 45.15 total weight of remaining 8 boys = 45.15 × 8 total weight of all boys in the class = ( 50.25 × 20 ) + ( 45.15 × 8 ) total boys = 20 + 8 = 28 average weight of all the boys = ( 50.25 × 20 ) + ( 45.15 × 8 ) / 28 = answer : option a"
Answer: a
Question (general): what is the difference between the c . i . on rs . 9000 for 1 1 / 2 years at 4 % per annum compounded yearly and half - yearly ?
Options: a ) s . 2.04 , b ) s . 2.08 , c ) s . 3.67 , d ) s . 2.83 , e ) s . 2.42
Rationale: c . i . when interest is compounded yearly = [ 9000 * ( 1 + 4 / 100 ) * ( 1 + ( 1 / 2 * 4 ) / 100 ] = 9000 * 26 / 25 * 51 / 50 = rs . 9547.2 c . i . when interest is compounded half - yearly = [ 9000 * ( 1 + 2 / 100 ) 2 ] = ( 9000 * 51 / 50 * 51 / 50 * 51 / 50 ) = rs . 9550.87 difference = ( 9550.87 - 9547.2 ) = rs . 3.67 . answer : c
Answer: c
Question (physics): a tank is filled by 3 pipes a , b , c in 3 hours . pipe c is twice as fast as b and b is twice as fast as a . how much will pipe a alone take to fill the tank ?
Options: a ) 25 hr , b ) 35 hr , c ) 40 hr , d ) 20 hr , e ) 21 hr
Rationale: "suppose pipe a alone take x hours to fill the tank then pipe b and c will take x / 2 and x / 4 hours respectively to fill the tank . 1 / x + 2 / x + 4 / x = 1 / 3 7 / x = 1 / 3 x = 21 hours answer is e"
Answer: e
Question (other): a girl multiplies 987 by a certain number and obtains 559981 as her answer . if in the answer , both 9 ’ s are wrong but the other digits are correct , then the correct answer will be
Options: a ) 553681 , b ) 555181 , c ) 555681 , d ) 556581 , e ) none of these
Rationale: 987 = 3 x 7 x 47 . so , required number must be divisible by each one of 3 , 7 , 47 . none of the numbers in 553681 and 555181 are divisible by 3 . while 556581 is not divisible by 7 . correct answer is 555681 . answer : c
Answer: c
Question (general): subash can copy 50 pages in 10 hrs . subash and prakash together can copy 300 pages in 40 hours . in how much time prakash can copy 20 pages .
Options: a ) 8 , b ) 10 , c ) 12 , d ) 14 , e ) 16
Rationale: "subhas ' s 1 hr copy page = 50 / 10 = 5 page ( subhas + prakash ) ' s 1 hr copy page = 300 / 40 = 7.5 page from above prakash ' s 1 hr copy page = 2.5 page so time taken in 20 page ' s copy = ( 20 / 2.5 ) = 8 hrs answer : a"
Answer: a
Question (general): a couple spent $ 198 in total while dining out and paid this amount using a credit card . the $ 198 figure included a 20 percent tip which was paid on top of the price which already included a sales tax of 10 percent on top of the price of the food . what was the actual price of the food before tax and tip ?
Options: a ) $ 130 , b ) $ 140 , c ) $ 150 , d ) $ 160 , e ) $ 170
Rationale: let the price of the meal be x . after a 10 % sales tax addition , the price is 1.1 * x after a 20 % tip on this amount , the total is 1.2 * 1.1 * x = 1.32 x 1.32 x = 198 x = $ 150 the correct answer is c .
Answer: c
Question (general): in an election , candidate douglas won 58 percent of the total vote in counties x and y . he won 64 percent of the vote in county x . if the ratio of people who voted in county x to county y is 2 : 1 , what percent of the vote did candidate douglas win in county y ?
Options: a ) 15 % , b ) 18 % , c ) 25 % , d ) 36 % , e ) 46 %
Rationale: "given voters in ratio 2 : 1 let x has 200 votersy has 100 voters for x 64 % voted means 64 * 200 = 128 votes combined for xy has 300 voters and voted 58 % so total votes = 174 balance votes = 174 - 128 = 46 as y has 100 voters so 46 votes means 46 % of votes required ans e"
Answer: e
Question (general): if x is an integer and 2.134 × 10 ^ x is less than 21,000 , what is the greatest possible value for x ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 4 , e ) 3
Rationale: "x is an integer and 2.134 × 10 x is less than 21,000 , what is the greatest possible value for x ? for 2.134 × 10 x is less than 21,000 to remain true , the greatest number is 2,134 , which makes x = 3 e . 3"
Answer: e
Question (physics): a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 4 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ? a . 480 liters
Options: a ) 480 , b ) 489 , c ) 486 , d ) 482 , e ) 483
Rationale: 1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 4 = 480 answer : a
Answer: a
Question (general): what is the units digit of ( 147 ^ 17 ) ^ 48 ?
Options: a ) 1 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: the units digit of the exponents of 7 repeat in a cycle of four , which is { 7,9 , 3,1 } . the number 17 has the form 4 n + 1 so the units digit is 7 inside the bracket . the exponent 48 has the form 4 n , so the units digit is 1 . the answer is a .
Answer: a
Question (physics): from an island , it is possible to reach the mainland by either ferry p or ferry q . ferry p travels for 3 hours at 8 kilometers per hour , while ferry q takes a route that is two times longer . if ferry p is slower than ferry q by 4 kilometers per hour , how many hours longer is the journey of ferry q compared with the journey of ferry p ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "the distance traveled by ferry p is 24 km . then the distance traveled by ferry q is 48 km . ferry q travels at a speed of 12 kph . the time of the journey for ferry q is 48 / 12 = 4 hours , which is 1 hour more than ferry p . the answer is a ."
Answer: a
Question (physics): find the cost of fencing around a circular field of diameter 39 m at the rate of rs . 1.50 a meter ?
Options: a ) 287 , b ) 132 , c ) 156 , d ) 158 , e ) 128.73
Rationale: "2 * 22 / 7 * 19.5 = 122.6 122.6 * 1 1 / 2 = rs . 128.73 answer : e"
Answer: e
Question (general): the average weight of a group of persons increased from 48 kg to 51 kg , when two persons weighing 78 kg and 93 kg join the group . find the initial number of members in the group ?
Options: a ) 87 , b ) 67 , c ) 23 , d ) 75 , e ) 25
Rationale: let the initial number of members in the group be n . initial total weight of all the members in the group = n ( 48 ) from the data , 48 n + 78 + 93 = 51 ( n + 2 ) = > 51 n - 48 n = 69 = > n = 23 therefore there were 23 members in the group initially . answer : c
Answer: c
Question (general): in δ pqs above , if pq = 4 and ps = 5 , then
Options: a ) 9 / 4 , b ) 12 / 5 , c ) 16 / 5 , d ) 15 / 4 , e ) 10 / 3
Rationale: "there are two ways to calculate area of pqs . area remains same , so both are equal . 4 * 5 / 2 = pr * 6 / 2 pr = 10 / 3 e"
Answer: e
Question (physics): convert 0.34 in to a vulgar fraction ?
Options: a ) 18 / 50 , b ) 16 / 50 , c ) 17 / 50 , d ) 19 / 50 , e ) none
Rationale: "answer 0.34 = 34 / 100 = 17 / 50 correct option : c"
Answer: c
Question (general): dhoni bought 5 toys with the average cost of $ 10 . if david also buys the sixth toy with the price of $ 16 , what is the average ( arithmetic mean ) price of those 6 toys ?
Options: a ) $ 10 , b ) $ 7 , c ) $ 8.5 , d ) $ 9 , e ) $ 11
Rationale: 5 toys - > total cost = 5 * avg cost = 5 * 10 = 50 sixth toy cost = 16 total cost for 6 toys = 50 + 16 = 66 am = 66 / 6 = 11 hence e
Answer: e
Question (physics): a train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds . what is the length of the train in meters ?
Options: a ) 400 meters , b ) 1111 meters , c ) 1777 meters , d ) 1822 meters , e ) none of these
Rationale: "relative speed of the train with respect to the motorbike should be the speed with which the length of the train is covered in 40 secs . calculate the relative speed = > 100 - 64 = 36 kmph and time is 40 sec = 40 / 3600 hrs distance ( in this case the length of the train ) = s * t = 36 * 40 / 3600 . 4 km or 400 meters . so answer ( a )"
Answer: a
Question (physics): a train running at a speed of 36 kmph crosses an electric pole in 12 seconds . in how much time will it cross a 350 m long platform ?
Options: a ) 44 sec , b ) 49 sec , c ) 42 sec , d ) 47 sec , e ) none of these
Rationale: "let the length of the train be x m . when a train crosses an electric pole , the distance covered is its own length . so , x = 12 * 36 * 5 / 18 m = 120 m . time taken to cross the platform = ( 120 + 350 ) / 36 * 5 / 18 = 47 min . answer : d"
Answer: d
Question (general): gold is 10 times as heavy as water and copper is 6 times as heavy as water . in what ratio should these be mixed to get an alloy 8 times as heavy as water ?
Options: a ) 3 : 2 , b ) 1 : 1 , c ) 3 : 1 , d ) 5 : 2 , e ) 4 : 3
Rationale: "g = 10 w c = 6 w let 1 gm of gold mixed with x gm of copper to get 1 + x gm of the alloy 1 gm gold + x gm copper = x + 1 gm of alloy 10 w + 6 wx = x + 1 * 8 w 10 + 6 x = 8 ( x + 1 ) x = 1 / 1 ratio of gold with copper = 1 : 1 = 1 : 1 answer is b"
Answer: b
Question (geometry): points a , b , and , c have xy - coordinates ( 2,0 ) , ( 8,12 ) , and ( 14,0 ) , respectively . points x , y , and z have xy - coordinates ( 6,0 ) , ( 8,4 ) , and ( 10,0 ) , respectively . what fraction q of the area of triangle abc is the area of triangle xyz ?
Options: a ) 1 / 9 , b ) 1 / 8 , c ) 1 / 6 , d ) 1 / 5 , e ) 1 / 3
Rationale: "if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 8,12 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives q = 1 / 9 . a"
Answer: a
Question (gain): what will be the compound interest on a sum of rs . 20,000 after 3 years at the rate of 12 % p . a . ?
Options: a ) rs . 8098.56 , b ) rs . 9720 , c ) rs . 10123.20 , d ) rs . 10483.20 , e ) none
Rationale: "amount = [ 20000 * ( 1 + 12 / 100 ) ^ 3 ] = 20000 * 28 / 25 * 28 / 25 * 28 / 25 = rs . 28098.56 c . i . = ( 28098.56 - 20000 ) = rs . 8098.56 answer : a"
Answer: a
Question (general): a waitress ' s income consists of her salary and tips . during one week , her tips were 3 / 4 of her salary . what fraction of her income for the week came from tips ?
Options: a ) 1 / 9 , b ) 1 / 6 , c ) 3 / 7 , d ) 4 / 9 , e ) 5 / 9
Rationale: "her tips were 3 / 4 of her salary . let ' s say her salary = $ 4 this mean her tips = ( 3 / 4 ) ( $ 4 ) = $ 3 so , her total income = $ 4 + $ 3 = $ 7 what fraction of her income for the week came from tips $ 3 / $ 7 = 3 / 7 = c"
Answer: c
Question (geometry): the height of a triangle is decreased by 5 % and its base increased by 10 % . its area will
Options: a ) decrease by 12.5 %
b ) increase by 12.5 %
c ) increase by 4.5 %
d ) increase by 25 %
e ) none of these
Rationale: explanation : let the initial height be 100 and the base be 200 units . â ˆ ´ area = 1 / 2 x 100 x 200 = 10000 sq units now , height = 95 units and base = 220 units â ˆ ´ new area = 1 / 2 x 95 x 220 = 10450 â ˆ ´ area is increased by ( 10450 - 10000 ) / 10000 x 10 = 4.5 % answer : option c
Answer: c
Question (general): how many different positive integers exist between 10 ^ 5 and 10 ^ 6 , the sum of whose digits is equal to 2 ?
Options: a ) 6 , b ) 7 , c ) 5 , d ) 8 , e ) 18
Rationale: "so , the numbers should be from 100,000 to 1 , 000,000 the following two cases are possible for the sum of the digits to be 2 : 1 . two 1 ' s and the rest are 0 ' s : 100,001 100,010 100,100 101,000 110,000 5 numbers . 2 . one 2 and the rest are 0 ' s : 200,000 1 number . total = 6 numbers . answer : a"
Answer: a
Question (general): the average age of 20 students of a class is 20 years . out of these , the average age of 9 students is 11 years and that of the other 10 students is 24 years . the age of the 20 th student is ?
Options: a ) 65 , b ) 61 , c ) 59 , d ) 63 , e ) 64
Rationale: "age of the 20 th student = 20 * 20 - ( 9 * 11 + 10 * 24 ) = 400 - 339 = 61 years answer is b"
Answer: b