Cheukting/mathqa huggingface dataset:
Question (gain): a fashion designer sold a pair of jeans to a retail store for 40 percent more than it cost to manufacture the pair of jeans . a customer bought the pair of jeans for 35 percent more than the retailer paid for them . the price the customer paid was what percent greater than the cost of manufacturing the jeans ?
Options: a ) 65 % , b ) 70 % , c ) 75 % , d ) 89 % , e ) 95 %
Rationale: "find the product of the two increases : ( 1.4 ) * ( 1.35 ) which is 1.89 and a 89 % increase . d"
Answer: d
Question (general): what least number must be added to 9879 , so that the sum is completely divisible by 10 ?
Options: a ) 3 , b ) 4 , c ) 1 , d ) 2 , e ) 6
Rationale: "if we divide 9879 by 10 remainder is 9 10 - 9 = 1 answer : c"
Answer: c
Question (general): solution x is 10 percent alcohol by volume , and solution y is 30 percent alcohol by volume . how many milliliters of solution y must be added to 150 milliliters of solution x to create a solution that is 25 percent alcohol by volume ?
Options: a ) 250 / 3 , b ) 500 / 3 , c ) 400 , d ) 450 , e ) 600
Rationale: "we know that x is 10 % , y is 30 % and w . avg = 25 % . what does this mean with respect to w . avg technique ? w . avg is 1 portion away from y and 3 portion away from x so for every 1 portion of x we will have to add 3 portions of y . if x = 150 then y = 450 answer : d"
Answer: d
Question (gain): a cycle is bought for rs . 750 and sold for rs . 1080 , find the gain percent ?
Options: a ) 22 , b ) 44 , c ) 99 , d ) 88 , e ) 11
Rationale: "750 - - - - 180 100 - - - - ? = > 44 % answer : b"
Answer: b
Question (gain): a , b and c invested rs . 6500 , rs . 1300 and rs . 7800 respectively , in a partnership business . find the share of b in profit of rs . 11700 after a year ?
Options: a ) 1300 , b ) 3877 , c ) 1170 , d ) 975 , e ) 7800
Rationale: "explanation : 6500 : 1300 : 7800 5 : 1 : 6 1 / 12 * 11700 = 975 answer : d"
Answer: d
Question (general): the average ( arithmetic mean ) of 16 students first quiz scores in a difficult english class is 62.5 . when one student dropped the class , the average of the remaining scores increased to 65.0 . what is the quiz score of the student who dropped the class ?
Options: a ) a ) 10 , b ) b ) 25 , c ) c ) 40 , d ) d ) 55 , e ) e ) 70
Rationale: "total score of 16 students is 16 * 62.50 = 1000 total score of 15 students is 15 * 65 = 975 so , the score of the person who left is 25 ( 1000 - 975 ) answer will be ( b )"
Answer: b
Question (gain): evaluate 35 % of 450 + 45 % of 350
Options: a ) 232 , b ) 242 , c ) 315 , d ) 262 , e ) 272
Rationale: "explanation : = ( 35 / 100 ) * 450 + ( 45 / 100 ) * 350 = 315 option c"
Answer: c
Question (general): when positive integer x is divided by positive integer y , the remainder is 8 . if x / y = 96.12 , what is the value of y ?
Options: a ) 96 , b ) 75 , c ) 66.7 , d ) 25 , e ) 12
Rationale: "when positive integer x is divided by positive integer y , the remainder is 8 - - > x = qy + 8 ; x / y = 96.12 - - > x = 96 y + 0.12 y ( so q above equals to 96 ) ; 0.12 y = 8 - - > y = 66.7 . answer : c ."
Answer: c
Question (physics): a bullock cart has to cover a distance of 80 km in 10 hrs . if it covers half of the journey in 3 / 5 th time . what should be its speed to cover the remaining distance in the time left .
Options: a ) 10 kmph , b ) 20 kmph , c ) 30 kmph , d ) 40 kmph , e ) 50 kmph
Rationale: a 10 kmph time left = 10 - 3 / 5 * 10 = 4 hr 10 km / h speed = 40 km / 4 hr = 10 kmph
Answer: a
Question (gain): reena took a loan of $ . 1200 with simple interest for as many years as the rate of interest . if she paid $ 300 as interest at the end of the loan period , what was the rate of interest ?
Options: a ) 5 , b ) 6 , c ) 18 , d ) can not be determined , e ) none of these
Rationale: "let rate = r % and time = r years . then , 1200 x r x r / 100 = 300 12 r 2 = 300 r 2 = 25 r = 5 . answer : a"
Answer: a
Question (general): if the number 872 , 152,24 x is divisible by 11 , what must be the value of x ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "multiplication rule of 11 : ( sum of digits at odd places - sum of digits at even places ) should be divisible by 11 given number : 872 , 152,24 x sum of digits at odd places = 8 + 2 + 5 + 2 + x = 17 + x ( i ) sum of digits at even places = 7 + 1 + 2 + 4 = 14 ( ii ) ( i ) - ( ii ) = 17 + x - 14 = x - 3 hence x should be = 3 to make this a multiple of 11 ( 0 ) option c"
Answer: c
Question (physics): darcy lives 1.5 miles from work . she can walk to work at a constant rate of 3 miles per hour , or she can ride the train to work at a constant rate of 20 miles per hour . if she rides the train , there is an additional x minutes spent walking to the nearest train station , waiting for the train , and walking from the final train station to her work . if it takes darcy a total of 20 more minutes to commute to work by walking than it takes her to commute to work by riding the train , what is the value of x ?
Options: a ) 5.5 , b ) 15 , c ) 25.5 , d ) 30 , e ) 60
Rationale: "the time it takes darcy to walk to work is ( 1.5 / 3 ) * 60 = 30 minutes the time it takes darcy to take the train is ( 1.5 / 20 ) * 60 + x = 4.5 + x minutes it takes 15 minutes longer to walk , so 30 = 4.5 + x + 20 x = 5.5 minutes answer : a"
Answer: a
Question (gain): one ball will drop from a certain height . the height it will reach after rebounding from the floor is 50 percent of the previous height . the total travel is 150 cm when it touches the floor on third time . what is the value of the original height ?
Options: a ) 60 cm , b ) 90 cm , c ) 100 cm , d ) 120 cm , e ) 130 cm
Rationale: "when ball comes down , then i have indicated the distance covered in green when ball goes up , then i have indicated the distance covered in red distance travelled uptil the ball touches the floor 3 rd time : h + 0.5 h + 0.5 h + 0.5 * 0.5 h + 0.5 * 0.5 h h + 2 * 0.5 * h + 2 * 0.25 * h = h ( 1 + 2 * 0.5 + 2 * 0.25 ) = h ( 1 + 1 + 0.5 ) = 150 2.5 h = 150 h = 60 . a is the answer ."
Answer: a
Question (physics): a furniture manufacturer has two machines , but only one can be used at a time . machine w is utilized during the first shift and machine b during the second shift , while both work half of the third shift . if machine w can do the job in 12 days working two shifts and machine b can do the job in 15 days working two shifts , how many days will it take to do the job with the current work schedule ?
Options: a ) 14 , b ) 13 , c ) 11 , d ) 9 , e ) 7
Rationale: ' approximately ' could actually make such a question ambiguous . not this one though but a similar question with the answer as 9.2 days . you round off 8.89 days as 9 days and everything is fine in this question . what do you do when you get 9.2 days ? do you need 9 days or 10 days ? can you round off 9.2 as 9 even though that is what you do with numbers ? no , because in 9 days your work is not over . you do need 10 days . to finish a work machine w say you need to work full 9 days and a part of the 10 th day . if i ask you how many days do you need to complete the work , will you say 9 or 10 ? you will say 10 even if you do n ' t use the 10 th day fully = d
Answer: d
Question (general): what will be the remainder when 17 ^ 200 is divided by 18 ?
Options: a ) 3 , b ) 8 , c ) 5 , d ) 1 , e ) 7
Rationale: "when n is even , ( x ^ n - a ^ n ) is completely divisible by ( x - a ) . ( 17 ^ 200 - 1 ^ 200 ) is completely divisible by ( 17 + 1 ) , ( 17 ^ 200 - 1 ) is completely divisible by 18 . on dividing 17 ^ 200 by 18 , we get 1 as remainder . answer is d"
Answer: d
Question (general): calculate 469200 x 9999 = ?
Options: a ) 4586970843 , b ) 4686970743 , c ) 4691100843 , d ) 4586870843 , e ) 4691530800
Rationale: "answer 469200 x 9999 = 469200 x ( 10000 - 1 ) = 4692000000 - 469200 = 4691100843 . option : e"
Answer: e
Question (physics): how many seconds will a train 100 meters long take to cross a bridge 130 meters long if the speed of the train is 36 kmph ?
Options: a ) 26 , b ) 72 , c ) 25 , d ) 23 , e ) 27
Rationale: "explanation : d = 100 + 130 = 230 s = 36 * 5 / 18 = 10 mps t = 230 / 10 = 23 sec answer : option d"
Answer: d
Question (general): the average of first six prime numbers which are between 60 and 90 is
Options: a ) 35.4 , b ) 42 , c ) 45.7 , d ) 57 , e ) 72.33
Rationale: "explanation : first six prime numbers which are between 60 and 90 = 61 , 67 , 71 , 73 , 79 , 83 average = ( 61 + 67 + 71 + 73 + 79 + 83 ) / 6 = 72.33 answer : e"
Answer: e
Question (general): a is two years older than b who is twice as old as c . if the total ages of a , b and c be 27 . what is the age of b ?
Options: a ) 12 years , b ) 10 years , c ) 8 years , d ) 14 years , e ) 16 years
Rationale: "c age x , then b age is 2 x so a age is 2 x + 2 . ( 2 x + 2 ) + 2 x + x = 27 5 x = 25 x = 5 so b is 2 x = 2 ( 5 ) 2 x 5 = 10 answer : b"
Answer: b
Question (general): a certain debt will be paid in 52 installments from january 1 to december 31 of a certain year . each of the first 22 payments is to be $ 410 ; each of the remaining payments is to be $ 65 more than each of the first 22 payments . what is the average ( arithmetic mean ) payment that will be made on the debt for the year ?
Options: a ) 447.5 , b ) 450 , c ) 465 , d ) 468 , e ) 475
Rationale: total number of installments = 52 payment per installment for the first 22 installments = 410 payment per installment for the remaining 30 installments = 410 + 65 = 475 average = ( 22 * 410 + 30 * 475 ) / 52 = 447.50 answer a
Answer: a
Question (other): the ratio of numbers is 5 : 6 and their h . c . f is 4 . their l . c . m is :
Options: a ) 12 , b ) 16 , c ) 24 , d ) 48 , e ) 120
Rationale: "let the numbers be 5 x and 6 x . then their h . c . f = x . so , x = 4 . so , the numbers are 20 and 24 . l . c . m of 20 and 24 = 120 . answer : e"
Answer: e
Question (general): a number when divided by a certain divisor left remainder 241 , when twice the number was divided by the same divisor , the remainder was 102 . find the divisor ?
Options: a ) 370 , b ) 365 , c ) 380 , d ) 456 , e ) 460
Rationale: "easy solution : n = dq 1 + 241 2 n = 2 dq 1 + 482 - ( 1 ) 2 n = dq 2 + 102 - ( 2 ) as ( 1 ) = ( 2 ) = 2 n d * ( q 2 - 2 q 1 ) = 380 d * some integer = 380 checking all options only ( c ) syncs with it . answer c"
Answer: c
Question (gain): the banker â € ™ s discount of a certain sum of money is rs . 90 and the true discount on the same sum for the same time is rs . 60 . the sum due is
Options: a ) 210 , b ) 180 , c ) 360 , d ) 450 , e ) none
Rationale: "sol . sum = b . d . * t . d . / b . d . - t . d . = rs . [ 90 * 60 / 90 - 60 ] = rs . [ 90 * 60 / 30 ] = rs . 180 answer b"
Answer: b
Question (general): s is a positive integer and multiple of 2 ; p = 4 ^ s , what is the remainder when p is divided by 10 ?
Options: a ) 10 , b ) 6 , c ) 4 , d ) 0 , e ) it can not be determined
Rationale: it is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer . to help see this , consider the following examples : 4 / 10 is 0 with a remainder of 4 14 / 10 is 1 with a remainder of 4 5 / 10 is 0 with a remainder of 5 105 / 10 is 10 with a remainder of 5 it is also essential to remember that the s is a positive integer and multiple of 2 . any integer that is a multiple of 2 is an even number . so , s must be a positive even integer . with these two observations , the question can be simplified to : what is the units digit of 4 raised to an even positive integer ? the units digit of 4 raised to an integer follows a specific repeating pattern : 4 ^ 1 = 4 4 ^ 2 = 16 4 ^ 3 = 64 4 ^ 4 = 256 4 ^ ( odd number ) - - > units digit of 4 4 ^ ( even number ) - - > units digit of 6 there is a clear pattern regarding the units digit . 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6 . since s must be an even integer , the units digit of p = 4 ^ s will always be 6 . consequently , the remainder when p = 4 ^ s is divided by 10 will always be 6 . in case this is too theoretical , consider the following examples : s = 2 - - > p = 4 ^ z = 16 - - > s / 10 = 1 with a remainder of 6 s = 4 - - > p = 4 ^ z = 256 - - > s / 10 = 25 with a remainder of 6 s = 6 - - > p = 4 ^ z = 4096 - - > s / 10 = 409 with a remainder of 6 s = 8 - - > p = 4 ^ z = 65536 - - > s / 10 = 6553 with a remainder of 6 answer : b .
Answer: b
Question (general): if the sum of two numbers is 22 and the sum of their squares is 386 , then the product of the numbers is
Options: a ) 40 , b ) 49 , c ) 80 , d ) 88 , e ) 90
Rationale: "sol . let the numbers be x and y . then , ( x + y ) = 22 and x 2 + y 2 = 386 . now , 2 xy = ( x + y ) 2 - ( x 2 + y 2 ) = ( 22 ) 2 - 386 = 484 - 386 = 98 xy = 49 . answer b"
Answer: b
Question (general): the largest 4 digit number exactly divisible by 88 is ?
Options: a ) 9934 , b ) 9938 , c ) 9940 , d ) 9942 , e ) 9944
Rationale: "largest 4 - digit number = 9999 88 ) 9999 ( 113 88 - - - - 119 88 - - - - 319 264 - - - 55 - - - required number = ( 9999 - 55 ) = 9944 . e )"
Answer: e
Question (gain): a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 80 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 50 , b ) 60 , c ) 70 , d ) 80 , e ) 90
Rationale: "round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 80 % of 50 % i . e 40 % . so he completed 50 + 40 = 90 % of total trip . e"
Answer: e
Question (general): if m is an integer such that ( - 2 ) ^ 2 m = 2 ^ ( 15 - m ) then m = ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 5 , e ) 6
Rationale: "( - 2 ) ^ ( 2 m ) = 4 ^ m and 2 ^ ( 15 - m ) = 4 ^ ( ( 15 - m ) / 2 ) therefore , m = ( 15 - m ) / 2 2 m = 15 - m m = 5 answer d"
Answer: d
Question (physics): the ratio between the length and the breadth of a rectangular park is 3 : 4 . if a man cycling along the boundary of the park at the speed of 15 km / hr completes one round in 10 min , then the area of the park ( in sq . m ) is ?
Options: a ) 244907.04 m , b ) 244000 m , c ) 244900 m , d ) 400000 m , e ) 154300 m
Rationale: "perimeter = distance covered in 10 min . = ( 15000 x 8 ) / 60 m = 2000 m . let length = 3 x metres and breadth = 4 x metres . then , 2 ( 3 x + 4 x ) = 2000 or x = 142.86 . length = 428.58 m and breadth = 571.44 m . area = ( 428.58 x 571.44 ) m 2 = 244907.76 m a"
Answer: a
Question (general): $ 378 is divided among a , b , and c so that a receives half as much as b , and b receives half as much as c . how much money is c ' s share ?
Options: a ) $ 200 , b ) $ 208 , c ) $ 216 , d ) $ 224 , e ) $ 232
Rationale: "let the shares for a , b , and c be x , 2 x , and 4 x respectively . 7 x = 378 x = 54 4 x = 216 the answer is c ."
Answer: c
Question (gain): harkamal purchased 8 kg of grapes at the rate of 75 per kg and 9 kg of mangoes at the rate of 55 per kg . how much amount did he pay to the shopkeeper ?
Options: a ) a ) 1000 , b ) b ) 1055 , c ) c ) 1065 , d ) d ) 1075 , e ) e ) 1095
Rationale: "cost of 8 kg grapes = 75 × 8 = 600 . cost of 9 kg of mangoes = 55 × 9 = 495 . total cost he has to pay = 600 + 495 = 1095 . e )"
Answer: e
Question (geometry): if the side length of square b is sqrt ( 5 ) times that of square a , the area of square b is how many times the area of square a ?
Options: a ) 1.5 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "let x be the side length of square a . then the area of square a is x ^ 2 . the area of square b is ( sqrt ( 5 ) x ) ^ 2 = 5 x ^ 2 . the answer is e ."
Answer: e
Question (other): a certain quantity of 50 % solution is replaced with 25 % solution such that the new concentration is 35 % . what is the fraction of the solution that was replaced ?
Options: a ) 1 / 4 , b ) 1 / 3 , c ) 1 / 2 , d ) 2 / 3 , e ) 3 / 5
Rationale: "let ' s say that the total original mixture a is 100 ml the original mixture a thus has 50 ml of alcohol out of 100 ml of solution you want to replace some of that original mixture a with another mixture b that contains 25 ml of alcohol per 100 ml . thus , the difference between 50 ml and 25 ml is 25 ml per 100 ml of mixture . this means that every time you replace 100 ml of the original mixture a by 100 ml of mixture b , the original alcohol concentration will decrease by 25 % . the question says that the new mixture , let ' s call it c , must be 35 % alcohol , a decrease of only 15 % . therefore , 15 out of 25 is 3 / 5 and e is the answer ."
Answer: e
Question (general): a customer bought a product at the shop . however , the shopkeeper increased the price of the product by 20 % so that the customer could not buy the required amount of the product . the customer managed to buy only 80 % of the required amount . what is the difference in the amount of money that the customer paid for the second purchase compared to the first purchase ?
Options: a ) 10 % , b ) 8 % , c ) 6 % , d ) 4 % , e ) 2 %
Rationale: "let x be the amount of money paid for the first purchase . the second time , the customer paid 0.8 ( 1.2 x ) = 0.96 x . the difference is 4 % . the answer is d ."
Answer: d
Question (general): there is a lot of speculation that the economy of a country depends on how fast people spend their money in addition to how much they save . auggie was very curious to test this theory . auggie spent all of his money in 5 stores . in each store , he spent rs . 4 more than one - half of what he had when he went in . how many rupees did auggie have when he entered the first store ?
Options: a ) 248 , b ) 120 , c ) 252 , d ) 250 , e ) 350
Rationale: amount left = 0.5 x − 4 for fifth store this is zero . so x = 8 . that means he entered fifth store with 8 . now for fourth store , amount left = 8 so 0.5 x − 4 = 8 ⇒ x = 24 for third store , amount left = 24 so 12 x − 4 = 24 ⇒ x = 56 for second store , amount left = 56 so 0.5 x − 4 = 56 ⇒ x = 120 for first store , amount left = 120 so 0.5 x − 4 = 120 ⇒ x = 248 so he entered first store with 248 . answer : a
Answer: a
Question (geometry): an artist wishes to paint a circular region on a square poster that is 2.4 feet on a side . if the area of the circular region is to be 1 / 2 the area of the poster , what must be the radius of the circular region in feet ?
Options: a ) 1 / pi , b ) sqrt ( 2.88 / pi ) , c ) 1 , d ) 2 / sqrt ( pi ) , e ) pi / 2
Rationale: "area of the poster is 2.4 x 2.4 = 5.76 1 / 2 the area = 2.88 pi * r ^ 2 = 2.88 r ^ 2 = 2.88 / pi r = sqrt ( 2.88 / pi ) answer ( b )"
Answer: b
Question (general): 5359 x 51 = ?
Options: a ) 273232 , b ) 273243 , c ) 273247 , d ) 273250 , e ) 273309
Rationale: "5359 x 51 = 5359 x ( 50 + 1 ) = 5359 x 50 + 5359 x 1 = 267950 + 5359 = 273309 e )"
Answer: e
Question (general): 3 people are planning to share equally the cost of a rental car . if one person withdraws from the arrangement and the others share equally the entire cost of the car , then the share of each of the remaining persons increased by :
Options: a ) 1 / 2 , b ) 2 / 7 , c ) 3 / 2 , d ) 4 / 7 , e ) none of them
Rationale: original share of 1 person = 1 / 3 new share of 1 person = 1 / 2 increase = ( 1 / 2 - 1 / 3 = 1 / 6 ) therefore , required fraction = ( 1 / 6 ) / ( 1 / 3 ) = ( 1 / 6 ) x ( 3 / 1 ) = 1 / 2 answer is a .
Answer: a
Question (physics): two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 45 kmph respectively . in how much time will they cross each other , if they are running in the same direction ?
Options: a ) 72 sec , b ) 132 sec , c ) 192 sec , d ) 252 sec , e ) none
Rationale: solution relative speed = ( 45 - 40 ) kmph = 5 kmph = ( 5 x 5 / 18 ) m / sec = ( 25 / 18 ) m / sec time taken = ( 350 x 18 / 25 ) sec = 252 sec . answer d
Answer: d
Question (gain): a dealer purchases 15 articles for rs . 25 and sells 12 articles for rs . 35 . find the profit percentage ?
Options: a ) 80 % , b ) 50 % , c ) 75 % , d ) 40 % , e ) 53 %
Rationale: "l . c . m of 15 and 12 = 60 cp of 60 articles = rs . 100 ( 25 * 4 ) sp of 60 articles = rs . 175 ( 35 * 5 ) profit percentage = ( 175 - 100 ) / 100 * 100 = 75 % answer : c"
Answer: c
Question (general): how many 1 / 8 s are there in 37 1 / 2 ?
Options: a ) 300 , b ) 400 , c ) 500 , d ) 600 , e ) 700
Rationale: "required number = ( 75 / 2 ) / ( 1 / 8 ) = ( 75 / 2 x 8 / 1 ) = 300 . answer : a"
Answer: a
Question (physics): pipe p can drain the liquid from a tank in 2 / 4 the time that it takes pipe q to drain it and in 2 / 3 the time that it takes pipe r to do it . if all 3 pipes operating simultaneously but independently are used to drain liquid from the tank , then pipe q drains what portion of the liquid from the tank ?
Options: a ) 3 / 13 , b ) 8 / 23 , c ) 3 / 8 , d ) 17 / 29 , e ) 3 / 4
Rationale: "suppose q can drain in 1 hr . so , rq = 1 / 1 = 1 so , rp = 1 / [ ( 2 / 4 ) rq ] = 4 / 2 also , rp = rr / ( 2 / 3 ) = > 2 = rr / ( 2 / 3 ) = > rr = 4 / 3 let h is the time it takes to drain by running all 3 pipes simultaneously so combined rate = rc = 1 / h = 1 + 2 + 4 / 3 = 13 / 3 = 1 / ( 3 / 13 ) thus running simultaneously , pipe q will drain 3 / 13 of the liquid . thus answer = a ."
Answer: a
Question (geometry): in triangle pqr , the angle q = 90 degree , pq = 5 cm , qr = 8 cm . x is a variable point on pq . the line through x parallel to qr , intersects pr at y and the line through y , parallel to pq , intersects qr at z . find the least possible length of xz
Options: a ) 3.6 cm , b ) 2.4 cm , c ) 4.0 cm , d ) 2.16 cm , e ) 3.2 cm
Rationale: "look at the diagram below : now , in case when qy is perpendicular to pr , two right triangles pqr and pqy are similar : qy : qp = qr : pr - - > qy : 5 = 8 : 10 - - > qy = 4.0 . answer : c ."
Answer: c
Question (general): the average runs of a cricket player of 10 innings was 20 . how many runs must he make in his next innings so as to increase his average of runs by 4 ?
Options: a ) 22 , b ) 77 , c ) 64 , d ) 19 , e ) 17
Rationale: "explanation : average after 11 innings = 24 required number of runs = ( 24 * 11 ) – ( 20 * 10 ) = 264 – 200 = 64 answer : c"
Answer: c
Question (gain): a , b and c start a business each investing 20,000 . after 10 months a withdrew 5000 , b withdrew 4000 and c invests 6000 more . at the end of the year , a total profit of 71400 was recorded . find the share of b .
Options: a ) 20,000 , b ) 21,200 , c ) 23,200 , d ) 20,500 , e ) none of these
Rationale: "ratio of the capitals of a , b and c = 20000 ã — 10 + 15000 ã — 2 : 20000 ã — 10 + 16000 ã — 2 : 20000 ã — 10 + 26000 ã — 2 = 230000 : 232000 : 252000 = 230 : 232 : 252 . b â € ™ s share = ( 71400 ã — 232 â  „ 714 ) = 23200 ; answer c"
Answer: c
Question (general): the sum of the even numbers between 1 and k is 79 * 80 , where k is an odd number , then k =
Options: a ) 79 , b ) 80 , c ) 81 , d ) 157 , e ) 159
Rationale: "the number of terms in this set would be : n = ( k - 1 ) / 2 ( as k is odd ) last term : k - 1 average would be first term + last term / 2 = ( 2 + k - 1 ) / 2 = ( k + 1 ) / 2 also average : sum / number of terms = 79 * 80 / ( ( k - 1 ) / 2 ) = 158 * 80 / ( k - 1 ) ( k + 1 ) / 2 = 158 * 80 / ( k - 1 ) - - > ( k - 1 ) ( k + 1 ) = 158 * 160 - - > k = 159 answer e ."
Answer: e
Question (physics): how long does a train 125 m long running at the speed of 78 km / hr takes to cross a bridge 125 m length ?
Options: a ) 12.7 sec , b ) 10.1 sec , c ) 11.5 sec , d ) 12.1 sec , e ) 11.7 sec
Rationale: "speed = 78 * 5 / 18 = 21.7 m / sec total distance covered = 125 + 125 = 250 m . required time = 250 / 21.7 ' = 11.5 sec . answer : c"
Answer: c
Question (general): ele , the circus elephant , is currently 3 times older than lyn , the circus lion . in 15 years from now , lyn the circus lion will be exactly half as old as ele , the circus elephant . how old is ele today ?
Options: a ) 40 , b ) 48 , c ) 43 , d ) 45 , e ) 41
Rationale: ele , the circus elephant , is currently three times older than lyn , the circus lion . ele = 3 * lyn usually , ages are integers so there is a good possibility that the age of ele is 45 ( the only option that is a multiple of 3 ) . then age of lyn would be 15 . in 15 yrs , ele would be 60 and lyn would be 30 - so lyn would be half as old as ele . answer ( d )
Answer: d