Cheukting/mathqa huggingface dataset:
Question (gain): what is 30 % of 80 ?
Options: a ) 24 , b ) 66 , c ) 367 , d ) 28 , e ) 267
Rationale: "30 % of 80 = 30 / 100 × 80 = ( 30 × 80 ) / 100 = 2400 / 100 = 24 answer : a"
Answer: a
Question (gain): a particular library has 75 books in a special collection , all of which were in the library at the beginning of the month . these book are occasionally loaned out through an inter - library program . if , by the end of the month , 80 percent of books that were loaned out are returned and there are 69 books in the special collection at that time , how many books of the special collection were loaned out during that month ?
Options: a ) 20 , b ) 30 , c ) 35 , d ) 40 , e ) 55
Rationale: "there are 6 books less ( 75 - 69 ) which represents 20 % of the loaned books ( 100 - 80 ) so total loaned out books = 30 answer b"
Answer: b
Question (physics): if an object travels 300 feet in 6 seconds , what is the object ' s approximate speed in miles per hour ? ( note : 1 mile = 5280 feet )
Options: a ) 30 , b ) 31 , c ) 32 , d ) 33 , e ) 34
Rationale: "1 mile = 5280 feet = > 1 feet = 1 / 5280 miles if the object travels 300 feet in 6 sec then it travels 300 / 6 * 60 * 60 feet in 1 hour ( 1 hr = 60 min * 60 sec ) = 3600 * 50 feet in 1 hour = 180000 feet in 1 hr = 180000 / 5280 miles in 1 hour = 18000 / 528 miles / hr ~ 34 miles / hr answer - e"
Answer: e
Question (general): there are 9 baskets numbered from 1 to 9 and filled with apples . 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket . if there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process , how many apples were left in the end ?
Options: a ) 440 , b ) 550 , c ) 660 , d ) 770 , e ) 880
Rationale: "each child takes a total of 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 9 * 10 / 2 = 45 apples . the total number of apples taken by 10 children is 10 * 45 = 450 the number of apples left in the end is 1000 - 450 = 550 apples . the answer is b ."
Answer: b
Question (other): in a sports club with 80 members , 48 play badminton and 46 play tennis and 7 do not play either . how many members play both badminton and tennis ?
Options: a ) 23
b ) 21
c ) 20
d ) 26
e ) 27
Rationale: 48 + 46 = 94 but where as total number is 80 - 7 = 73 therefore answer is 94 - 73 = 21 hence answer is b
Answer: b
Question (general): in a fuel station the service costs $ 2.10 per vehicle and every liter of fuel costs $ 0.60 . assuming that you fill up 3 mini - vans and 2 trucks , what will be the total cost , if a mini - van ' s tank is 65 liters and a truck ' s tank is 120 % bigger and they are all empty ?
Options: a ) $ 287.50 , b ) $ 290.40 , c ) $ 293.30 , d ) $ 296.20 , e ) $ 299.10
Rationale: "the service cost of 3 vans and 2 trucks is 5 * 2.10 $ 10.50 the fuel in 3 vans is 3 * 65 = 195 liters the fuel in 2 trucks is 2 * 65 * 2.2 = 286 liters the total fuel ( vans + trucks ) = 481 liters the total fuel cost is 481 * 0.6 = $ 288.60 the total cost is $ 288.60 + $ 10.50 = $ 299.10 the answer is e ."
Answer: e
Question (general): what is the ratio of 3 / 7 to the product 3 * ( 7 / 3 ) ?
Options: a ) 3 : 7 , b ) 1 : 3 , c ) 3 : 21 , d ) 1 : 7 , e ) 3 : 49
Rationale: "3 * ( 7 / 3 ) = 7 so , we need to find the ratio of 3 / 7 : 7 = > 3 : 49 hence , answer will be ( e ) 3 : 49"
Answer: e
Question (general): ( 212 + 222 + 232 + . . . + 302 ) = ?
Options: a ) 385 , b ) 2485 , c ) 2570 , d ) 3255 , e ) none
Rationale: "solution ( 212 + 222 + 232 + . . . + 302 ) = a + ( n - 1 ) d = last number . . . . . so 212 + ( n - 1 ) 10 = 302 . . . . . so n = 10 . so sum = n / 2 ( 2 a + ( n - 1 ) d ) = 10 / 2 ( 2 * 212 + 9 * 10 ) = 2570 . answer c"
Answer: c
Question (physics): a train of length 250 m crosses a bridge of length 150 m in 20 seconds . what is the speed of train ?
Options: a ) 33 , b ) 27 , c ) 25 , d ) 22 , e ) 72
Rationale: "sol : ( length of train + length of bridge ) = speed of train x time ( 250 + 150 ) = 20 x speed speed = 400 / 20 = 20 m / s = 72 km / h answer = e"
Answer: e
Question (general): half a number plus 7 is 17 . what is the number ?
Options: a ) 8 , b ) 9 , c ) 10 , d ) 11 , e ) 20
Rationale: "let x be the number . always replace ` ` is ' ' with an equal sign ( 1 / 2 ) x + 7 = 17 ( 1 / 2 ) x = 17 - 7 ( 1 / 2 ) x = 20 x = 20 correct answer is e"
Answer: e
Question (gain): how much interest will $ 8,000 earn in 9 months at an annual rate of 6 % ?
Options: a ) $ 250 , b ) $ 350 , c ) $ 360 , d ) $ 550 , e ) $ 650
Rationale: "soln : - 9 months = 3 / 4 of year ; 6 % = 6 / 100 = 3 / 50 ; $ 8,000 ( principal ) * 3 / 50 ( interest rate ) * 3 / 4 ( time ) = $ 360 . answer : c"
Answer: c
Question (other): if the ratio of the sum of the first 6 terms of a g . p . to the sum of the first 3 terms of the g . p . is 343 , what is the common ratio of the g . p ?
Options: a ) 3 , b ) 1 / 3 , c ) 2 , d ) 7 , e ) 1 / 7
Rationale: "343 = ( a 1 + a 2 + a 3 + a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) factorize the same terms 343 = 1 + ( a 4 + a 5 + a 6 ) / ( a 1 + a 2 + a 3 ) write every term with respect to r a 1 = a 1 a 2 = a 1 * r ^ 1 a 3 = a 1 * r ^ 2 . . . . . . . . . 343 = 1 + ( a 1 ( r ^ 3 + r ^ 4 + r ^ 5 ) ) / ( a 1 ( 1 + r ^ 1 + r ^ 2 ) ) 342 = ( r ^ 3 ( 1 + r ^ 1 + r ^ 2 ) ) / ( ( 1 + r ^ 1 + r ^ 2 ) ) 342 = r ^ 3 r = 7 d"
Answer: d
Question (gain): bert and rebecca were looking at the price of a condominium . the price of the condominium was 50 % more than bert had in savings , and separately , the same price was also 25 % more than rebecca had in savings . what is the ratio of what bert has in savings to what rebecca has in savings .
Options: a ) 1 : 6 , b ) 1 : 3 , c ) 1 : 2 , d ) 3 : 4 , e ) 5 : 6
Rationale: "suppose bert had 100 so price becomes 150 , this 150 = 1.25 times r ' s saving . . so r ' s saving becomes 120 so required ratio is 100 : 120 = 5 : 6 answer : e"
Answer: e
Question (gain): a shopkeeper sells 500 metres of cloth for rs . 18000 at a loss of rs . 5 per metre . find his cost price for one metre of cloth ?
Options: a ) 12 , b ) 27 , c ) 29 , d ) 50 , e ) 41
Rationale: sp per metre = 18000 / 500 = rs . 36 loss per metre = rs . 5 cp per metre = 36 + 5 = rs . 41 . answer : e
Answer: e
Question (general): the difference of two numbers is 1565 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder . what is the smaller number ?
Options: a ) a ) 270 , b ) b ) 280 , c ) c ) 290 , d ) d ) 300 , e ) e ) 310
Rationale: "let the smaller number be x . then larger number = ( x + 1565 ) . x + 1565 = 6 x + 15 5 x = 1550 x = 310 smaller number = 310 . e )"
Answer: e
Question (general): how many even number in the range between 15 to 100 inclusive are not divisible by 3
Options: a ) 29 , b ) 30 , c ) 31 , d ) 33 , e ) 46
Rationale: "we have to find the number of terms that are divisible by 2 but not by 6 ( as the question asks for the even numbers only which are not divisible by 3 ) for 2 , 16,18 . . . 100 using ap formula , we can say 100 = 16 + ( n - 1 ) * 2 or n = 43 . for 6 , 18 , . . . 96 using ap formula , we can say 96 = 18 + ( n - 1 ) * 6 or n = 14 . hence , only divisible by 2 but not 3 = 43 - 14 = 29 . hence , answer a"
Answer: a
Question (geometry): the area of a circular field is 17.56 hectares . find the cost of fencing it at the rate of rs . 7 per metre approximately
Options: a ) 4457 , b ) 10400 , c ) 4235 , d ) 4547 , e ) 4675
Rationale: "explanation : area = ( 17.56 x 10000 ) m 2 = 175600 m 2 . π r 2 = 175600 ⇔ ( r ) 2 = ( 175600 x ( 7 / 22 ) ) ⇔ r = 236.37 m . circumference = 2 π r = ( 2 x ( 22 / 7 ) x 236.37 ) m = 1485.78 m . cost of fencing = rs . ( 1485.78 x 7 ) = rs . 10400 . answer : option b"
Answer: b
Question (general): a confectioner decides to sell all of his pastry due to the coming holiday . his pastry goods are equally divided among a group of 50 regular customers . if only 49 customers come to the bakery , each one will receive 6 less pastry goods . how much pastry does the confectioner needs to sell ?
Options: a ) 500 . , b ) 412 . , c ) 432 . , d ) 502 . , e ) 522 .
Rationale: "pastry is divided in 50 customers equally . so , total number of pastry must be a multiple of 50 only option a satisfies the condition , and hence is the answer"
Answer: a
Question (general): if 5400 mn = k ^ 4 , where m , n , and k are positive integers , what is the least possible value of 2 m + n ?
Options: a ) 11 , b ) 18 , c ) 20 , d ) 25 , e ) 35
Rationale: k ^ 4 = 5400 ∗ mn k ^ 4 = 3 ^ 3.2 ^ 3.5 ^ 2 . mn in order to make rhs a perfect power of 4 , we require it to be multiplied by 3 , 2 & 5 ^ 2 mn = 3 . 2.5 ^ 2 mn = 150 = 10 * 15 ( least possible ) answer = 2 * 10 + 15 = 35 answer : e
Answer: e
Question (physics): tabby is training for a triathlon . she swims at a speed of 1 mile per hour . she runs at a speed of 7 miles per hour . she wants to figure out her average speed for these two events . what is the correct answer for her ?
Options: a ) 8 mph , b ) 5.25 mph , c ) 3.5 mph , d ) 4 mph , e ) 0.5 mph
Rationale: "( 1 mph + 7 mph ) / 2 = 4 mph correct option is : d"
Answer: d
Question (physics): a train of 25 carriages , each of 60 meters length , when an engine also of 60 meters length is running at a speed of 60 kmph . in what time will the train cross a bridge 1.0 km long ?
Options: a ) 2.5 , b ) 3 , c ) 5 , d ) 7 , e ) 9
Rationale: "d = 25 * 60 + 1000 = 2500 m t = 2500 / 60 * 18 / 5 = 150 sec = 2.5 mins answer : a"
Answer: a
Question (gain): jerome anticipated that the webweb . com stock price would fall and sold all his webweb . com stocks for $ 5 per stock . he paid $ 10,000 tax on the revenue . a week later , jerome became convinced that the webweb . com stock price would rise , and he used the money that he had gotten from selling the webweb . com stocks to purchase them again , this time at $ 6 per stock . if jerome ended up having 7000 webweb . com stocks fewer than the number he had before selling them , how many webweb . com stocks did he have originally ?
Options: a ) 10,000 , b ) 11,600 , c ) 17,000 , d ) 14,000 , e ) 16,400
Rationale: "let the number of shares be x . 5 * x - 10000 ( money paid in taxes ) = 6 ( x - 7000 ) solving for x , we get the shares as 17000 . ans : ( option c )"
Answer: c
Question (general): find the principle on a certain sum of money at 9 % per annum for 2 2 / 5 years if the amount being rs . 1120 ?
Options: a ) 1000 , b ) 912.88 , c ) 927.78 , d ) 926.82 , e ) 921.05
Rationale: 1120 = p [ 1 + ( 9 * 12 / 5 ) / 100 ] p = 921.05 answer : e
Answer: e
Question (general): if 40 % of a number is equal to two - third of another number , what is the ratio of first number to the second number .
Options: a ) 5 : 3 , b ) 2 : 5 , c ) 4 : 7 , d ) 5 : 2 , e ) none of these
Rationale: "explanation : let the first number is a and second number is b . as per question ( 40 / 100 ) a = ( 2 / 3 ) b a / b = 2 / 3 x 100 / 40 a / b = 5 / 3 = > a : b = 5 : 3 answer : option a"
Answer: a
Question (gain): vijay lent out an amount rs . 10000 into two parts , one at 8 % p . a . and the remaining at 10 % p . a . both on simple interest . at the end of the year he received rs . 890 as total interest . what was the amount he lent out at 8 % pa . a ?
Options: a ) 5529 , b ) 5500 , c ) 5520 , d ) 5521 , e ) 5192
Rationale: "let the amount lent out at 8 % p . a . be rs . a = > ( a * 8 ) / 100 + [ ( 10000 - a ) * 10 ] / 100 = 890 = > a = rs . 5500 . answer : b"
Answer: b
Question (general): a man whose bowling average is 12.4 , takes 5 wickets for 26 runs and there by decreases his average by 0.4 . the number of wickets taken by him before his last match is ?
Options: a ) 82 , b ) 83 , c ) 84 , d ) 85 , e ) 86
Rationale: "12.4 x + 26 / ( 5 + x ) = 12 12.4 x + 26 = 60 + 12 x x = 34 / 0.4 = 85 answer : d"
Answer: d
Question (physics): anand finishes a work in 7 days , bittu finishes the same job in 8 days and chandu in 6 days . they take turns to finish the work . anand on the first day , bittu on the second and chandu on the third day and then anand again and so on . on which day will the work get over ?
Options: a ) 3 rd , b ) 6 th , c ) 9 th , d ) 7 th , e ) 8 th
Rationale: they completed 146 / 168 work in 6 days working one by one on eacg day . on 7 th day , 22 / 168 work is left which will be completed by anand on 7 th day . answer : d
Answer: d
Question (physics): if the product of two numbers is 45276 and their h . c . f . is 22 , find their l . c . m .
Options: a ) 2574 , b ) 2500 , c ) 2100 , d ) 2058 , e ) none of these
Rationale: explanation : hcf * lcm = 45276 , because we know product of two numbers = product of hcf and lcm lcm = 45276 / 22 = 2058 option d
Answer: d
Question (general): a person saved $ 10 in buying an item on sale . if he spent $ 500 for the item , approximately how much percent he saved in the transaction ?
Options: a ) 8 % , b ) 10 % , c ) 2 % , d ) 5 % , e ) 6 %
Rationale: "actual price = 500 + 10 = $ 510 saving = 10 / 510 * 100 = 100 / 51 = 2 % approximately answer is c"
Answer: c
Question (gain): okeydokey paid 5 apples at the apple investment booth for an unopened box of earthworms . artichokey paid 7 apples towards the same lot . the booth pays off earthworms proportional to the apples invested . the box turned out to contain 60 earthworms . how many of them should okeydokey receive ?
Options: a ) 25 , b ) 27 , c ) 28 , d ) 29 , e ) 30
Rationale: i 1 = 5 i 2 = 7 i 1 share 5 parts & i 2 share 7 parts total 12 parts - - - - - > 60 - - - - > 1 part - - - - - - - > 5 i 1 share = 5 parts - - - - - > 25 a
Answer: a
Question (gain): a glass was filled with 10 ounces of water , and 0.01 ounce of the water evaporated each day during a 20 - day period . what percent of the original amount of water evaporated during this period ?
Options: a ) 0.002 % , b ) 0.02 % , c ) 0.2 % , d ) 2 % , e ) 20 %
Rationale: "in 20 days 20 * 0.01 = 0.2 ounces of water evaporated , which is 0.2 / 10 ∗ 100 = 2 of the original amount of water . answer : d ."
Answer: d
Question (general): a certain store sells all maps at one price and all books at another price . on monday the store sold 10 maps and 8 books for a total of $ 22.00 , and on tuesday the store sold 20 maps and 15 books for a total of $ 60.00 . at this store , how much less does a map sell for than a book ?
Options: a ) $ - 5.4 , b ) $ 0.50 , c ) $ 0.75 , d ) $ 1.00 , e ) $ l . 25
Rationale: 10 x + 8 y = 22 20 x + 15 y = 60 multiply eq 1 by 2 and eq 2 by 1 20 x + 16 y = 44 20 x + 15 y = 60 subtracting 1 from 2 y = - 16 therefore x = 10.6 difference in price = - 5.4 a
Answer: a
Question (general): a 64 gallon solution of salt and water is 10 % salt . how many gallons of water must be added to the solution in order to decrease the salt to 8 % of the volume ?
Options: a ) 8 , b ) 12 , c ) 13 , d ) 14 , e ) 16
Rationale: amount of salt = 6.4 assume x gallons of water are added . 6.4 / 64 + x = 8 / 100 640 = 8 x + 512 8 x = 128 x = 16 correct option : e
Answer: e
Question (general): a gambler bought $ 5,000 worth of chips at a casino in denominations of $ 20 and $ 100 . that evening , the gambler lost 16 chips , and then cashed in the remainder . if the number of $ 20 chips lost was 2 more or 2 less than the number of $ 100 chips lost , what is the largest amount of money that the gambler could have received back ?
Options: a ) $ 4,040 , b ) $ 4,120 , c ) $ 1,960 , d ) $ 4,920 , e ) $ 1,400
Rationale: "in order to maximize the amount of money that the gambler kept , we should maximize # of $ 20 chips lost and minimize # of $ 100 chips lost , which means that # of $ 20 chips lost must be 2 more than # of $ 100 chips lost . so , if # of $ 20 chips lost is x then # of $ 100 chips lost should be x - 2 . now , given that total # of chips lost is 16 : x + x - 2 = 16 - - > x = 9 : 9 $ 20 chips were lost and 9 - 2 = 7 $ 100 chips were lost . total worth of chips lost is 9 * 20 + 7 * 100 = $ 880 , so the gambler kept $ 5,000 - $ 880 = $ 4,120 . answer : b ."
Answer: b
Question (general): in the coordinate plane , line a has a slope of - 2 and an x - intercept of 2 . line b has a slope of 5 and a y - intercept of - 10 . if the two lines intersect at the point ( a , b ) , what is the sum a + b ?
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: "the equation of line a is y = - 2 x + 4 the equation of line b is y = 5 x - 10 5 x - 10 = - 2 x + 4 x = 2 y = 0 the point of intersection is ( 2,0 ) and then a + b = 2 . the answer is c ."
Answer: c
Question (general): for any positive integer n , the sum of the first n positive integers equals n ( n + 1 ) / 2 . what is the sum of all the integers between 100 and 200 ?
Options: a ) 4545 , b ) 5050 , c ) 6525 , d ) 4352 , e ) 4652
Rationale: "sum = 100 * 101 / 2 = 50 * 101 = 5050 answer is b"
Answer: b
Question (general): a library has an average of 510 visitors on sundays and 240 on other day . the average number of visitors in a month of 50 days starting with sunday is
Options: a ) 280 , b ) 285 , c ) 171 , d ) 295 , e ) 275
Rationale: "explanation : as the month begin with sunday , so there will be five sundays in the month . so result will be : = ( 510 × 5 + 240 × 25 / 30 ) = ( 8550 / 50 ) = 171 answer : option c"
Answer: c
Question (gain): there are 200 employees in a room . 99 % are managers . how many managers must leave the room to bring down the percentage of managers to 98 % ?
Options: a ) 150 , b ) 100 , c ) 99 , d ) 50 , e ) 25
Rationale: "there are 198 managers and 2 others . the 2 others would compose 2 % of the total number of people if there were 100 people in the room . thus 100 managers must leave . the answer is b ."
Answer: b
Question (general): 387 x 387 + 114 x 114 + 2 x 387 x 114 = ?
Options: a ) 250001 , b ) 251001 , c ) 260101 , d ) 261001 , e ) none of these
Rationale: "answer given expression = a 2 + b 2 + 2 ab = ( a + b ) 2 where a = 387 and b = 114 = ( 387 + 114 ) 2 = ( 501 ) 2 = ( 500 + 1 ) 2 = ( 500 ) 2 + ( 1 ) 2 + 2 x 500 x 1 = 250000 + 1 + 1000 = 251001 . option : b"
Answer: b
Question (general): if a and b are the roots of the equation x 2 - 9 x + 9 = 0 , then the value of a 2 + b 2 is :
Options: a ) 63 , b ) 24 , c ) 17 , d ) 6 , e ) 5
Rationale: "sol . ( b ) the sum of roots = a + b = 9 product of roots = ab = 9 now , a 2 + b 2 = ( a + b ) 2 - 2 ab = 81 - 18 = 63 answer a"
Answer: a
Question (gain): a light has a rating of 80 watts , it is replaced with a new light that has 25 % higher wattage . how many watts does the new light have ?
Options: a ) 105 , b ) 95 , c ) 80 , d ) 60 , e ) 100
Rationale: "final number = initial number + 25 % ( original number ) = 80 + 25 % ( 80 ) = 80 + 20 = 100 . answer e"
Answer: e
Question (other): in the class of 40 students , 30 speak hindi and 20 speak english . what is the lowest possible number of students who speak both the languages ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: let the student who speaks hindi - x let the student who speaks english - y as ( xuy ) - ( xny ) = total 30 + 20 - ( xny ) = 40 = 10 a )
Answer: a
Question (general): two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 30 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 30 % , d ) 23 % , e ) can not be determined
Rationale: answer : c .
Answer: c
Question (general): if k is an integer and 0.00010101 x 10 ^ k is greater than 100 , what is the least possible value of k ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: 0.00010101 * 10 ^ k > 100 we need to move the decimal point to the right 6 places to get 101.01 this is equivalent to multiplying by 10 ^ 6 . the answer is d .
Answer: d
Question (general): how many numbers from 10 to 50 are exactly divisible by 3 .
Options: a ) 13 , b ) 14 , c ) 16 , d ) 17 , e ) 19
Rationale: "12 , 15 , 18 , 21 , 24 , 27 , 30 , 33 , 36 , 39 , 42 , 45,48 . 13 numbers . 10 / 3 = 3 and 50 / 3 = 16 = = > 16 - 3 = 13 . therefore 13 digits . a )"
Answer: a
Question (general): the ratio of laxmi ' s age to the age of her mother is 3 : 11 . the difference of their ages is 24 years . the ratio of their ages after 3 years will be ?
Options: a ) 1 : 9 , b ) 1 : 3 , c ) 1 : 2 , d ) 1 : 1 , e ) 3 : 3
Rationale: suppose age of laxmi is x years . the difference of their ages \ inline \ therefore ratio of their ages after 3 years = = = 12 : 36 = 1 : 3 answer : b
Answer: b
Question (general): what is the total number of integers between 10 and 50 that are divisible by 2 ?
Options: a ) 18 , b ) 19 , c ) 22 , d ) 25 , e ) 10
Rationale: "12 , 14 , 16 , . . . , 46,48 this is an equally spaced list ; you can use the formula : n = ( largest - smallest ) / ( ' space ' ) + 1 = ( 48 - 12 ) / ( 2 ) + 1 = 36 / 2 + 1 = 18 + 1 = 19 answer is b"
Answer: b
Question (general): company x provides bottled water to its employees in 10 liter bottles , $ 2 each . at least how many 10 l bottles must company x buy monthly , so that new contract with $ 50 fixed monthly rate and $ 1 for 50 l bottle each paid off ? ( assume that no other costs apply )
Options: a ) 28 , b ) 29 , c ) 30 , d ) 31 , e ) 32
Rationale: let the no . of 10 liter bottles be x , so the no . of 50 l bottles will be x / 5 ( to equate the vol . ) since the total cost will be equal , 2 x = 50 + x / 5 so x = 27.77 or 28 . answer is ( a ) .
Answer: a
Question (gain): solution y is 30 percent liquid x and 70 percent water . if 2 kilograms of water evaporate from 6 kilograms of solution y and 2 kilograms of solution y are added to the remaining 4 kilograms of liquid , what percent of this new solution is liquid x ?
Options: a ) 33 % , b ) 35 1 / 2 % , c ) 37 % , d ) 40 % , e ) 42 %
Rationale: "in 8 kilograms of solution y there are 0.3 * 6 = 1.8 kilograms of solution x ; after 2 kilograms of water are replaced by 2 kilograms of solution y , to the existing 1.8 kilograms of solution x , 0.3 * 2 = 0.6 kilograms of solution x are added , so in the new solution of 6 kilograms there are 1.8 + 0.6 = 2.4 kilograms of solution x , which is 2.4 / 6 * 100 = 40 % of this new solution . answer : d ."
Answer: d
Question (general): 10 % people of a village in sri lanka died by bombardment , 20 % of the remainder left the village on account of fear . if now the population is reduced to 3312 , how much was it in the beginning ?
Options: a ) a ) 3800 , b ) b ) 4200 , c ) c ) 4400 , d ) d ) 4500 , e ) e ) 4600
Rationale: "x * ( 90 / 100 ) * ( 80 / 100 ) = 3312 x = 4600 answer : e"
Answer: e
Question (physics): a is twice as good a workman as b and they took 11 days together to do the work b alone can do it in .
Options: a ) 17 days , b ) 12 days , c ) 29 days , d ) 25 days , e ) 33 days
Rationale: "wc = 2 : 1 2 x + x = 1 / 11 x = 1 / 33 = > 33 days answer : e"
Answer: e
Question (general): 160 % of 5 / 8 =
Options: a ) 0.2 , b ) 0.5 , c ) 0.6 , d ) 0.75 , e ) 1.0
Rationale: "should be simple . 1.6 * 5 / 8 = 8 / 8 = 1.0 correct option : e"
Answer: e
Question (general): what is the sum of all the multiples of 9 between 0 and 99 ?
Options: a ) 500 , b ) 594 , c ) 450 , d ) 340 , e ) 440
Rationale: "the multiples of 9 between 0 and 99 are 9 , 18 , 27 , 36 , 45 , 54 , 63 , 72 , 81 , 90 , 99 . if these are all added together , the result is 594 . final answer : b"
Answer: b
Question (general): if the price of 357 apples is rs . 1517.25 , what will be the approximate price of 49 dozens of such apples ?
Options: a ) rs . 2500 , b ) rs . 2300 , c ) rs . 2200 , d ) rs . 1400 , e ) rs . 1600
Rationale: explanation : price of 357 apples = rs . 1517.25 price of 1 apple = rs . 1517.25 / 357 price of 49 dozens apples = rs ( 49 × 12 × 1517.25 / 357 ) ≈ rs . 2500 answer : option a
Answer: a
Question (gain): in the first 10 overs of a cricket game , the run rate was only 3.8 . what should be the run rate in the remaining 40 overs to reach the target of 282 runs ?
Options: a ) 6.25 , b ) 6.5 , c ) 6.75 , d ) 6.1 , e ) 8
Rationale: "10 overs - run rate = 3.8 runs scored in first 10 overs = 38 remaining overs 40 total runs to be scored = 282 38 runs already scored 282 - 38 = 244 244 runs to be scored in 40 overs let required runrate be x 40 * x = 244 x = 244 / 40 x = 6.1 the required runrate is 6.1 answer : d"
Answer: d