regisss/math_qa huggingface dataset:
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: ( 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: 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
Problem: a person buys an article at rs . 480 . at what price should he sell the article so as to make a profit of 24 % ?
Options: a ) 595 , b ) 882 , c ) 772 , d ) 662 , e ) 521
Rationale: "cost price = rs . 480 profit = 24 % of 480 = rs . 115 selling price = cost price + profit = 480 + 115 = 595 answer : a"
Answer: a
Problem: what is the median of a set of consecutive integers if the sum of nth number from the beginning and nth number from the end is 110 ?
Options: a ) 10 , b ) 25 , c ) 55 , d ) 75 , e ) 100
Rationale: surprisingly no one answered this easy one . property of a set of consecutive integerz . mean = median = ( first element + last element ) / 2 = ( second element + last but one element ) / 2 = ( third element + third last element ) / 2 etc . etc . so mean = median = 110 / 2 = 55 answer is c
Answer: c
Problem: roses can be purchased individually for $ 6.30 , one dozen for $ 36 , or two dozen for $ 50 . what is the greatest number of roses that can be purchased for $ 680 ?
Options: a ) 156 , b ) 162 , c ) 316 , d ) 324 , e ) 325
Rationale: "buy as many $ 50 deals as possible . we can by 650 / 50 = 13 two dozen roses , thus total of 13 * 24 = 312 roses . we are left with 680 - 650 = $ 30 . we can buy 30 / 6.3 = ~ 4 roses for that amount . total = 312 + 4 = 316 . answer : c ."
Answer: c
Problem: the sub - duplicate ratio of 25 : 49 is
Options: a ) 4 : 3 , b ) 5 : 7 , c ) 6 : 4 , d ) 1 : 4 , e ) 2 : 3
Rationale: "root ( 25 ) : root ( 49 ) = 5 : 7 answer : b"
Answer: b
Problem: a man walking at a rate of 10 km / hr crosses a bridge in 24 minutes . the length of the bridge is ?
Options: a ) 1521 , b ) 1492 , c ) 1667 , d ) 4000 , e ) 1112
Rationale: "speed = 10 * 5 / 18 = 50 / 18 m / sec distance covered in 24 minutes = 50 / 18 * 24 * 60 = 4000 m answer is d"
Answer: d
Problem: find the ratio in which rice at rs . 7.10 a kg be mixed with rice at rs . 5.70 a kg to produce a mixture worth rs . 6.30 a kg ?
Options: a ) 1 : 3 , b ) 2 : 3 , c ) 3 : 4 , d ) 4 : 5 , e ) none of these
Rationale: "solution required ratio = 60 : 80 = 3 : 4 answer c"
Answer: c
Problem: 11 : 35 : : 17 : ?
Options: a ) 3 , b ) 22 , c ) 58 , d ) 10 , e ) 54
Rationale: "11 : 35 : : 17 : x 11 x : 35 x 17 11 x = 595 x = 54 answer : d"
Answer: d
Problem: a class consists of 15 biology students and 10 chemistry students . if you pick two students at the same time , what ' s the probability that one is maths and one is chemistry ?
Options: a ) 2 / 7 , b ) 5 / 7 , c ) 1 / 2 , d ) 3 / 7 , e ) 1 / 2
Rationale: p ( 1 st b , 2 nd c ) = 15 / 25 * 10 / 24 = 150 / 600 = 1 / 4 ; p ( 1 st c , 2 nd b ) = 10 / 25 * 15 / 24 = 150 / 600 = 1 / 4 . p = 1 / 4 + 1 / 4 = 1 / 2 . answer : c .
Answer: c
Problem: an aeroplane covers a certain distance of 420 kmph in 6 hours . to cover the same distance in 4 2 / 3 hours , it must travel at a speed of
Options: a ) 440 , b ) 540 , c ) 640 , d ) 740 , e ) 250
Rationale: "speed of aeroplane = 420 kmph distance travelled in 6 hours = 420 * 6 = 2520 km speed of aeroplane to acver 2520 km in 14 / 3 = 2520 * 3 / 14 = 540 km answer b ."
Answer: b
Problem: jane and thomas are among the 8 people from which a committee of 4 people is to be selected . how many different possible committees of 4 people can be selected from these 8 people if at least one of either jane or thomas is to be selected ?
Options: a ) 28 , b ) 46 , c ) 55 , d ) 63 , e ) 70
Rationale: "solution : j + t + 6 = total 8 , we need to select at least one of the j and t or both = total 4 out of 8 - 4 out of 6 8 c 4 - 6 c 4 = 55 ans : c"
Answer: c
Problem: the average mark of the students of a class in a particular exam is 80 . if 8 students whose average mark in that exam is 20 are excluded , the average mark of the remaining will be 90 . find the number of students who wrote the exam .
Options: a ) 15 , b ) 25 , c ) 35 , d ) 45 , e ) 56
Rationale: "let the number of students who wrote the exam be x . total marks of students = 80 x . total marks of ( x - 8 ) students = 90 ( x - 8 ) 80 x - ( 8 * 20 ) = 90 ( x - 8 ) 560 = 10 x = > x = 56 answer : e"
Answer: e
Problem: what is the smallest integer k for which 64 ^ k > 4 ^ 17 ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "64 ^ k > 4 ^ 17 4 ^ ( 3 k ) > 4 ^ 17 3 k > 17 k = 6 the answer is c ."
Answer: c
Problem: a rectangular swimming pool is 20 feet by 18 feet . a deck that has uniform width surrounds the pool . the total area of the pool and deck is 624 square feet . what is the width of the deck ?
Options: a ) 2 , b ) 3 , c ) 4 , d ) 5 , e ) 6
Rationale: "let the width = w total area of the pool and deck = ( 2 w + 20 ) ( 2 w + 18 ) we can test the answer choices along with unit digit method a ) 2 feet . . . . . . . . . . . 24 * 22 has unit digit 8 . . . . . . . . . . eliminate b ) 2.5 feet . . . . . . . . . 25 * 23 has unit digit 5 . . . . . . . . . . eliminate c ) 3 feet . . . . . . . . . . . . 26 * 24 has unit digit 4 . . . . . . . . . . . hold d ) 4 feet . . . . . . . . . . . . 28 * 26 has unit digit 8 . . . . . . . . . . . eliminate e ) 5 feet . . . . . . . . . . . . 30 * 38 has unit digit 0 . . . . . . . . . . . eliminate answer : b w = 3"
Answer: b
Problem: what is the least integer greater than 0 + 0.5 ?
Options: a ) – 2 , b ) – 1 , c ) 0 , d ) 1 , e ) 2
Rationale: "this question is just about doing careful arithmetic and remembering what makes a numberbiggerorsmallercompared to another number . first , let ' s take care of the arithmetic : ( 0 ) + ( 0.5 ) = 0.5 on a number line , since we ' re adding + . 5 to a number , the total moves to the right ( so we ' re moving from 0 to 0.5 ) . next , the question asks for the least integer that is greater than 0.5 again , we can use a number line . numbers become greater as you move to the right . the first integer to the right of 0.5 is 1 . final answer : d"
Answer: d
Problem: two diagonals of a rhombus are 72 cm and 30 cm respectively . what is its perimeter ?
Options: a ) 136 cm
b ) 156 cm
c ) 144 cm
d ) 121 cm
e ) 126 cm
Rationale: all sides of rhombus are congruent let pr = 72 sq = 30 cm po = 0 r = 72 / 1 = 36 cm so = 0 q = 30 / 2 = 15 cm pq = qr = rs = sp = root ( 36 ^ 2 + 15 ^ 2 ) = rppt ( 1296 + 225 ) = root ( 1521 ) = 39 cm perimeter = 4 * 39 = 156 cm answer b
Answer: b
Problem: to fill a tank , 25 buckets of water is required . how many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to 3 / 10 of its present ?
Options: a ) 61.5 , b ) 60.5 , c ) 63.5 , d ) 83.333 , e ) 64.5
Rationale: "let capacity of 1 bucket = x capacity of the tank = 25 x new capacity of the bucket = 3 x / 10 hence , number of buckets needed = 25 x / ( 3 x / 10 ) = ( 25 × 10 ) / 3 = 83.33333 answer is d ."
Answer: d
Problem: one side of a rectangular field is 14 m and one of its diagonal is 17 m . find the area of the field .
Options: a ) 134.4 , b ) 120 , c ) 150 , d ) 180 , e ) none
Rationale: "solution other side = √ ( 17 ) 2 - ( 14 ) 2 = √ 289 - 196 = √ 93 = 9.6 m . ∴ area = ( 14 x 9.6 ) m 2 = 134.4 m 2 . answer a"
Answer: a
Problem: a hiker walking at a constant rate of 4 kilometers per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 24 kilometers per hour . the cyclist stops and waits for the hiker 5 minutes after passing her while the hiker continues to walk at her constant rate . how many minutes must the cyclist wait until the hiker catches up ?
Options: a ) 10 , b ) 15 , c ) 20 , d ) 25 , e ) 30
Rationale: "in 5 minutes , the cyclist travels a distance of ( 5 / 60 ) * 24 = 2 km . the time it takes the hiker to complete this distance is 2 / 4 hours = 30 minutes the cyclist needs to wait 30 - 5 = 25 minutes the answer is d ."
Answer: d
Problem: the average weight of 29 students is 28 kg . by the admission of a new student , the average weight is reduced to 27.1 kg . the weight of the new student is
Options: a ) 22 kg , b ) 1 kg , c ) 22.4 kg , d ) 21 kg , e ) none of these
Rationale: "exp . the total weight of 29 students = 29 * 28 the total weight of 30 students = 30 * 27.1 weight of the new student = ( 30 * 27.1 – 29 * 28 ) = 813 - 812 = 1 answer : b"
Answer: b
Problem: what will be in unit ' s place digit of 3 to the power 34 .
Options: a ) 1 , b ) 6 , c ) 3 , d ) 0 , e ) 9
Rationale: as the unit place digit of 3 to the power of 1 is 3 , to the power of 2 is 9 . to the power of 3 is 7 , to the power of 4 is 1 and it ' ll be repeated again in the same order . . . . so the unit place digit of 3 to the power of 34 is 9 . . answer : e
Answer: e
Problem: a group of 8 friends want to play doubles tennis . how many different ways can the group be divided into 4 teams of 2 people ?
Options: a ) 420 , b ) 2520 , c ) 168 , d ) 90 , e ) 105
Rationale: c 28 ∗ c 26 ∗ c 24 ∗ c 22 / 4 ! = 105 , we are dividing by 4 ! ( factorial of the # of teams ) as the order of the teams does not matter . if 8 people are - 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , then ( 12 ) ( 34 ) ( 56 ) ( 78 ) would be the same 4 teams as ( 56 ) ( 78 ) ( 12 ) ( 34 ) , as we do n ' t have team # 1 , team # 2 , . . . you can think about this in another way . for the first person we can pick a pair in 7 ways ; for the second one in 5 ways ( as two are already chosen ) ; for the third one in 3 ways ( as 4 people are already chosen ) ; for the fourth one there is only one left . so we have 7 * 5 * 3 * 1 = 105 answer : e
Answer: e
Problem: a retail appliance store priced a video recorder at 20 percent above the wholesale cost of $ 200 . if a store employee applied the 10 percent employee discount to the retail price to buy the recorder , how much did the employee pay for the recorder ?
Options: a ) $ 198 , b ) $ 216 , c ) $ 220 , d ) $ 230 , e ) $ 240
Rationale: "wholesale cost of video recorder = 200 $ video recorder was priced at 20 percent above 200 = 240 $ % discount given by store employee = 10 employee paid = . 9 * 240 = 216 $ answer b"
Answer: b
Problem: an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1,455 , what was the total number of pairs of contact lenses that she sold ?
Options: a ) 11 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: ( x + 5 ) * 150 + x * 85 = 1455 = > x = 3 total lens = 3 + ( 3 + 5 ) = 11 answer a
Answer: a
Problem: it costs $ 5 for the first 1 / 3 hour to use the laundry machine at the laundromat . after the first ¼ hour it costs $ 12 per hour . if a certain customer uses the laundry machine for 2 hours and 30 minutes , how much will it cost him ?
Options: a ) $ 27 . , b ) $ 29 . , c ) $ 31 . , d ) $ 33 . , e ) $ 35 .
Rationale: 2 hrs 30 min = 150 min first 20 min - - - - - - > $ 5 time left is 130 min . . . now , 60 min costs $ 12 1 min costs $ 12 / 60 150 min costs $ 12 / 60 * 130 = > $ 26.00 so , total cost will be $ 26 + $ 5 = > $ 31 hence answer will be c
Answer: c
Problem: a computer is programmed to multiply consecutive even integers 2 * 4 * 6 * 8 * … * n until the product is divisible by 1881 , what is the value of n ?
Options: a ) 22 , b ) 38 , c ) 114 , d ) 122 , e ) 672
Rationale: "factorise 1881 . . 3 * 11 * 57 . . so n has to be a multiple of largest prime number , 61 . . so n = 2 * 57 = 114 . . ans : c"
Answer: c
Problem: 2,7 , 17,3 , 11,19 , 5,13 , __
Options: a ) 20 , b ) 21 , c ) 22 , d ) 23 , e ) 24
Rationale: "2 = 1 st prime no . 3 = 2 nd p . n . 5 = 3 rd p . n . 7 = 4 th p . n . 11 = 5 th p . n . 13 = 6 th p . n . 17 = 7 th p . n . 19 = 8 th p . n . , and 23 = 9 th p . n . 2 , 7,17 = 1 st p . n . , ( 1 + 3 ) th p . n . , ( 1 + 3 + 3 ) th p . n . 3 , 11,19 = 2 nd p . n . , ( 2 + 3 ) th p . n . , ( 2 + 3 + 3 ) th p . n . 5 , 13,23 = 3 rd p . n . , ( 3 + 3 ) th p . n . , ( 3 + 3 + 3 ) th p . n . answer : d"
Answer: d
Problem: if 8 workers can build 8 cars in 8 days , then how many days would it take 4 workers to build 4 cars ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 12 , e ) 16
Rationale: 8 workers can build 1 car per day on average . 1 worker can build 1 / 8 of a car per day . 4 workers can build 1 / 2 car per day . the time required to build 4 cars is 4 / ( 1 / 2 ) = 8 days the answer is c .
Answer: c
Problem: in 10 years , a will be twice as old as b was 10 years ago . if a is now 9 years older than b , the present age of b is
Options: a ) 9 years , b ) 19 years , c ) 29 years , d ) 39 years , e ) none
Rationale: "solution let b ' s present age = x years . then , a ' s present age ‹ = › ( x + 9 ) years . ∴ ( x + 9 ) + 10 = 2 ( x - 10 ) ‹ = › x + 19 = 2 x - 20 ‹ = › x = 39 . answer d"
Answer: d
Problem: if 50 apprentices can finish a job in 4 hours , and 30 journeymen can finish the same job in 8 hours , how much of the job should be completed by 10 apprentices and 15 journeymen in one hour ?
Options: a ) 1 / 9 , b ) 29 / 180 , c ) 9 / 80 , d ) 1 / 5 , e ) 39 / 121
Rationale: "50 apprentices can finish the job in 4 hours , thus : 10 apprentices can finish the job in 4 * 5 = 20 hours ; in 1 hour 10 apprentices can finish 1 / 20 of the job . 30 journeymen can finish the same job in 4,5 hours , thus : 15 journeymen can finish the job in 8 * 2 = 16 hours ; in 1 hour 15 journeymen can finish 1 / 16 of the job . therefore , in 1 hour 10 apprentices and 15 journeymen can finish 1 / 20 + 1 / 16 = 9 / 80 of the job . answer : c"
Answer: c
Problem: two ships are sailing in the sea on the two sides of a lighthouse . the angle of elevation of the top of the lighthouse is observed from the ships are 30 º and 45 º respectively . if the lighthouse is 100 m high , the distance between the two ships is :
Options: a ) 173 m , b ) 200 m , c ) 273 m , d ) 300 m , e ) none of these
Rationale: "xplanation : let ab be the lighthouse and c and d be the positions of the ships . then , ab = 100 m , < acb = 30 º and < adb = 45 º . ab / ac = tan 30 answer : c"
Answer: c
Problem: in a class , 5 people like baseball and football , 2 people only like baseball , 3 people only like football , and 6 people like neither . how many people are in the class ?
Options: a ) 10
b ) 14
c ) 16
d ) 20
e ) 22
Rationale: 16 . to get the answer , you can simply add the different types of students , as there are no overlaps in the categories : 5 + 2 + 3 + 6 = 16 . as such , the correct answer is c : 16 .
Answer: c
Problem: how many bricks , each measuring 25 cm x 11.25 cm x 6 cm , will be needed to build a wall of 8.5 m x 6 m x 22.5 cm ?
Options: a ) 6400 , b ) 6410 , c ) 6440 , d ) 6500 , e ) 6800
Rationale: "number of bricks = volume of wall / volume of bricks = 850 x 600 x 22.5 / 25 x 11.25 x 6 = = 6800 answer : e"
Answer: e
Problem: given that p is a positive even integer with a positive units digit , if the units digit of p ^ 3 minus the units digit of p ^ 2 is equal to 0 , what is the units digit of p + 4 ?
Options: a ) 7 , b ) 8 , c ) 10 , d ) 11 , e ) 12
Rationale: p is a positive even integer with a positive units digit - - > the units digit of p can be 2 , 4 , 6 , or 8 - - > in order the units digit of p ^ 3 - p ^ 2 to be 0 , the units digit of p ^ 3 and p ^ 2 must be the same . thus the units digit of p can be 0 , 1 , 5 or 6 . intersection of values is 6 , thus the units digit of p + 4 is 6 + 4 = 10 . answer : c .
Answer: c
Problem: a palindrome is a number that reads the same forward and backward , such as 196 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 90 , e ) 2500
Rationale: "a palindrome is a number that reads the same forward and backward . examples of four digit palindromes are 1221 , 4334 , 2222 etc you basically get to choose the first two digits and you repeat them in opposite order . say , you choose 45 as your first two digits . the next two digits are 54 and the number is 4554 . also , you need only odd palindromes . this means that you need an odd digit at the end i . e . 1 / 3 / 5 / 7 / 9 . this means that you need to start the number with an odd digit . only then will it end with an odd digit . in how many ways can you pick two digits such that the first one is an odd digit ? the first digit can be selected in 5 ways . ( 1 / 3 / 5 / 7 / 9 ) the second digit can be selected in 10 ways . ( 0 / 1 / 2 / 3 . . . 8 / 9 ) total = 5 * 18 = 90 ways d"
Answer: d
Problem: the profit obtained by selling an article for rs . 56 is the same as the loss obtained by selling it for rs . 42 . 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 56 - c . p = c . p - 42 2 c . p = 56 + 42 ; c . p = 98 / 2 = 49 answer : c"
Answer: c
Problem: what is the maximum number of points that 10 circles of different radii intersect ?
Options: a ) 24 , b ) 26 , c ) 33 , d ) 90 , e ) 100
Rationale: "the maximum number of points that two circles intersect is two . therefore , each of these 10 circles intersect two point with each of the other 9 circles . as a consequence , the number of these points is equal to two times the number of combination of the 10 circles . 2 ∗ ( 10 ! ) / ( 2 ! ∗ 10 ! ) = 90 answer : d"
Answer: d
Problem: an 80 - liter solution of cool - drink is made from 10 % jasmine water . if 5 liters of jasmine and 15 liters of water were added to the solution , what percent of the solution is jasmine ?
Options: a ) 11 % , b ) 13 % , c ) 15 % , d ) 17 % , e ) 19 %
Rationale: the percent of jasmine in the resulting solution is : ( amount of jasmine ) / ( total volume ) ( 0.1 ( 80 ) + 5 ) / 100 = 13 / 100 = 13 % the answer is b .
Answer: b
Problem: an error 3 % in excess is made while measuring the side of a square . the percentage of error in the calculated area of the square is
Options: a ) 6.04 % , b ) 6.14 % , c ) 6.23 % , d ) 6.26 % , e ) 6.09 %
Rationale: "100 cm is read as 102 cm . a 1 = ( 100 x 100 ) cm 2 and a 2 ( 103 x 103 ) cm 2 . ( a 2 - a 1 ) = [ ( 103 ) 2 - ( 100 ) 2 ] = ( 103 + 100 ) x ( 103 - 100 ) = 609 cm 2 . percentage error = 6.09 e"
Answer: e
Problem: share rs . 6600 among john , jose & binoy in the ration 2 : 4 : 6 . find the amount received by john ?
Options: a ) 2200 , b ) 980 , c ) 1200 , d ) 1240 , e ) 1400
Rationale: "amount received by sanjay . 4 / 12 x 6600 = 2200 = ( related ratio / sum of ratio ) x total amount so , the amount received by sanjay is 2200 . a"
Answer: a
Problem: the cash realised on selling a 14 % stock is rs . 105.25 , brokerage being 1 / 4 % is ?
Options: a ) 366 , b ) 106 , c ) 102 , d ) 105 , e ) 122
Rationale: "cash realised = rs . ( 105.25 - 0.25 ) = rs . 106 . answer : d"
Answer: d
Problem: there are 6 boxes numbered 1 , 2 , … , . 6 . each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered . the total number of ways in which this can be done is
Options: a ) 22 , b ) 21 , c ) 45 , d ) 27 , e ) 25
Rationale: list down possibilities : from only 1 box all the way to all 6 if only one of the boxes has a green ball , it can be any of the 6 boxes . so , we have 6 possibilities . if two of the boxes have green balls and then there are 5 consecutive sets of 2 boxes . 12 , 23 , 34 , 45 , 56 . if 3 of the boxes have green balls , there are 4 possibilities : 123 , 234 , 345 , 456 . if 4 boxes have green balls , there are 3 possibilities : 1234 , 2345 , 3456 . if 5 boxes have green balls , there are 2 possibilities : 12345 , 23456 . if all 6 boxes have green balls , there is just 1 possibility . total number of possibilities = 6 + 5 + 4 + 3 + 2 + 1 = 21 . ans : b
Answer: b
Problem: a tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume . if 2,500 gallons of water evaporate from the tank , the remaining solution will be approximately what percent sodium chloride ?
Options: a ) 1.25 % , b ) 3.75 % , c ) 6.25 % , d ) 6.67 % , e ) 11.7 %
Rationale: "10000 gallons solution has 500 gallons sodium chloride 9500 gallons water = > 2500 gallons water evaporates = > 7000 gallons water remains hence , concentration of sodium chloride is 500 / 7500 = 6.67 % answer : d"
Answer: d
Problem: a , b , c and d enter into partnership . a subscribes 1 / 3 of the capital b 1 / 4 , c 1 / 5 and d the rest . how much share did a get in a profit of rs . 2490 ?
Options: a ) rs . 832 , b ) rs . 830 , c ) rs . 822 , d ) rs . 812 , e ) rs . 810
Rationale: "let the total amount in the partnership be ' x ' . then a ' s share = x / 3 b ' s share = x / 4 c ' s share = x / 5 d ' s share = x - ( x / 3 + x / 4 + x / 5 ) = 13 x / 60 a : b : c : d = x / 3 : x / 4 : x / 5 : 13 x / 60 = 20 : 15 : 12 : 13 a ' s share in the profit of rs . 2490 = 20 ( 2490 / 60 ) = rs . 830 . answer : b"
Answer: b
Problem: the area of an isosceles trapezoid with sides of length 5 and bases of length 9 and 15 is ?
Options: a ) 44 , b ) 48 , c ) 46 , d ) 47 , e ) 50
Rationale: "isosceles trapezoid indicates that if we draw perpendicular from two vertex of the smaller side , the longer side with side 15 will be divided into 3 parts = 9 , 3 and 3 ( making one square and two right triangles ) for the right triangle , height will be = ( 5 ^ 2 - 3 ^ 2 ) ^ 1 / 2 = 4 and the area of trapezoid = 1 / 2 ( b 1 + b 2 ) h = 1 / 2 * 24 * 4 = 48 b"
Answer: b
Problem: a train covers a distance at a speed of 240 kmph in 5 hours . to cover the same distance in 5 / 3 hours , it must travel at a speed of ?
Options: a ) 516 , b ) 840 , c ) 560 , d ) 720 , e ) 920
Rationale: "distance = 240 * 5 = 1200 km required speed = 1200 * 3 / 5 = 720 km / hr answer is d"
Answer: d
Problem: each week a restaurant serving mexican food uses the same volume of chili paste , which comes in either 25 - ounce cans or 15 - ounce cans of chili paste . if the restaurant must order 40 more of the smaller cans than the larger cans to fulfill its weekly needs , then how many larger cans are required to fulfill its weekly needs ?
Options: a ) 40 , b ) 30 , c ) 60 , d ) 45 , e ) 55
Rationale: "let x be the number of 25 ounce cans . therefore ( x + 40 ) is the number of 15 ounce cans . total volume is same , therefore 25 x = 15 ( x + 40 ) 10 x = 600 x = 60 ans is c"
Answer: c
Problem: a 270 metres long bullet train running at the speed of 120 kmph crosses another bullet train running in opposite direction at the speed of 80 kmph in 9 seconds . what is the length of the other bullet train ?
Options: a ) 226 , b ) 230 , c ) 430 , d ) 310 , e ) 260
Rationale: b 230 relative speed = ( 120 + 80 ) km / hr = 200 x 5 / 18 = 500 / 9 m / sec then , ( x + 270 ) / 9 = 500 / 9 - - > x + 270 = 500 - - > x = 230 .
Answer: b
Problem: winson traveled the entire 60 miles trip . if he did the first 10 miles of at a constant rate 20 miles per hour and the remaining trip of at a constant rate 48 miles per hour , what is the his average speed , in miles per hour ?
Options: a ) 20 mph , b ) 24 mph , c ) 30 mph , d ) 32 mph , e ) 40 mph
Rationale: average speed = sum of distance / sum of time . if he travelled the first 10 miles at 20 miles / hr , it would take 0.5 hr . for the remaining trip , if he went at 48 miles / 1 hr , it would take 1 hour . then , the average speed is 60 miles / ( 0.5 + 1 ) hrs = 40 miles / 1 hr . therefore , the answer is e .
Answer: e
Problem: a pet store holds cats and dogs . if the difference between the number of cats and the number of dogs is 7 . what could be the ratio of cats to dogs in the pet store ?
Options: a ) 1 : 3 , b ) 1 : 4 , c ) 28 : 35 , d ) 2 : 5 , e ) 4 : 6
Rationale: "say theratioof cats to dogs is a / b . then thenumberof cats would be ax and thenumberof dogs bx , for some positive integer x . we are told that ax - bx = 7 - - > x ( a - b ) = 7 . since 7 is a prime number it could be broken into the product of two positive multiples only in one way : x ( a - b ) = 1 * 7 . the above implies that either x = 1 and a - b = 7 or x = 7 and ( a - b ) = 1 . therefore the correct answer should have the difference between numerator and denominator equal to 1 or 7 . for the original question only option which fits is e , 4 : 5 . cats = 7 * 4 = 28 and dogs = 7 * 5 = 35 . answer : c ."
Answer: c
Problem: a train running at the speed of 60 km / hr crosses a pole in 18 seconds . find the length of the train ?
Options: a ) 150 meter , b ) 170 meter , c ) 156 meter , d ) 300 meter , e ) 154 meter
Rationale: "speed = 60 * ( 5 / 18 ) m / sec = 50 / 3 m / sec length of train ( distance ) = speed * time ( 50 / 3 ) * 18 = 300 meter answer : d"
Answer: d
Problem: the h . c . f of two numbers is 23 and the other two factors of their l . c . m are 13 and 14 . the larger of the two numbers is :
Options: a ) 338 , b ) 278 , c ) 322 , d ) 231 , e ) 121
Rationale: "clearly , the numbers are ( 23 * 13 ) and ( 23 * 14 ) . larger number = ( 23 * 14 ) = 322 . answer : c"
Answer: c
Problem: 60 is subtracted from 50 % of a number , the result is 10 . find the number ?
Options: a ) 150 , b ) 120 , c ) 266 , d ) 288 , e ) 271
Rationale: "( 50 / 100 ) * x – 50 = 10 5 x = 600 x = 120 answer : b"
Answer: b
Problem: 80 is divided into two parts in such a way that seventh part of first and ninth part of second are equal . find the smallest part ?
Options: a ) 35 , b ) 32 , c ) 36 , d ) 40 , e ) 52
Rationale: "x / 7 = y / 9 = > x : y = 7 : 9 7 / 16 * 80 = 35 answer : a"
Answer: a
Problem: the value of ( . 02 ) 2 + ( 0.52 ) 2 + ( 0.035 ) 2 / ( 0.002 ) 2 + ( 0.052 ) 2 + ( 0.0035 ) 2
Options: a ) 100 , b ) 1000 , c ) . 001 , d ) . 0001 , e ) . 01
Rationale: ( . 02 ) 2 + ( 0.52 ) 2 + ( 0.035 ) 2 / ( 0.002 ) 2 + ( 0.052 ) 2 + ( 0.0035 ) 2 = a 2 + b 2 + c 2 / ( a / 10 ) 2 + ( b / 10 ) 2 + ( c / 10 ) 2 where a = . 02 , b = . 52 , c = . 035 = 100 ( a 2 + b 2 + c 2 ) / a 2 + b 2 + c 2 = 100 answer : a
Answer: a