Cheukting/mathqa huggingface dataset:
Question (general): a corporation that had $ 2 billion in profits for the year paid out $ 100 million in employee benefits . approximately what percent of the profits were the employee benefits ? ( note : 1 billion = 10 ^ 9 )
Options: a ) 50 % , b ) 20 % , c ) 5 % , d ) 2 % , e ) 0.2 %
Rationale: "required answer = [ employee benefit / profit ] * 100 = [ ( 100 million ) / ( 2 billion ) ] * 100 = [ ( 100 * 10 ^ 6 ) / ( 2 * 10 ^ 9 ) ] * 100 = ( 50 / 1000 ) * 100 = 5 % so answer is ( c )"
Answer: c
Question (physics): a man and a boy complete a work together in 24 days . if for the last 6 days man alone does the work then it is completed in 26 days . how long the boy will take to complete the work alone ?
Options: a ) 72 days , b ) 20 days , c ) 24 days , d ) 36 days , e ) 34 days
Rationale: explanation : ( man + boy ) ’ s 1 day ’ s work = 1 / 24 their 20 day ’ s work = 1 / 24 × 20 = 5 / 6 the remaining 1 / 6 work is done by the man in 6 days therefore , the man alone will finish the work in 6 × 6 days = 36 days man ’ s 1 day ’ s work = 1 / 36 therefore , boy ’ s 1 day ’ s work = 1 / 24 – 1 / 36 = 3 – 2 / 72 = 1 / 72 therefore , the boy alone will finish the work in 72 days . answer : option a
Answer: a
Question (general): mathew is planning a vacation trip to london next year from today for 5 days , he has calculated he would need about $ 3000 for expenses , including a round - trip plane ticket from l . a to london . he nets around $ 1500 monthly in gross income , after all bills are paid , he is left with about $ 350 each month free for whatever he desires . how much money would mathew need to evenly save from his $ 350 to have $ 3000 in his bank within 12 months ?
Options: a ) $ 240 , b ) $ 350 , c ) $ 217 , d ) $ 250 , e ) $ 340
Rationale: answer is ( d ) . if mathew is left with about $ 350 after all expenses each month , he would need to divide the total expense budget to london ( $ 3000 ) by 12 months to determine how much he would need to put away every single month to hit his target . $ 3000 / 12 = $ 250 .
Answer: d
Question (physics): three pipes a , b and c can fill a tank from empty to full in 30 minutes , 20 minutes and 10 minutes respectively . when the tank is empty , all the three pipes are opened . a , b and c discharge chemical solutions p , q and r respectively . what is the proportion of solution r in the liquid in the tank after 3 minutes ?
Options: a ) 6 / 15 , b ) 6 / 11 , c ) 6 / 14 , d ) 6 / 12 , e ) 6 / 13
Rationale: "part filled by ( a + b + c ) in 3 minutes = 3 ( 1 / 30 + 1 / 20 + 1 / 10 ) = 11 / 20 part filled by c in 3 minutes = 3 / 10 required ratio = 3 / 10 * 20 / 11 = 6 / 11 answer : b"
Answer: b
Question (gain): the present worth of rs . 1014 due in 2 years at 4 % per annum compound interest is
Options: a ) rs . 150.50 , b ) rs . 937.5 , c ) rs . 156.25 , d ) rs . 158 , e ) none
Rationale: "solution present worth = rs . [ 1014 / ( 1 + 4 / 100 ) ² ] = rs . ( 1014 x 25 / 26 x 25 / 26 ) = rs . 937.5 answer b"
Answer: b
Question (general): if ( a – b ) is 15 more than ( c + d ) and ( a + b ) is 3 less than ( c – d ) , then ( a – c ) is :
Options: a ) 6 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( a – b ) – ( c + d ) = 15 and ( c – d ) – ( a + b ) = 3 = > ( a – c ) – ( b + d ) = 15 and ( c – a ) – ( b + d ) = 3 = > ( b + d ) = ( a – c ) – 15 and ( b + d ) = ( c – a ) – 3 = > ( a – c ) – 15 = ( c – a ) – 3 = > 2 ( a – c ) = 12 = > ( a – c ) = 6 answer : a"
Answer: a
Question (general): if jake loses 8 pounds , he will weigh twice as much as his sister kendra . together they now weigh 281 pounds . what is jake ’ s present weight , in pounds ?
Options: a ) 125 , b ) 135 , c ) 140 , d ) 165 , e ) 190
Rationale: "j + k = 281 and so k = 281 - j j - 8 = 2 k j - 8 = 2 ( 281 - j ) 3 j = 570 j = 190 the answer is e ."
Answer: e
Question (gain): the total cost of 100 paper plates and 200 paper cups is $ 8.00 at the same rates what is the total cost of 20 of the plates and 40 of the cups ?
Options: a ) $ . 90 , b ) $ 1.00 , c ) $ 1.20 , d ) $ 1.50 , e ) $ 1.60
Rationale: "u dont need to go through all this what u have with u is 100 p + 200 c = $ 8.00 just divide the equation by 5 and you will get what u are looking for 20 p + 40 c = $ 1.60 therefore oa is e"
Answer: e
Question (general): 4242 × 9999 = ?
Options: a ) 42415758 , b ) 42415751 , c ) 42415752 , d ) 42415753 , e ) 42415754
Rationale: "a 42415758 4242 × 9999 = 4242 × ( 10000 - 1 ) = 4242 × 10000 - 4242 × 1 = 42420000 - 4242 = 42415758"
Answer: a
Question (general): 2 cow ’ s and 5 goats are brought for rs . 1050 . if the average price of a goat be rs . 90 . what is the average price of a cow .
Options: a ) 300 , b ) 320 , c ) 330 , d ) 350 , e ) 375
Rationale: "explanation : average price of a goat = rs . 90 total price of 5 goats = 5 * 90 = rs . 450 but total price of 2 cows and 5 goats = rs . 1050 total price of 2 cows is = 1050 - 450 = 600 average price of a cow = 600 / 2 = rs . 300 answer : a"
Answer: a
Question (other): 24 oz of juice p and 25 oz of juice v are mixed to make smothies x and y . the ratio of p to v in smothie x is 4 is to 1 and that in y is 1 is to 5 . how many ounces of juice p are contained in the smothie x ?
Options: a ) 5 , b ) 10 , c ) 15 , d ) 20 , e ) 25
Rationale: let us now solve for x : ( 4 / 5 ) x + ( 1 / 6 ) ( 49 - x ) = 24 24 x + 5 ( 49 - x ) = ( 24 ) ( 30 ) 24 x + 245 - 5 x = ( 24 ) ( 30 ) 19 x = 720 - 245 19 x = 475 x = 25 answer : e
Answer: e
Question (physics): a certain industrial loom weaves 0.13 meters of cloth every second . approximately how many seconds will it take for the loom to weave 15 meters of cloth ?
Options: a ) 114 , b ) 115 , c ) 116 , d ) 117 , e ) 118
Rationale: "let the required number of seconds be x more cloth , more time , ( direct proportion ) hence we can write as ( cloth ) 0.13 : 15 : : 1 : x = > 0.13 * x = 15 = > x = 15 / 0.13 = > x = 115 answer : b"
Answer: b
Question (probability): in a garden , there are yellow and green flowers which are straight and curved . if the probability of picking a green flower is 1 / 8 and picking a straight flower is 1 / 2 , then what is the probability of picking a flower which is yellow and straight
Options: a ) 1 / 7 , b ) 1 / 8 , c ) 1 / 4 , d ) 3 / 4 , e ) 4 / 9
Rationale: "good question . so we have a garden where all the flowers have two properties : color ( green or yellow ) and shape ( straight or curved ) . we ' re told that 1 / 8 of the garden is green , so , since all the flowers must be either green or yellow , we know that 7 / 8 are yellow . we ' re also told there is an equal probability of straight or curved , 1 / 2 . we want to find out the probability of something being yellow and straight , pr ( yellow and straight ) . so if we recall , the probability of two unique events occurring simultaneously is the product of the two probabilities , pr ( a and b ) = p ( a ) * p ( b ) . so we multiply the two probabilities , pr ( yellow ) * pr ( straight ) = 7 / 8 * 1 / 2 = 4 / 9 , or e ."
Answer: e
Question (general): how many 3 digit positive integers with distinct digits are there , which are not multiples of 10 ?
Options: a ) 576 , b ) 520 , c ) 504 , d ) 432 , e ) 348
Rationale: a number not to be a multiple of 10 should not have the units digit of 0 . xxx 9 options for the first digit ( from 1 to 9 inclusive ) . 8 options for the third digit ( from 1 to 9 inclusive minus the one we used for the first digit ) . 8 options for the second digit ( from 0 to 9 inclusive minus 2 digits we used for the first and the third digits ) 9 * 8 * 8 = 576 . answer : a .
Answer: a
Question (general): 3 pounds of 05 grass seed contain 1 percent herbicide . a different type of grass seed , 20 , which contains 20 percent herbicide , will be mixed with 3 pounds of 05 grass seed . how much grass seed of type 20 should be added to the 3 pounds of 05 grass seed so that the mixture contains 15 percent herbicide ?
Options: a ) 3 , b ) 3.75 , c ) 4.5 , d ) 8.4 , e ) 9
Rationale: 05 grass seed contains 5 % herbicide and its amount is 3 pound 20 grass seed contains 20 % herbicide and its amount is x when these two types of grass seeds are mixed , their average becomes 15 % thus we have 3 ( 1 ) + x ( 20 ) / ( x + 3 ) = 15 3 + 20 x = 15 x + 45 5 x = 42 or x = 8.4 d
Answer: d
Question (general): if f ( f ( n ) ) + f ( n ) = 2 n + 3 and f ( 0 ) = 1 , what is the value of f ( 2012 ) ?
Options: a ) 222 , b ) 2787 , c ) 2013 , d ) 2778 , e ) 10222
Rationale: "put n = 0 then f ( f ( 0 ) ) + f ( 0 ) = 2 ( 0 ) + 3 ⇒ ⇒ f ( 1 ) + 1 = 3 ⇒ ⇒ f ( 1 ) = 2 put n = 1 f ( f ( 1 ) ) + f ( 1 ) = 2 ( 1 ) + 3 ⇒ ⇒ f ( 2 ) + 2 = 5 ⇒ ⇒ f ( 2 ) = 3 put n = 2 f ( f ( 2 ) ) + f ( 2 ) = 2 ( 2 ) + 3 ⇒ ⇒ f ( 3 ) + 3 = 7 ⇒ ⇒ f ( 3 ) = 4 . . . . . . f ( 2012 ) = 2013 answer : c"
Answer: c
Question (geometry): a certain barrel , which is a right circular cylinder , is filled to capacity with 60 gallons of oil . the first barrel is poured into a second barrel , also a right circular cylinder , which is empty . the second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel . if all of the oil in the first barrel is poured into the second barrel , how much empty capacity , in gallons , is left in the second barrel ?
Options: a ) there is no empty capacity
b ) 100 gallons
c ) 300 gallons
d ) 420 gallons
e ) 840 gallons
Rationale: radius of first cylinder = r , diameter = 2 r , height = h radius of second cylinder = 2 r , diamter = 2 d and height = 2 h volume of first cylinder = pie ( r ^ 2 ) * h = 60 volume of second cylinder = pie ( 2 r ^ 2 ) 2 h put the value of pie ( r ^ 2 ) * h = 60 in the second cylinder , volume = pie ( r ^ 2 ) * 4 * 2 = 60 * 8 = 480 gallons empty capacity = 420 gallons answer d
Answer: d
Question (gain): concentrated apples juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches . the tubes are packed into wooden boxes , each with dimensions of 11 inches by 10 inches by 31 inches . how many tubes of concentrated apples juice , at the most , can fit into 3 wooden boxes ?
Options: a ) 24 . , b ) 28 . , c ) 36 . , d ) 42 . , e ) 48 .
Rationale: concentrated apples juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way now , diameter of each tube = 5 inches therefore , 4 * 2 can be put in each wooden box in 3 boxes 3 * 4 * 2 can be accommodated = 24 = a
Answer: a
Question (general): a group of students decided to collect as many paise from each member of group as is the number of members . if the total collection amounts to rs . 51.84 , the number of the member is the group is :
Options: a ) 57 , b ) 67 , c ) 72 , d ) 87 , e ) 97
Rationale: "explanation : money collected = ( 51.84 x 100 ) paise = 5184 paise . ∴ number of members = √ ( 5184 ) = 72 . answer : c"
Answer: c
Question (general): john purchased some shirts and trousers for $ 1550 . he paid $ 250 less for the shirts than he did for the trousers . if he bought 5 shirts and the cost of a shirt is $ 20 less than that of a trouser , how many trousers did he buy ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "given that the total purchase of two items cost 1550 . so the average purchase of one item will cost 1550 / 2 = 775 . its given as total shirt cost 250 $ less . hence total shirt cost = 775 - 125 and total trouser cost = 775 + 125 5 shirts = 650 $ = = > one shirt = 130 $ one trouser = 130 + 20 = 150 $ total trousers = 900 / 150 = 6 . c"
Answer: c
Question (geometry): a cube has a volume of 125 cubic feet . if a similar cube is twice as long , twice as wide , and twice as high , then the volume , in cubic feet of such cube is ?
Options: a ) 24 , b ) 48 , c ) 64 , d ) 80 , e ) 1000
Rationale: "volume = 125 = side ^ 3 i . e . side of cube = 5 new cube has dimensions 10 , 10 , and 10 as all sides are twice of teh side of first cube volume = 10 * 10 * 10 = 1000 square feet answer : option e"
Answer: e
Question (physics): a car is running at a speed of 110 kmph . what distance will it cover in 9 sec ?
Options: a ) 100 m , b ) 279 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: "speed = 110 kmph = 110 * 5 / 18 = 31 m / s distance covered in 9 sec = 31 * 9 = 279 m answer is b"
Answer: b
Question (gain): in an election , candidate a got 65 % of the total valid votes . if 15 % of the total votes were declared invalid and the total numbers of votes is 560000 , find the number of valid vote polled in favor of candidate ?
Options: a ) 355600 , b ) 355800 , c ) 356500 , d ) 309400 , e ) 357000
Rationale: "total number of invalid votes = 15 % of 560000 = 15 / 100 × 560000 = 8400000 / 100 = 84000 total number of valid votes 560000 – 84000 = 476000 percentage of votes polled in favour of candidate a = 65 % therefore , the number of valid votes polled in favour of candidate a = 65 % of 476000 = 65 / 100 × 476000 = 30940000 / 100 = 309400 d )"
Answer: d
Question (general): if a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land heads up exactly twice in 2 consecutive flips ?
Options: a ) 0.125 , b ) 0.225 , c ) 0.25 , d ) 0.5 , e ) 0.666
Rationale: "total number of ways in which h or t can appear in 3 tosses of coin is = 2 * 2 = 4 ways for 2 h hh , thus probability is = p ( hh ) = 1 / 4 = . 25 answer : c"
Answer: c
Question (physics): in a manufacturing plant , it takes 36 machines 4 hours of continuous work to fill 6 standard orders . at this rate , how many hours of continuous work by 72 machines are required to fill 12 standard orders ?
Options: a ) 4 , b ) 6 , c ) 8 , d ) 9 , e ) 12
Rationale: the choices give away the answer . . 36 machines take 4 hours to fill 8 standard orders . . in next eq we aredoubling the machines from 36 to 72 , but thework is not doubling ( only 1 1 / 2 times ) , = 4 * 48 / 72 * 12 / 6 = 4 ans a
Answer: a
Question (physics): a car is running at a speed of 90 kmph . what distance will it cover in 10 sec ?
Options: a ) 100 m , b ) 150 m , c ) 180 m , d ) 200 m , e ) 250 m
Rationale: "speed = 90 kmph = 90 * 5 / 18 = 25 m / s distance covered in 10 sec = 25 * 10 = 250 m answer is e"
Answer: e
Question (general): how many 3 digit number formed by using 23 , 45 , 67 once such that number is divisible by 15 .
Options: a ) 8 , b ) 13 , c ) 12 , d ) 20 , e ) 22
Rationale: 4 * 2 * 1 = 8 at one ' s place only 5 will come and at ten ' s place 4 and 7 can be placed , and at 100 th place rest of the 4 digits can come . . . so the answer is 8 answer : a
Answer: a
Question (general): how many 3 digit positive integers t exist that when divided by 7 leave a remainder of 5 ?
Options: a ) 128 , b ) 142 , c ) 143 , d ) 141 , e ) 129
Rationale: "minimum three digit number is 100 and maximum three digit number is 999 . the first three digit number that leaves remainder 5 when divided by 7 is 103 . 14 * 7 = 98 + 5 = 103 the second three digit number that leaves remainder 5 when divided by 7 is 110 . 15 * 7 = 105 + 5 = 110 the third three digit number that leaves remainder 5 when divided by 7 is 117 and so on the last three digit number that leaves remainder 5 when divided by 7 is 999 142 * 7 = 994 + 5 = 999 therefore , we identify the sequence 103 , 110,117 . . . . . 999 use the formula of last term last term = first term + ( n - 1 ) * common difference you will get the answer 129 that is definitely e ."
Answer: e
Question (gain): in a 100 member association consisting of men and women , exactly 10 % of men and exactly 20 % women are homeowners . what is the maximum number of members who are homeowners ?
Options: a ) 29 , b ) 27 , c ) 25 , d ) 23 , e ) 21
Rationale: "solution simple out of 100 10 % are male i . e 10 and 20 % are female i . e 20 , so total homeowner is 30 . now min number homeowner is 10 and max is 30 so question ask us to find maximum and 29 has maximum value among all option . so ans is 29 . ans : a"
Answer: a
Question (general): how many single - digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6 ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: the possible number n can be written as follow : n = multiple of lcm ( 610 ) + 1 st such number n = 30 x + 1 possible values = 1 answer : b
Answer: b
Question (general): the average of 10 numbers is calculated as 16 . it is discovered later on that while calculating the average , one number namely 36 was wrongly read as 26 . the correct average is ?
Options: a ) a ) 17 , b ) b ) 18 , c ) c ) 19 , d ) d ) 22 , e ) e ) 24
Rationale: "explanation : 10 * 16 + 36 – 26 = 170 = > 170 / 10 = 17 a )"
Answer: a
Question (physics): 48 persons can repair a road in 12 days , working 5 hours a day . in how many days will 30 persons , working 6 hours a day , complete the work ?
Options: a ) 10 , b ) 16 , c ) 13 , d ) 18 , e ) 19
Rationale: "let the required number of days be x . less persons , more days ( indirect proportion ) more working hours per day , less days ( indirect proportion ) persons 30 : 48 : : 12 : x working hours / day 6 : 5 30 x 6 x x = 48 x 5 x 12 x = ( 48 x 5 x 12 ) / ( 30 x 6 ) x = 16 answer b"
Answer: b
Question (geometry): in the coordinate plane , a circle centered on point ( - 3 , 4 ) passes through point ( 1 , 1 ) . what is the area of the circle ?
Options: a ) 9 π , b ) 18 π , c ) 25 π , d ) 37 π , e ) 41 π
Rationale: "r ^ 2 = ( - 3 - 1 ) ^ 2 + ( 4 - 1 ) ^ 2 = 16 + 9 = 25 area of circle = π r ^ 2 = 25 π answer : c"
Answer: c
Question (physics): a cistern has a leak which would empty the cistern in 20 minutes . a tap is turned on which admits 7 liters a minute into the cistern , and it is emptied in 24 minutes . how many liters does the cistern hold ?
Options: a ) 480 , b ) 487 , c ) 481 , d ) 840 , e ) 268
Rationale: "1 / x - 1 / 20 = - 1 / 24 x = 120 120 * 7 = 840 answer : d"
Answer: d
Question (general): the ratio between x and y is 8 / 3 ; x is multiplied by x and y is multiplied by y , what is the ratio between the new values of x and y ?
Options: a ) 8 / 3 , b ) 3 / 8 , c ) 1 , d ) 64 / 9 , e ) it can not be determined
Rationale: "ratio = 7 k / 9 k = 7 / 9 , 14 / 18 , etc . x is multiplied by x and y is multiplied by y - - > ( 7 k * 7 k ) / ( 9 k * 9 k ) = 49 k ^ 2 / 81 k ^ 2 = 49 / 81 = 7 / 9 answer : a"
Answer: a
Question (general): a , b and c play a cricket match . the ratio of the runs scored by them in the match is a : b = 2 : 3 and b : c = 2 : 5 . if the total runs scored by all of them are 100 , the runs scored by a are ?
Options: a ) 11 , b ) 18 , c ) 13 , d ) 16 , e ) 12
Rationale: "a : b = 2 : 3 b : c = 2 : 5 a : b : c = 4 : 6 : 15 4 / 25 * 100 = 16 answer : d"
Answer: d
Question (general): 1 , 3,5 , 7,9 , . . 50 find term of sequnce
Options: a ) 1230 , b ) 1300 , c ) 1500 , d ) 1679 , e ) 2500
Rationale: "this is an arithmetic progression , and we can write down a = 1 a = 1 , d = 2 d = 2 , n = 50 n = 50 . we now use the formula , so that sn = 12 n ( 2 a + ( n − 1 ) l ) sn = 12 n ( 2 a + ( n − 1 ) l ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) s 50 = 12 × 50 × ( 2 × 1 + ( 50 − 1 ) × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 49 × 2 ) = 25 × ( 2 + 98 ) = 25 × ( 2 + 98 ) = 2500 = 2500 . e"
Answer: e
Question (general): a palindrome is a number that reads the same forward and backward , such as 120 . how many odd , 4 - digit numbers are palindromes ?
Options: a ) 40 , b ) 55 , 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 * 11 = 55 ways b"
Answer: b
Question (general): the operation is defined for all integers a and b by the equation ab = ( a - 1 ) ( b - 1 ) . if x 20 = 190 , what is the value of x ?
Options: a ) 10 , b ) 12 , c ) 11 , d ) 13 , e ) 14
Rationale: "ab = ( a - 1 ) ( b - 1 ) x 20 = ( x - 1 ) ( 20 - 1 ) = 190 - - > x - 1 = 10 - - > x = 11 answer : c"
Answer: c
Question (general): how many 5 digit nos are there if the 2 leftmost digits are odd and the digit 4 ca n ' t appear more than once in the number ? could someone please provide a solution using a approach other than ( 1 - x ( none ) ) approach ?
Options: a ) 24300 , b ) 25700 , c ) 26500 , d ) 24400 , e ) 26300
Rationale: a . 4 is used once : oo * * 4 - - > ( 5 * 5 * 9 * 9 ) * 3 : 5 choices for the first digit as there are 5 odd numbers , 5 choices for the second digit for the same reason , 9 choices for one of the two * ( not - 4 digit ) , 9 choices for another * ( not - 4 digit ) , multiplied by 3 as 4 can take the place of any of the three last digits ( oo * * 4 , oo * 4 * , oo 4 * * ) ; b . 4 is not used : oo * * * - - > 5 * 5 * 9 * 9 * 9 : the same logic as above . 5 * 5 * 9 * 9 * 3 + 5 * 5 * 9 * 9 * 9 = 24300 . answer : a
Answer: a
Question (physics): the population of a bacteria colony doubles every day . if it was started 8 days ago with 3 bacteria and each bacteria lives for 12 days , how large is the colony today ?
Options: a ) 512 , b ) 768 , c ) 13122 , d ) 2048 , e ) 4096
Rationale: "3 ^ 8 * ( 2 ) = 13122 the answer is c"
Answer: c
Question (other): a cat leaps 6 leaps for every 5 leaps of a dog , but 2 leaps of the dog are equal to 3 leaps of the cat . what is the ratio of the speed of the cat to that of the dog ?
Options: a ) 4 : 5 , b ) 2 : 3 , c ) 4 : 1 , d ) 1 : 9 , e ) 3 : 2
Rationale: "given ; 2 dog = 3 cat ; or , dog / cat = 3 / 2 ; let cat ' s 1 leap = 2 meter and dogs 1 leap = 3 meter . then , ratio of speed of cat and dog = 2 * 6 / 3 * 5 = 4 : 5 ' ' answer : 4 : 5 ;"
Answer: a
Question (geometry): a horse is tethered to one corner of a rectangular grassy field 36 m by 20 m with a rope 18 m long . over how much area of the field can it graze ?
Options: a ) 154 cm 2 , b ) 308 m 2 , c ) 254 m 2 , d ) 260 m 2 , e ) none of these
Rationale: "area of the shaded portion = 1 ⁄ 4 × π × ( 18 ) 2 = 254 m 2 answer c"
Answer: c
Question (general): if the arithmetic mean of seventy 5 numbers is calculated , it is 35 . if each number is increased by 5 , then mean of new number is ?
Options: a ) 87 , b ) 40 , c ) 37 , d ) 28 , e ) 26
Rationale: a . m . of 75 numbers = 35 sum of 75 numbers = 75 * 35 = 2625 total increase = 75 * 5 = 375 increased sum = 2625 + 375 = 3000 increased average = 3000 / 75 = 40 . answer : b
Answer: b
Question (general): 8873 + x = 13200 , then x is ?
Options: a ) 3327 , b ) 4327 , c ) 3337 , d ) 2337 , e ) none of these
Rationale: answer x = 13200 - 8873 = 4327 option : b
Answer: b
Question (general): a box contains 8 pairs of shoes ( 16 shoes in total ) . if two shoes are selected at random , what it is the probability that they are matching shoes ?
Options: a ) 1 / 190 , b ) 1 / 20 , c ) 1 / 19 , d ) 1 / 10 , e ) 1 / 15
Rationale: "the problem with your solution is that we do n ' t choose 1 shoe from 16 , but rather choose the needed one after we just took one and need the second to be the pair of it . so , the probability would simply be : 1 / 1 * 1 / 15 ( as after taking one at random there are 15 shoes left and only one is the pair of the first one ) = 1 / 15 answer : e ."
Answer: e
Question (gain): sales price is $ 60 , gross profit is 140 % of cost , what is the value of gross profit ?
Options: a ) 32 , b ) 33 , c ) 39 , d ) 35 , e ) 42
Rationale: "cost + profit = sales cost + ( 140 / 100 ) cost = 60 cost = 25 profit = 60 - 25 = 35 answer ( d )"
Answer: d