Cheukting/mathqa huggingface dataset:
Question (general): in february wilson ’ s earnings were 40 percent of his family ’ s total income . in march wilson earned 25 percent less than in february . if the rest of his family ’ s income was the same in both months , then , in march , wilson ’ s earnings were approximately what percent s of his family ’ s total income ?
Options: a ) 15 % , b ) 17 % , c ) 24 % , d ) 30 % , e ) 33 %
Rationale: "lets suppose the total family income in feb = 100 x wilson ' s earning in feb = 40 % of 100 x = 40 x earnings of remaining family in feb = 100 x - 40 x = 60 x wilson ' s earning in march = 75 % of wilson ' s feb earnings = 75 % of 40 x = 30 x earnings of remaining family in march = earnings of remaining family in feb = 60 x thus wilson ' s earning as % of total family income in march s = 30 x / ( 30 + 60 ) x = 30 x / 90 x = 33.33 % thus answer is e"
Answer: e
Question (general): if a : b = 1 : 4 , b : c = 13 : 9 , c : d = 5 : 13 , find a : d ?
Options: a ) 5 / 46 , b ) 7 / 36 , c ) 1 / 36 , d ) 5 / 36 , e ) 5 / 37
Rationale: a / d = ( 1 / 4 ) * ( 13 / 9 ) * ( 5 / 13 ) = > 5 / 36 answer : d
Answer: d
Question (geometry): in a rectangular coordinate system , what is the area of a rectangle whose vertices have the coordinates ( - 5 , 1 ) , ( 1 , 1 ) , ( 1 , - 4 ) and ( - 5 , - 4 ) ?
Options: a ) 20
b ) 30
c ) 40
d ) 55
e ) 48
Rationale: length of side 1 = 5 + 1 = 6 length of side 2 = 4 + 1 = 5 area of rectangle = 6 * 5 = 30 b is the answer
Answer: b
Question (gain): population of a city in 20004 was 1000000 . if in 2005 there isan increment of 15 % , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 30 % , then find the population of city atthe end of the year 2007
Options: a ) 976374 , b ) 971750 , c ) 980241 , d ) 2356677 , e ) 1083875
Rationale: "required population = p ( 1 + r 1 / 100 ) ( 1 - r 2 / 100 ) ( 1 + r 3 / 100 ) = p ( 1 + 15 / 100 ) ( 1 - 35 / 100 ) ( 1 + 30 / 100 ) = 971750 b"
Answer: b
Question (general): what is the greatest value of positive integer x such that 2 ^ x is a factor of 100 ^ 90 ?
Options: a ) 180 , b ) 160 , c ) 140 , d ) 150 , e ) 120
Rationale: "put in simple words , we need to find the highest power of 2 in 100 ^ 90 100 = 2 ^ 2 * 5 ^ 2 therefore 100 ^ 90 = ( 2 ^ 2 * 5 ^ 2 ) ^ 90 = 2 ^ 180 * 5 ^ 180 answer : a"
Answer: a
Question (gain): alex takes a loan of $ 9,000 to buy a used truck at the rate of 9 % simple interest . calculate the annual interest to be paid for the loan amount .
Options: a ) 680 , b ) 810 , c ) 800 , d ) 730 , e ) 750
Rationale: from the details given in the problem principle = p = $ 9,000 and r = 9 % or 0.09 expressed as a decimal . as the annual interest is to be calculated , the time period t = 1 . plugging these values in the simple interest formula , i = p x t x r = 9,000 x 1 x 0.09 = 810.00 annual interest to be paid = $ 810 answer : b
Answer: b
Question (gain): last month , john rejected 0.7 % of the products that he inspected and jane rejected 0.8 percent of the products that she inspected . if total of 0.75 percent of the products produced last month were rejected , what fraction of the products did jane inspect ?
Options: a ) 1 / 6 , b ) 1 / 2 , c ) 5 / 8 , d ) 5 / 6 , e ) 15 / 16
Rationale: "x - fraction of products jane inspected ( 1 - x ) - fraction of products john inspected 0.8 ( x ) + 0.7 ( 1 - x ) = 0.75 0.1 x = 0.75 - 0.7 x = 0.05 / 0.1 x = 1 / 2 therefore the answer is b : 1 / 2 ."
Answer: b
Question (general): if the average ( arithmetic mean ) of x and y is 60 , and z – x = 80 , what is the average of y and z ?
Options: a ) 100 , b ) 120 , c ) 125 , d ) 115 , e ) 90
Rationale: "x + y / 2 = 60 = > x + y = 120 x = z - 80 . . . sub this value z - 80 + y = 120 = > z + y = 200 = > z + y / 2 = 100 answer : a"
Answer: a
Question (general): what is the smallest integer z for which 27 ^ z > 3 ^ 24 ?
Options: a ) 7 , b ) 8 , c ) 9 , d ) 10 , e ) 12
Rationale: "27 ^ z > 3 ^ 24 converting into the same bases : 27 ^ z > 27 ^ 8 therefore for the equation to hold true , z > 8 or z = 9 option c"
Answer: c
Question (physics): a is twice as good a work man as b and together they finish the work in 8 days . in how many days a alone can finish the work ?
Options: a ) 23 , b ) 12 , c ) 77 , d ) 92 , e ) 61
Rationale: "wc = 2 : 1 2 x + x = 1 / 8 = > x = 1 / 24 2 x = 1 / 12 a can do the work in 12 days . answer : b"
Answer: b
Question (general): the sum of two numbers is 21 and the sum of their squares is 527 . find the product of the numbers .
Options: a ) 48 , b ) 41 , c ) 46 , d ) 43 , e ) 96
Rationale: let a and b be the two numbers ( a + b ) ^ 2 = a ^ 2 + 2 ab + b ^ 2 given ( a + b ) = 21 a ^ 2 + b ^ 2 = 527 so , 21 ^ 2 = 527 + 2 ab 2 ab = 527 - 441 2 ab = 86 ab = 43 ans d
Answer: d
Question (general): thabo owns exactly 280 books , and each book is either paperback fiction , paperback nonfiction , or hardcover nonfiction . if he owns 20 more paperback nonfiction books than hardcover nonfiction books , and twice as many paperback fiction books as paperback nonfiction books , how many hardcover books nonfiction books does thabo own ?
Options: a ) 10 , b ) 20 , c ) 30 , d ) 40 , e ) 55
Rationale: "i think we can use double - matrix method and solve using only one variable . our goal is to find the number of hardcover nonfiction books . let that number be x . we are given that all 140 books are either paperback fiction , paperback nonfiction , or hardcover nonfiction . this implies that number of hardcover fiction books is 0 . double - matrix : p = paperback ; h = hardcover ; f = fiction ; nf = nonfiction p h total f 2 x + 40 0 nf x + 20 x total 3 x + 60 x 280 3 x + 60 + x = 280 x = 55 answer ( e . )"
Answer: e
Question (general): in the number 100 ab , a and b represent the tens and units digits , respectively . if 110 ab is divisible by 55 , what is the greatest possible value of b × a ?
Options: a ) 0 , b ) 5 , c ) 10 , d ) 15 , e ) 25
Rationale: you should notice that 55 * 2 = 110 so 11,000 is divisible by 55 : 55 * 200 = 11,000 ( or you can notice that 11,000 is obviously divisible by both 5 and 11 so by 55 ) - - > b * a = 0 * 0 = 0 . next number divisible by 55 is 11,000 + 55 = 11,055 : b * a = 5 * 5 = 15 ( next number wo n ' t have 110 as the first 3 digits so we have only two options 0 and 25 ) . answer : e . ! please post ps questions in the ps subforum : gmat - problem - solving - ps - 140 / please post ds questions in the ds subforum : gmat - data - sufficiency - ds - 141 / no posting of ps / ds questions is allowed in the mainmath forum . d
Answer: d
Question (physics): a train 350 m long , running with a speed of 63 km / hr will pass a tree in ?
Options: a ) 22 sec , b ) 16 sec , c ) 17 sec , d ) 88 sec , e ) 20 sec
Rationale: "speed = 63 * 5 / 18 = 35 / 2 m / sec time taken = 350 * 2 / 35 = 20 sec answer : e"
Answer: e
Question (physics): a car travelling with 5 / 7 km of its actual speed covers 42 km in 1 hr 40 min 48 sec find the actual speed of the car ?
Options: a ) 78 kmph , b ) 85 kmph , c ) 35 kmph , d ) 24 kmph , e ) 74 kmph
Rationale: time taken = 1 hr 40 min 48 sec = 126 / 75 hrs let the actual speed be x kmph then 5 / 7 x * 126 / 75 = 42 x = ( 42 * 7 * 75 ) / 5 * 126 = 35 kmph answer ( c )
Answer: c
Question (gain): compare the rates of two trains , one travelling at 90 km / hr and other is at 50 m / s ?
Options: a ) 2 : 1 , b ) 1 : 2 , c ) 1 : 3 , d ) 3 : 1 , e ) 2 : 3
Rationale: speed of the 1 st train = 90 km / hr speed of the 2 nd train = 50 m / s = 50 * 18 / 5 = 180 km / hr ratio of the speeds of the train = 90 : 180 = 1 : 2 answer is b
Answer: b
Question (general): a computer manufacturer produces a certain electronic component at a cost of $ 100 per component . shipping costs for delivering the components are $ 2 per unit . further , the manufacturer has costs of $ 10,000 a month related to the electronic component regardless of how many it produces . if the manufacturer produces and sells 1000 components a month , what is the lowest price it can sell them for such that the costs do n ' t exceed the revenues ?
Options: a ) 122 , b ) 112 , c ) 134 , d ) 108 , e ) 101
Rationale: "$ 10000 is a fixed cost each component is $ 102 ( $ 100 to produce , $ 2 to ship ) manufacturer will be producing and selling 1000 components so therefore the equation to find price would be 1000 * p = 10000 + ( 1000 * 100 ) + ( 1000 * 2 ) p = ( 10000 + 100000 + 2000 ) / 1000 p = 112 answer : b"
Answer: b
Question (physics): sari and ken climb up a mountain . at night , they camp together . on the day they are supposed to reach the summit , sari wakes up at 08 : 00 and starts climbing at a constant pace . ken starts climbing only at 10 : 00 , when sari is already 700 meters ahead of him . nevertheless , ken climbs at a constant pace of 500 meters per hour , and reaches the summit before sari . if sari is 50 meters behind ken when he reaches the summit , at what time did ken reach the summit ?
Options: a ) 13 : 00 , b ) 13 : 30 , c ) 14 : 00 , d ) 15 : 00 , e ) 15 : 30
Rationale: "both sari and ken climb in the same direction . speed of sari = 700 / 2 = 350 meters / hr ( since she covers 700 meters in 2 hrs ) speed of ken = 500 meters / hr at 8 : 00 , distance between ken and sari is 700 meters . ken needs to cover this and another 50 meters . time he will take = total distance to be covered / relative speed = ( 700 + 50 ) / ( 500 - 350 ) = 5 hrs starting from 10 : 00 , in 5 hrs , the time will be 15 : 00 answer ( d )"
Answer: d
Question (general): the average weight of a , b and c is 30 kg . if the average weight of a and b be 25 kg and that of b and c be 28 kg , then the weight of b is :
Options: a ) 14 kg , b ) 15 kg , c ) 18 kg , d ) 19 kg , e ) 16 kg
Rationale: explanation let a , b , c represent their respective weights . then , we have : a + b + c = ( 30 x 3 ) = 90 â € ¦ . ( i ) a + b = ( 25 x 2 ) = 50 â € ¦ . ( ii ) b + c = ( 28 x 2 ) = 56 â € ¦ . ( iii ) adding ( ii ) and ( iii ) , we get : a + 2 b + c = 106 â € ¦ . ( iv ) subtracting ( i ) from ( iv ) , we get : b = 16 . b â € ™ s weight = 16 kg . answer e
Answer: e
Question (general): the cost of a one - family home was $ 120000 in 1980 . in 1988 , the price had increased to $ 192000 . what was the percent increase in the cost of the home ?
Options: a ) 60 % , b ) 50 % , c ) 55 % , d ) 40 % , e ) 33.3 %
Rationale: increase = 192000 - 120000 = 72000 % increase = 72000 * 100 / 120000 = 60 % answer : option a
Answer: a
Question (gain): one fourth of one third of two fifth of a number is 20 . what will be 40 % of that number
Options: a ) a ) 140 , b ) b ) 150 , c ) c ) 180 , d ) d ) 240 , e ) e ) 220
Rationale: explanation : ( 1 / 4 ) * ( 1 / 3 ) * ( 2 / 5 ) * x = 20 then x = 20 * 30 = 600 40 % of 600 = 240 answer : option d
Answer: d
Question (general): a card board of 34 * 14 has to be attached to a wooden box and a total of 35 pins are to be used on the each side of the cardbox . find the total number of pins used .
Options: a ) 135 , b ) 136 , c ) 137 , d ) 138 , e ) 139
Rationale: ( 35 * 4 ) - 4 = 136 answer : b
Answer: b
Question (physics): a 200 meter long train crosses a platform in 50 seconds while it crosses a signal pole in 42 seconds . what is the length of the platform ?
Options: a ) 39.9 , b ) 37.88 , c ) 35 , d ) 38.88 , e ) 38.09
Rationale: "speed = [ 200 / 42 ] m / sec = 100 / 21 m / sec . let the length of the platform be x meters . then , x + 200 / 50 = 100 / 21 21 ( x + 200 ) = 5000 è x = 38.09 m . answer : e"
Answer: e
Question (general): how much water should be added to 11 liters of a 20 % - solution of alcohol to reduce the concentration of alcohol in the solution by 75 % ?
Options: a ) 25 liters , b ) 29 liters , c ) 30 liters , d ) 32 liters , e ) 35 liters
Rationale: "let x ltr water to be added 2 ltr alcohol to be represented as ( 20 ( 1 - 3 / 4 ( new soln . = 11 + x ) ) ) 2 = 5 % * ( 11 + x ) - - - - - - - - > x = 29 ans b"
Answer: b
Question (physics): a van takes 5 hours to cover a distance of 600 km . what speed in kph should the van maintain to cover the same distance in 3 / 2 of the previous time ?
Options: a ) 80 , b ) 84 , c ) 88 , d ) 92 , e ) 96
Rationale: "( 3 / 2 ) * 5 = 7.5 hours 600 / 7.5 = 80 kph the answer is a ."
Answer: a
Question (general): the ratio of ages of aman , bren , and charlie are in the ratio 5 : 8 : 7 respectively . if 8 years ago , the sum of their ages was 76 , what will be the age of bren 12 years from now ?
Options: a ) 17 , b ) 25 , c ) 27 , d ) 52 , e ) 60
Rationale: "let the present ages of aman , bren , and charlie be 5 x , 8 x and 7 x respectively . 5 x - 8 + 8 x - 8 + 7 x - 8 = 76 x = 5 present age of bren = 8 * 5 = 40 bren ' s age 12 years hence = 40 + 12 = 52 answer = e"
Answer: e
Question (physics): a and b undertake to do a piece of work for $ 500 . a alone can do it in 5 days while b alone can do it in 10 days . with the help of c , they finish it in 2 days . find the share of c ?
Options: a ) $ 200 , b ) $ 150 , c ) $ 300 , d ) $ 25 , e ) $ 100
Rationale: "c ' s 1 day work = ( 1 / 2 ) - ( 1 / 5 + 1 / 10 ) = 1 / 5 a : b : c = 1 / 5 : 1 / 10 : 1 / 5 = 2 : 1 : 2 b ' s share = 500 * 2 / 5 = $ 200 answer is a"
Answer: a
Question (general): a clock store sold a certain clock to a collector for 15 percent more than the store had originally paid for the clock . when the collector tried to resell the clock to the store , the store bought it back at 45 percent of what the collector had paid . the shop then sold the clock again at a profit of 85 percent on its buy - back price . if the difference between the clock ' s original cost to the shop and the clock ' s buy - back price was $ 80 , for how much did the shop sell the clock the second time ?
Options: a ) $ 168.58 , b ) $ 187.54 , c ) $ 158.74 , d ) $ 120.56 , e ) $ 200.84
Rationale: "now , in the question above , lets say the original cost of the clock to store was c $ and then it sold the same to the collector at 15 % profit . this means the clocks ' selling price was c ( 1.15 ) and this becomes cost price for the collector . now , when the collector tries to sell the same clock to the store , the store buys it for 45 % the price at which the collector bought it . thus , you get = 1.15 * 0.45 * c = 0.5175 c furthermore , the store sells the clock for the second time for 85 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.85 = 1.85 * 0.5175 c finally given that c - 0.5175 c = 80 - - - - > c = 165.80 $ thus , the cost of the clock the second time around = 1.85 * 0.5175 c = 1.85 * 0.5175 * 165.80 = 158.74 $ . hence c is the correct answer ."
Answer: c
Question (physics): angelina walked 100 meters from her home to the grocery at a constant speed . she then walked 180 meters to the gym at double the speed . she spent 40 seconds less on her way from the grocery to the gym than on her way from home to the grocery . what was angelina ' s speed , in meters per second , from the grocery to the gym ?
Options: a ) 2 , b ) 3 , c ) 0.5 , d ) 6 , e ) 12
Rationale: "let the speed be x . . . so time taken from home to grocery = 100 / x . . the speed to gym = 2 x . . so time taken = 180 / 2 x = 90 / x . . its given 100 / x - 90 / x = 40 . . 10 / x = 40 . . x = 0.25 m / secs . . so grocery to gym = 2 * 0.25 = 0.5 m / s . . . answer : c"
Answer: c
Question (gain): if 45 % of z is 39 % of y and y is 75 % of x , what percent of x is z ?
Options: a ) 200 , b ) 160 , c ) 100 , d ) 65 , e ) 50
Rationale: "( 45 / 100 ) z = ( 39 / 100 ) y and y = ( 75 / 100 ) x i . e . y = ( 3 / 4 ) x i . e . ( 45 / 100 ) z = ( 39 / 100 ) * ( 3 / 4 ) x i . e . z = ( 39 * 3 ) x / ( 45 * 4 ) i . e . z = ( 0.65 ) x = ( 65 / 100 ) x i . e . z is 65 % of x answer : option d"
Answer: d
Question (general): 10 camels cost as much as 24 horses , 16 horses cost as much as 4 oxen and 6 oxen as much as 4 elephants . if the cost of 10 elephants is rs . 130000 , find the cost of a camel ?
Options: a ) s . 9800 , b ) s . 3800 , c ) s . 9800 , d ) s . 5200 , e ) s . 6880
Rationale: "cost of the camel = p 10 camels = 24 horses 16 horses = 4 oxen 6 oxen = 4 elephants 10 elephants = rs . 130000 p = rs . [ ( 24 * 4 * 4 * 130000 ) / ( 10 * 16 * 6 * 10 ) ] p = rs . ( 49920000 / 9600 ) = > p = rs . 5200 answer : d"
Answer: d
Question (physics): a worker makes a toy in every 3 h . if he works for 150 h , then how many toys will he make ?
Options: a ) 40 , b ) 54 , c ) 45 , d ) 50 , e ) none
Rationale: no . of toys = 150 / 3 = 50 answer : d
Answer: d
Question (physics): in one hour , a boat goes 11 km along the stream and 5 km against the stream . the speed of the boat in still water in ( km / hr ) is
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 7
Rationale: "solution speed in still water = 1 / 2 ( 11 + 5 ) km / hr = 8 km / hr . answer c"
Answer: c
Question (physics): 45 workers work 8 hours to dig a hole 30 meters deep . how many extra workers should be hired to dig another hole 40 meters deep by working for 6 hours ?
Options: a ) 75 , b ) 80 , c ) 50 , d ) 35 , e ) 40
Rationale: 45 workers * 8 hours / 30 meters = x * 6 / 40 x = 80 total workers 80 - 45 = 35 the answer is d .
Answer: d
Question (general): if an amount of rs 42,900 is distributed equally amongst 22 persons , how much amount would each person get ?
Options: a ) rs 1950 , b ) rs 2000 , c ) rs 745 , d ) rs 765 , e ) none
Rationale: required amount = 42900 / 22 = rs 1950 answer a
Answer: a
Question (geometry): what is the perimeter , in meters , of a rectangular garden 8 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide ?
Options: a ) 48 , b ) 56 , c ) 64 , d ) 76 , e ) 192
Rationale: "say length of garden is l meters . then ( l * 8 ) = 16 * 12 [ given area is same . area = l * b ] therefore l works out to 24 meters . perimeter of garden = 2 * ( 24 + 8 ) = 64 meter . answer is c"
Answer: c
Question (general): what is the value of : - 9 ^ 7 + 9 ^ 9 ?
Options: a ) 9 ^ 2 , b ) - 18 ^ 16 , c ) 63 ( 9 ^ 7 ) , d ) - 80 ( 9 ^ 7 ) , e ) 80 ( 9 ^ 7 )
Rationale: - 9 ^ 7 + 9 ^ 9 = 9 ^ 7 ( - 1 + 9 ^ 2 ) = 9 ^ 7 ( - 1 + 81 ) = 80 ( 9 ^ 7 ) , answer e .
Answer: e
Question (geometry): let the sides of a rectangular prism are consecutive multiples of 5 . which among the following could be the base area
Options: a ) 360
b ) 450
c ) 560
d ) 670
e ) 780
Rationale: length = 5 * a breadth = 5 * ( a + 1 ) or 5 * ( a + 2 ) base area - > multiple of 25 450 = 25 * 18 answer : b
Answer: b
Question (physics): if teena is driving at 55 miles per hour and is currently 7.5 miles behind joe , who is driving at 40 miles per hour in the same direction then in how many minutes will teena be 45 miles ahead of joe ?
Options: a ) 15 , b ) 60 , c ) 75 , d ) 90 , e ) 210
Rationale: "this type of questions should be solved without any complex calculations as these questions become imperative in gaining that extra 30 - 40 seconds for a difficult one . teena covers 55 miles in 60 mins . joe covers 40 miles in 60 mins so teena gains 15 miles every 60 mins teena need to cover 7.5 + 45 miles . teena can cover 7.5 miles in 30 mins teena will cover 45 miles in 180 mins so answer 30 + 180 = 210 mins . ( answer e )"
Answer: e
Question (general): the sum of ages of 4 children born at the intervals of 10 years each is 80 years . what is the age of the youngest child ?
Options: a ) 4 , b ) 5 , c ) 6 , d ) 7 , e ) 8
Rationale: "let the ages of children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) years . then , x + ( x + 10 ) + ( x + 20 ) + ( x + 30 ) = 80 4 x = 20 x = 5 . age of the youngest child = x = 5 years . answer : b"
Answer: b
Question (probability): a bag contains 3 blue and 5 white marbles . one by one , marbles are drawn out randomly until only two are left in the bag . what is the probability x that out of the two , one is white and one is blue ?
Options: a ) 15 / 56 , b ) 41 / 56 , c ) 13 / 28 , d ) 15 / 28 , e ) 5 / 14
Rationale: "the required probability x = probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls . ways to select 6 out of total 8 = 8 c 6 ways to select 4 out of 5 white balls = 5 c 4 ways to select 2 out of 3 blue balls = 3 c 2 thus the required probability = ( 5 c 4 * 3 c 2 ) / 8 c 6 = 15 / 28 . d is thus the correct answer ."
Answer: d
Question (physics): one hour after yolanda started walking from x to y , a distance of 17 miles , bob started walking along the same road from y to x . if yolanda ' s walking rate was 3 miles per hour and bob т ' s was 4 miles per hour , how many miles had bob walked when they met ?
Options: a ) 24 , b ) 23 , c ) 22 , d ) 21 , e ) 8
Rationale: when b started walking y already has covered 3 miles out of 17 , hence the distance at that time between them was 17 - 3 = 14 miles . combined rate of b and y was 3 + 4 = 7 miles per hour , hence they would meet each other in 14 / 7 = 2 hours . in 6 hours b walked 2 * 4 = 8 miles . answer : e .
Answer: e
Question (general): a dozen eggs and 10 pounds of oranges are currently at the same price . if the price of a dozen eggs rises by 9 percent and the price of oranges rises by 6 % . how much more will it cost to buy a dozen eggs and 10 pounds of oranges .
Options: a ) 5 % , b ) 10 % , c ) 15 % , d ) 20 % , e ) 25 %
Rationale: "say currently both a dozen eggs and 10 pounds of oranges cost $ 100 ( they are at the same price ) . so , to buy a dozen eggs and 10 pounds of oranges we need $ 100 . after the increase , the price of a dozen eggs will be $ 109 and the price of 10 pounds of oranges will be $ 106 . so after the increase , to buy a dozen eggs and 10 pounds of oranges we ' ll need $ 215 . increase = 15 % . answer : c ."
Answer: c
Question (gain): at what price must an article costing rs . 47.50 be marked in order that after deducting 5 % from the list price . it may be sold at a profit of 40 % on the cost price ?
Options: a ) 62.5 , b ) 69.5 , c ) 67.5 , d ) 62.5 , e ) 70
Rationale: "cp = 47.50 sp = 47.50 * ( 140 / 100 ) = 66.5 mp * ( 95 / 100 ) = 66.5 mp = 70 answer : e"
Answer: e
Question (physics): two friends decide to get together ; so they start riding bikes towards each other . they plan to meet halfway . each is riding at 6 mph . they live 36 miles apart . one of them has a pet carrier pigeon and it starts flying the instant the friends start traveling . the pigeon flies back and forth at 19 mph between the 2 friends until the friends meet . how many miles does the pigeon travel ?
Options: a ) 54 , b ) 57 , c ) 60 , d ) 36 , e ) 96
Rationale: "b 57 it takes 3 hours for the friends to meet ; so the pigeon flies for 3 hours at 19 mph = 57 miles"
Answer: b
Question (general): in a river flowing at 2 km / hr , a boat travels 48 km upstream and then returns downstream to the starting point . if its speed in still water be 6 km / hr , find the total journey time .
Options: a ) 10 hours , b ) 12 hours , c ) 14 hours , d ) 18 hours , e ) none of these
Rationale: "explanation : speed of the boat = 6 km / hr speed downstream = ( 6 + 2 ) = 8 km / hr speed upstream = ( 6 - 2 ) = 4 km / hr distance traveled downstream = distance traveled upstream = 48 km total time taken = time taken downstream + time taken upstream = ( 48 / 8 ) + ( 48 / 4 ) = 18 hr . answer : option d"
Answer: d
Question (general): in smithtown , the ratio of right - handed people to left - handed people is 3 to 1 and the ratio of men to women is 3 to 2 . if the number of right - handed men is maximized , then what x percent of all the people in smithtown are left - handed women ?
Options: a ) 50 % , b ) 40 % , c ) 25 % , d ) 20 % , e ) 10 %
Rationale: "looking at the ratio we can take total number of people = 20 . . ans 5 / 20 or 25 % c"
Answer: c
Question (physics): the number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is ?
Options: a ) 38 , b ) 27 , c ) 75 , d ) 28 , e ) 21
Rationale: explanation : the hour hand moves from pointing to 12 to pointing to half way between 2 and 3 . the angle covered between each hour marking on the clock is 360 / 12 = 30 . since the hand has covered 2.5 of these divisions the angle moved through is 75 . answer : c
Answer: c