Cheukting/mathqa huggingface dataset:
Question (general): ( 1000 ) 7 ÷ ( 10 ) 19 = ?
Options: a ) 10 , b ) 100 , c ) 1000 , d ) 10000 , e ) none of these
Rationale: "explanation : = ( 103 ) 7 / ( 10 ) 19 = ( 10 ) 21 / ( 10 ) 19 = 10 ( 2 ) = 100 option b"
Answer: b
Question (other): tea worth rs . 126 per kg are mixed with a third variety in the ratio 1 : 1 : 2 . if the mixture is worth rs . 143 per kg , the price of the third variety per kg will be
Options: a ) rs . 165.50 , b ) rs . 1700 , c ) rs . 175.50 , d ) rs . 180 , e ) none
Rationale: "solution since first second varieties are mixed in equal proportions , so their average price = rs . ( 126 + 135 / 2 ) = rs . 130.50 so , the mixture is formed by mixing two varieties , one at rs . 130.50 per kg and the other at say , rs . x per kg in the ratio 2 : 2 , i . e . , 1 : 1 . we have to find x . x - 143 / 22.50 = 1 = â € º x - 143 = 22.50 = â € º x = 165.50 . hence , price of the third variety = rs . 165.50 per kg . answer a"
Answer: a
Question (other): 3 numbers are in the ratio 3 : 5 : 7 . the largest number is 56 . what is the difference between smallest and largest number ?
Options: a ) 20 , b ) 24 , c ) 28 , d ) 32 , e ) 36
Rationale: the three numbers are 3 x , 5 x , and 7 x . the largest number is 56 = 7 * 8 , so x = 8 . the smallest number is 3 * 8 = 24 . 56 - 24 = 32 the answer is d .
Answer: d
Question (general): mixture a is 20 % oil and 80 % material b by weight . if 2 more kilograms of oil are added to the 8 kilograms mixture a , how many kilograms of mixture a must be added to make a 70 % material b in the new mixture ?
Options: a ) 6 , b ) 7 , c ) 8 , d ) 9 , e ) 10
Rationale: old mix has 20 % oil . you add 2 kgs of 100 % oil . you get new mix with 30 % oil ( 70 % material b ) . w 1 / w 2 = ( 100 - 30 ) / ( 30 - 20 ) = 70 / 10 = 7 / 1 for every 7 parts of mix a , you have added 1 part of oil . since you have added 2 kgs oil , mix a must be 7 * 2 = 14 kgs . you already had 8 kgs of mix a , so extra mix a added must be 14 - 8 = 6 kgs . answer ( a )
Answer: a
Question (gain): kanul spent $ 5000 in buying raw materials , $ 200 in buying machinery and 30 % of the total amount he had as cash with him . what was the total amount ?
Options: a ) $ 7456.00 , b ) $ 7500.55 , c ) $ 7428.57 , d ) $ 7852.56 , e ) $ 7864.00
Rationale: "let the total amount be x then , ( 100 - 20 ) % of x = 5000 + 200 70 % of x = 5200 70 x / 100 = 5200 x = $ 52000 / 7 x = $ 7428.57 answer is c"
Answer: c
Question (gain): there is 60 % increase in an amount in 6 yrs at si . what will be the ci of rs . 12,000 after 3 years at the same rate ?
Options: a ) 2354 , b ) 2450 , c ) 2540 , d ) 2650 , e ) 3972
Rationale: "let p = rs . 100 . then , s . i . rs . 60 and t = 6 years . r = 100 x 60 = 10 % p . a . 100 x 6 now , p = rs . 12000 . t = 3 years and r = 10 % p . a . c . i . = rs . 12000 x 1 + 10 3 - 1 100 = rs . 12000 x 331 1000 = 3972 . e"
Answer: e
Question (physics): amar takes as much time in running 18 meters as a car takes in covering 48 meters . what will be the distance covered by amar during the time the car covers 1.8 km ?
Options: a ) 660 m , b ) 650 m , c ) 570 m , d ) 670 m , e ) 680 m
Rationale: "distance covered by amar = ( 18 / 48 ) * 1800 = 670 m answer : d"
Answer: d
Question (general): find the value of x from the below equation : x ^ 2 − 7 x + 10 = 0
Options: a ) 5 , b ) 7 , c ) 6 , d ) 11 , e ) 12
Rationale: "here we need to find out a and b such that a + b = - 7 and ab = + 10 a = - 5 and b = - 2 satisfies the above condition . hence x ^ 2 − 7 x + 10 = ( x − 5 ) ( x − 2 ) x 2 − 7 x + 10 = ( x − 5 ) ( x − 2 ) x ^ 2 − 7 x + 10 = 0 ⇒ ( x − 5 ) ( x − 2 ) = 0 x 2 − 7 x + 10 = 0 ⇒ ( x − 5 ) ( x − 2 ) = 0 step 3 : equate each factor to 0 and solve the equations ( x − 5 ) ( x − 2 ) = 0 ⇒ ( x − 5 ) = 0 or ( x − 2 ) = 0 ⇒ x = 5 or 2 a"
Answer: a
Question (general): find the largest 7 digit number which is exactly divisible by 88 ?
Options: a ) 9998765 , b ) 9998907 , c ) 9999944 , d ) 9999954 , e ) 9999968
Rationale: "largest 7 digit number is 9999999 after doing 9999999 ÷ 88 we get remainder 31 hence largest 7 digit number exactly divisible by 88 = 9999999 - 31 = 9999968 e"
Answer: e
Question (general): in a theater , the first row has 15 seats and each row has 2 more seats than previous row . if the last row has 53 seats , what is the total number of seats in the theater ?
Options: a ) 600 , b ) 640 , c ) 680 , d ) 720 , e ) 760
Rationale: "the number of seats in the theater is 15 + ( 15 + 2 ) + . . . + ( 15 + 38 ) = 20 ( 15 ) + 2 ( 1 + 2 + . . . + 19 ) = 20 ( 15 ) + 2 ( 19 ) ( 20 ) / 2 = 20 ( 15 + 19 ) = 20 ( 34 ) = 680 the answer is c ."
Answer: c
Question (general): evaluate : 20 - 12 ÷ 12 × 2 =
Options: a ) a ) 4 , b ) b ) 8 , c ) c ) 12 , d ) d ) 16 , e ) e ) 20
Rationale: "according to order of operations , 12 ÷ 12 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 12 × 2 = 1 × 2 = 2 hence 20 - 12 ÷ 12 × 2 = 20 - 12 = 8 correct answer is b ) 8"
Answer: b
Question (general): shipment - - - no . of defective chips / shipment - - - total chips in shipment s 1 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 5,000 s 2 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 12,000 s 3 - - - - - - - - - - - - - - - - - - - - - - 2 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 15,000 s 4 - - - - - - - - - - - - - - - - - - - - - - 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 16,000 a computer chip manufacturer expects the ratio of the number of defective chips to the total number of chips in all future shipments to equal the corresponding ratio for shipments s 1 , s 2 , s 3 , and s 4 combined , as shown in the table above . what ’ s the expected number of defective chips in a shipment of 60,000 chips ?
Options: a ) 14 , b ) 20 , c ) 22 , d ) 24 , e ) 15
Rationale: for a total of 51000 chips ( adding s 1 , s 2 , s 3 , s 4 ) total number of defective chips is 17 ( ( adding defective chips of s 1 , s 2 , s 3 , s 4 ) so ratio is 12 / 48000 or 1 every 4000 chips . keeping this ratio constant for 60000 chips number of defective chips will be ( 1 / 4000 ) * 60000 = 15 e
Answer: e
Question (other): three numbers are in the ratio of 2 : 3 : 4 and their l . c . m . is 276 . what is their h . c . f . ?
Options: a ) 18 , b ) 23 , c ) 28 , d ) 32 , e ) 36
Rationale: "let the numbers be 2 x , 3 x , and 4 x . lcm of 2 x , 3 x and 4 x is 12 x . 12 x = 276 x = 23 hcf of 2 x , 3 x and 4 x = x = 23 the answer is b ."
Answer: b
Question (geometry): if the length of a rectangle is increased by 10 % and the area is unchanged , then its corresponding breadth must be decreased by ?
Options: a ) 9 1 / 19
b ) 9 1 / 15
c ) 9 1 / 16
d ) 9 1 / 11
e ) 9 1 / 10
Rationale: suppose length = 100 m and breadth = x m area = 100 m new length = 110 m and breadth = ( x - y % of x ) then , \ inline 110 \ times ( x - \ frac { y } { 100 } x ) = 100 \ times x \ inline \ rightarrow \ inline 110 \ times ( 1 - \ frac { y } { 100 } ) = 100 \ inline \ rightarrow \ inline 1 - \ frac { y } { 100 } = \ frac { 100 } { 110 } \ inline \ rightarrow \ frac { y } { 100 } = 1 - \ frac { 100 } { 110 } = \ frac { 1 } { 11 } \ inline y = \ frac { 100 } { 11 } = 9 \ frac { 1 } { 10 } % answer : e
Answer: e
Question (general): in a mayoral election , candidate x received 1 / 3 more votes than candidate y , and candidate y received 1 / 7 fewer votes than z . if z received 21,000 votes how many votes did candidate x received ?
Options: a ) 18000 , b ) 22000 , c ) 24000 , d ) 26000 , e ) 32000
Rationale: "z = 21 - - > y received 1 / 7 fewer votes than z - - > y = z - 1 / 7 * z = 18 ; x received 1 / 3 more votes than y - - > x = y + 1 / 3 * y = 24 . answer : c ."
Answer: c
Question (other): each factor of 200 is inscribed on its own plastic ball , and all of the balls are placed in a jar . if a ball is randomly selected from the jar , what is the probability that the ball is inscribed with a multiple of 42 ?
Options: a ) 1 / 16 , b ) 5 / 42 , c ) 1 / 8 , d ) 3 / 16 , e ) 1 / 9
Rationale: 200 = 2 * 3 * 5 * 7 , so the # of factors 210 has is ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) ( 1 + 1 ) = 16 ( see below ) ; 42 = 2 * 3 * 7 , so out of 16 factors only two are multiples of 42 : 42 and 210 , itself ; so , the probability is 2 / 16 = 1 / 9 . answer : e .
Answer: e
Question (physics): a car traveled 462 miles per tankful of gasoline on the highway and 336 miles per tankful of gasoline in the city . if the car traveled 18 fewer miles per gallon in the city than on the highway , how many miles per gallon did the car travel in the city ?
Options: a ) 14 , b ) 16 , c ) 21 , d ) 32 , e ) 48
Rationale: "i treat such problems as work ones . work = rate * time mileage ( m ) = rate ( mpg ) * gallons ( g ) x gallons is a full tank { 462 = rx { 336 = ( r - 18 ) x solve for r , r = 66 66 - 18 = 48 mpg e"
Answer: e
Question (geometry): can v and can в are both right circular cylinders . the radius of can v is twice the radius of can b , while the height of can v is half the height of can b . if it costs $ 4.00 to fill half of can b with a certain brand of gasoline , how much would it cost to completely fill can v with the same brand of gasoline ?
Options: a ) $ 1
b ) $ 2
c ) $ 4
d ) $ 8
e ) $ 16
Rationale: let x be the radius of b and 2 h be the height of b . therefore , radius of v = 2 x and height = h vol of b = 3.14 * x ^ 2 * 2 h vol of a = 3.14 * 4 x ^ 2 * h cost to fill half of b = $ 4 - - > cost to fill full b = $ 8 - - > 3.14 * x ^ 2 * 2 h = 8 - - > 3.14 * x ^ 2 * h = 4 - - > 4 * ( 3.14 * x ^ 2 * h ) = $ 16 ans e
Answer: e
Question (general): x can give y 100 meters start and z 200 meters start in x kilometer race . how much start can y give z in x kilometer race ?
Options: a ) 112.2 m , b ) 216.3 m , c ) 111.12 m , d ) 213.27 m , e ) 222.40 m
Rationale: c 111.12 m x runs 1000 m while y runs 900 m and z runs 800 m . the number of meters that z runs when y runs 1000 m , = ( 1000 * 800 ) / 900 = 8000 / 9 = 888.88 m . y can give z = 1000 - 888.88 = 111.12 m .
Answer: c
Question (gain): a sum of money deposited at c . i . amounts to rs . 1890 in 2 years and to rs . 2350 in 3 years . find the rate percent ?
Options: a ) 30 % , b ) 24 % , c ) 20 % , d ) 19 % , e ) 50 %
Rationale: "1890 - - - 460 100 - - - ? = > 24 % answer : b"
Answer: b
Question (general): what is the least number that should be added to 1053 , so the sum of the number is divisible by 23 ?
Options: a ) 1 , b ) 2 , c ) 3 , d ) 4 , e ) 5
Rationale: "( 1053 / 23 ) gives a remainder 18 so we need to add 5 . the answer is e ."
Answer: e
Question (general): the salary of a , b , c , d , e is rs . 8000 , rs . 5000 , rs . 16000 , rs . 7000 , rs . 9000 per month respectively , then the average salary of a , b , c , d , and e per month is
Options: a ) rs . 7000 , b ) rs . 8000 , c ) rs . 8500 , d ) rs . 9000 , e ) none
Rationale: "answer average salary = 8000 + 5000 + 16000 + 7000 + 9000 / 5 = rs . 9000 correct option : d"
Answer: d
Question (general): find out the c . i on rs . 3000 at 4 % p . a . compound half - yearly for 1 1 / 2 years
Options: a ) 183.62 , b ) 106.07 , c ) 106.04 , d ) 106.03 , e ) 186.01
Rationale: "a = 3000 ( 51 / 50 ) 3 = 3183.62 3000 - - - - - - - - - - - 183.62 answer : a"
Answer: a
Question (general): a number when divided by 20 leaves 6 as a remainder . what will be the remainder if the number is divided by 19 ?
Options: a ) 7 , b ) 6 , c ) 5 , d ) 11 , e ) 13
Rationale: let the minimum whole number be 20 + 6 = 26 where 6 is the remainder . 26 when divided by 19 then leaves 7 . correct answer a .
Answer: a
Question (physics): how many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km / hr in the direction of the moving train if the speed of the train is 63 km / hr ?
Options: a ) 65 , b ) 69 , c ) 30 , d ) 31 , e ) 32
Rationale: "let length of tunnel is x meter distance = 800 + x meter time = 1 minute = 60 seconds speed = 78 km / hr = 78 * 5 / 18 m / s = 65 / 3 m / s distance = speed * time 800 + x = ( 65 / 3 ) * 60 800 + x = 20 * 65 = 1300 x = 1300 - 800 = 500 meters answer : option c"
Answer: c
Question (gain): the compound interest earned by sunil on a certain amount at the end of two years at the rate of 5 % p . a . was rs . 492 . find the total amount that sunil got back at the end of two years in the form of principal plus interest earned .
Options: a ) rs . 4935 , b ) rs . 4925 , c ) rs . 5390 , d ) rs . 5290 , e ) rs . 5292
Rationale: "let the sum be rs . p p { [ 1 + 5 / 100 ] 2 - 1 } = 492 p ( 5 / 100 ) ( 2 + 5 / 100 ) = 492 [ a 2 - b 2 = ( a - b ) ( a + b ) ] p = 492 / ( 0.05 ) ( 2.05 ) = 4800 . amount = 4800 + 492 = rs . 5292 answer : e"
Answer: e
Question (physics): a train 220 m long is running with a speed of 90 km / hr . in what time will it pass a bus that is running with a speed of 60 km / hr in the direction opposite to that in which the train is going ?
Options: a ) 4.37 , b ) 5.28 , c ) 6.75 , d ) 8 , e ) 3.1
Rationale: "speed of train relative to bus = 90 + 60 = 150 km / hr . = 150 * 5 / 18 = 125 / 3 m / sec . time taken to pass the bus = 220 * 3 / 125 = 5.28 sec . answer : b"
Answer: b
Question (general): a number is doubled and 9 is added . if resultant is trebled , it becomes 57 . what is that number
Options: a ) 5 , b ) 10 , c ) 12 , d ) 14 , e ) 15
Rationale: "explanation : = > 3 ( 2 x + 9 ) = 57 = > 2 x + 9 = 19 = > x = 5 answer : option a"
Answer: a
Question (physics): tim and é lan are 30 miles away from one another . they are starting to move towards each other simultaneously , tim at a speed of 10 mph and é lan at a speed of 5 mph . if every hour they double their speeds , what is the distance that tim will pass until he meets é lan ?
Options: a ) 20 miles . , b ) 35 miles . , c ) 45 miles . , d ) 60 miles . , e ) 65 miles .
Rationale: "tim and elan will meet at the same time while their ratio of speed is 2 : 1 respectively . so their individual distance traveled ratio will be same . plugging in the answer choice only answer choice a meet the 2 : 1 ( tim : elan = 20 : 10 ) ratio of maintaining total distance traveled 30 miles so correct answer a"
Answer: a
Question (general): 2 pipes can separately fill a tank in 20 hrs and 30 hrs respectively . both the pipes are opened tofill the tank , a leak develops in the tank through which one - third of water supplied by both the pipes goes out . what is the total time taken to fill the tank ?
Options: a ) 10 hrs , b ) 12 hrs , c ) 16 hrs , d ) 18 hrs , e ) 20 hrs
Rationale: "1 / 20 + 1 / 30 = 1 / 12 1 + 1 / 3 = 4 / 3 1 - - - 12 4 / 3 - - - ? 4 / 3 * 12 = 16 hrs c"
Answer: c
Question (general): there are 99 people that own pets . 15 people own only dogs , 10 people own only cats , 5 people own only cats and dogs , 3 people own cats , dogs and snakes . how many total snakes are there ?
Options: a ) 2 , b ) 4 , c ) 8 , d ) 69 , e ) 32
Rationale: "lets assign variables to all the areas in venn diagram of three . three different units are dog , cat , snake = total = 99 only dog = d = 15 only cat = c = 10 only snake = s exactly dog and cat = 5 exactly dog and snake = x exactly cat and snake = y all three = 3 so 99 = 15 + 10 + 5 + 3 + x + y + s we need to know total snakes = x + y + s + 3 = 69 answer : d"
Answer: d
Question (other): a certain university will select 1 of 7 candidates eligible to fill a position in the mathematics department and 2 of 9 candidates eligible to fill 2 identical positions in the computer science department . if none of the candidates is eligible for a position in both departments , how many different sets of 3 candidates are there to fill the 3 positions ?
Options: a ) 42 , b ) 70 , c ) 140 , d ) 165 , e ) 252
Rationale: "ans : 252 7 c 1 * 9 c 2 answer e )"
Answer: e
Question (gain): the simple interest on rs . 8 for 12 months at the rate of 5 paise per rupeeper month is
Options: a ) 1.2 , b ) 4.8 , c ) 4.4 , d ) 3.21 , e ) none
Rationale: "sol . s . i . = rs . [ 8 * 5 / 100 * 12 ] = rs . 4.8 answer b"
Answer: b
Question (physics): an athlete runs 360 metres race in 24 seconds . what is his speed ?
Options: a ) 23 , b ) 64.8 , c ) 37 , d ) 30 , e ) 28
Rationale: "speed = distance / time = 360 / 20 = 18 m / s = 18 * 18 / 5 = 64.8 km / hr answer : b"
Answer: b
Question (physics): two trains , one from howrah to patna and the other from patna to howrah , start simultaneously . after they meet , the trains reach their destinations after 4 hours and 36 hours respectively . the ratio of their speeds is ?
Options: a ) 4 : 9 , b ) 4 : 3 , c ) 4 : 5 , d ) 3 : 1 , e ) 4 : 2
Rationale: "let us name the trains a and b . then , ( a ' s speed ) : ( b ' s speed ) = √ b : √ a = √ 36 : √ 4 = 6 : 2 = 3 : 1 answer : d"
Answer: d
Question (general): a batsman scored 120 runs which included 10 boundaries and 6 sixes . what % of his total score did he make by running between the wickets
Options: a ) 40 % , b ) 50 % , c ) 36.67 % , d ) 70 % , e ) 75 %
Rationale: "number of runs made by running = 120 - ( 10 x 4 + 6 x 6 ) = 120 - ( 76 ) = 44 now , we need to calculate 60 is what percent of 120 . = > 44 / 120 * 100 = 36.67 % c"
Answer: c
Question (general): the sum of the present ages of two persons a and b is 54 . if the age of a is twice that of b , find the sum of their ages 5 years hence ?
Options: a ) 50 , b ) 64 , c ) 70 , d ) 80 , e ) 90
Rationale: "a + b = 54 , a = 2 b 2 b + b = 54 = > b = 18 then a = 36 . 5 years , their ages will be 41 and 23 . sum of their ages = 41 + 23 = 64 . answer : b"
Answer: b
Question (general): if 12 % of x is equal to 6 % of y , then 18 % of x will be equal to how much % of y ?
Options: a ) 7 % , b ) 9 % , c ) 11 % , d ) 12 % , e ) none of these
Rationale: we have , 12 % of x = 6 % of y = > 2 % of x = 1 % of y = > ( 2 x 9 ) % of x = ( 1 x 9 ) % of y thus , 18 % of x = 9 % of y . answer : b
Answer: b
Question (gain): heinz produces tomato puree by boiling tomato juice . the tomato puree has only 20 % water while the tomato juice has 90 % water . how many liters of tomato puree will be obtained from 80 litres of tomato juice ?
Options: a ) 2.8 liters . , b ) 2.5 liters . , c ) 8.5 liters . , d ) 2.6 liters . , e ) 10 liters .
Rationale: "answer : explanation : in each of the solutions , there is a pure tomato component and some water . so while boiling , water evaporates but tomato not . so we equate tomato part in the both equations . â ‡ ’ â ‡ ’ 10 % ( 80 ) = 80 % ( x ) â ‡ ’ â ‡ ’ x = 10 liters . answer : e"
Answer: e
Question (gain): a technician makes a round - trip to and from a certain service center by the same route . if the technician completes the drive to the center and then completes 30 percent of the drive from the center , what percent of the round - trip has the technician completed ?
Options: a ) 60 , b ) 65 , c ) 55 , d ) 50 , e ) 55
Rationale: round trip means 2 trips i . e . to and fro . he has completed one i . e 50 % completed . then he traveled another 30 % of 50 % i . e 15 % . so he completed 50 + 15 = 65 % of total trip . b
Answer: b
Question (general): on dividing 127 by a number , the quotient is 9 and the remainder is 1 . find the divisor .
Options: a ) a ) 12 , b ) b ) 14 , c ) c ) 16 , d ) d ) 18 , e ) e ) 22
Rationale: "d = ( d - r ) / q = ( 127 - 1 ) / 9 = 126 / 9 = 14 b )"
Answer: b
Question (general): if x + | x | + y = 7 and x + | y | - y = 6 , then x + y =
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 9
Rationale: "if x + | x | + y = 7 and x + | y | - y = 6 , then x + y = can be done in 2.3 mins : there are 4 cases to be tested : 1 ) x is - ve and y is - ve substituting in the equation , we get x - x + y = 7 and x - y - y = 6 solve for x and y we get x = 20 and y = 7 , so x + y = 27 reject 2 ) x is + ve and y is + ve substitute in the equation , we ger x + x + y = 7 and x + y - y = 6 solve for x and y we get x = 6 and y = - 5 , therefore x + y = 1 not on list so reject 3 ) x is - ve and y is + ve substitute , we get x - x = y = 7 and x + y - y = 6 solve fo x and y we get x = 6 and y = 7 , x + y = 13 not on list so reject 4 ) x is + ve and y is - ve substitute , we get x + x = y = 7 and x - y - y = 6 solve for x and y , we get x = 4 and y = - 1 , x + y = 3 , answer choice answer a"
Answer: a
Question (physics): a 300 meter long train crosses a platform in 45 seconds while it crosses a signal pole in 18 seconds . what is the length of the platform ?
Options: a ) 99 , b ) 450 , c ) 350 , d ) 882 , e ) 281
Rationale: "speed = [ 300 / 18 ] m / sec = 50 / 3 m / sec . let the length of the platform be x meters . then , x + 300 / 45 = 50 / 3 3 ( x + 300 ) = 2250 è x = 450 m . answer : b"
Answer: b
Question (other): the ratio between the number of sheep and the number of horses at the stewart farm is 3 to 7 , if each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day , what is the number of sheep in the farm ?
Options: a ) 24 , b ) 28 , c ) 32 , d ) 56 , e ) 60
Rationale: let the number of sheeps and horses be 3 x and 7 x . now total number of horses = total consumption of horse food / consumption per horse = 12880 / 230 = 56 , which is equal to 7 x . = > x = 8 sheeps = 3 x = 3 * 8 = 24 . hence a
Answer: a
Question (general): one day a car rental agency rented 3 / 4 of its cars , including 4 / 5 of its cars with cd players . if 3 / 5 of its cars have cd players , what percent of the cars that were not rented had cd players ?
Options: a ) 23 / 40 , b ) 17 / 30 , c ) 12 / 25 , d ) 7 / 15 , e ) 3 / 10
Rationale: "the cars with cd players which were not rented is ( 1 / 5 ) ( 3 / 5 ) = 3 / 25 of all the cars . the cars which were not rented is 1 / 4 of all the cars . the percent of non - rented cars which had cd players is ( 3 / 25 ) / ( 1 / 4 ) = 12 / 25 the answer is c ."
Answer: c
Question (general): if a ( k ) = ( k + 1 ) ^ 2 , and k = 1 , what is the value of a ( a ( a ( a ( k ) ) ) ) ?
Options: a ) 328359 , b ) 557321 , c ) 258327 , d ) 458329 , e ) 4422
Rationale: a ( a ( a ( a ( 1 ) ) ) ) = a ( a ( a ( 4 ) ) ) = a ( a ( 25 ) ) = a ( 676 ) = 677 ^ 2 = 458329 thus , the answer is d .
Answer: d
Question (gain): from the beginning to the end of 2007 , the price of a stock rose 20 percent . in 2008 , it dropped 25 percent . in 2009 , it rose 20 percent . what percent of the stock ’ s 2007 starting price was the price of the stock at the end of 2009 ?
Options: a ) 80 , b ) 90 , c ) 95 , d ) 100 , e ) 108
Rationale: "assume a value at the beginning of 2007 . as this is a % question , assume p = 100 . at the end of 2007 it becmae = 1.2 * 100 = 120 at the end of 2008 it decreased by 25 % = 120 * . 75 = 90 at the end of 2009 it increased by 20 % = 90 * 1.2 = 108 thus ratio = 108 / 100 = 1.08 ( in % terms = 108 % ) . thus e is the correct answer ."
Answer: e
Question (gain): a 8 % stock yields 20 % . the market value of the stock is :
Options: a ) rs 48 , b ) rs 45 , c ) rs 40 , d ) rs 50 , e ) rs 55
Rationale: "explanation : for an income of rs . 20 , investment = rs . 100 . for an income of rs 8 , investment = rs . 100 / 20 x 8 = rs 40 market value of rs . 100 stock = rs 40 answer is c"
Answer: c
Question (gain): the difference between a number and its two fifth is 510 . what is 10 % of that number ?
Options: a ) 12.75 , b ) 50 , c ) 85 , d ) 204 , e ) none
Rationale: "solution let the number be x . then , x - 2 / 5 x = 510 . ‹ = › 3 / 5 x = 510 ‹ = › x = [ 510 x 5 / 3 ] = 850 . therefore 10 % of 850 = 85 . answer c"
Answer: c
Question (general): in a certain accounting class of 100 students , 70 % of the students took the final exam on the assigned day while the rest of the students took the exam on a make - up date . if the students on the assigned day had an average score of 65 % , and the students on the make - up date had an average score of 95 % , what was the average score for the entire class ?
Options: a ) 68 % , b ) 70 % , c ) 72 % , d ) 74 % , e ) 77 %
Rationale: "70 % of the class scored 65 % and 30 % of the class scored 95 % . the difference between 65 % and 95 % is 30 % . the average will be 65 % + 0.3 ( 30 % ) = 74 % . the answer is d ."
Answer: d