Cheukting/mathqa huggingface dataset:
Question (other): in a certain school , the ratio of boys to girls is 5 to 13 . if there are 128 more girls than boys , how many boys are there ?
Options: a ) 27 , b ) 36 , c ) 45 , d ) 72 , e ) 80
Rationale: "the ratio of b to g is 5 : 13 and the other data point is g are more than boys by 128 . . . looking at the ratio we can say that the 8 ( 13 - 5 ) extra parts caused this diff of 128 . so 1 part corresponds to 128 / 8 = 16 and so 5 parts correspond to 5 * 16 = 80 . e"
Answer: e
Question (physics): i remember during the school days , the teacher asked the class ` ` can you tell me the sum of the first 50 odd numbers ? ` ` . i ran quickly to the teacher and told her ` ` the answer is 2500 ' ' . the teacher replied ` ` lucky guess ' ' . she then asked me ` ` can you tell me the sum of first 75 odd numbers ? ` ` . i wait for approx 10 seconds and replied with the correct answer . how can i answer so quickly and whats the correct answer ?
Options: a ) 5624 , b ) 5625 , c ) 5626 , d ) 5627 , e ) none
Rationale: solution : 5625 n ^ 1 75 * 75 = 5625 ( sum of first 75 odd numbers ) . 50 * 50 = 2500 ( sum of first 50 odd numbers ) . answer b
Answer: b
Question (gain): in one hour , a boat goes 11 km along the stream and 7 km against the stream . the sped of the boat in still water ( in km / hr ) is :
Options: a ) 3 , b ) 5 , c ) 8 , d ) 9 , e ) 10
Rationale: "solution speed in still water = 1 / 2 ( 11 + 7 ) km / hr = 9 kmph . answer d"
Answer: d
Question (general): the average of first five prime numbers greater than 10 is ?
Options: a ) 16.6 , b ) 12.9 , c ) 31.3 , d ) 19.2 , e ) 15.7
Rationale: "11 + 13 + 17 + 19 + 23 = 83 / 5 = 16.6 answer : a"
Answer: a
Question (general): following an increase in prices , the price of a candy box was 15 pounds and the price of a can of soda was 6 pounds . if the price of a candy box was raised by 25 % , and the price of a can of soda was raised by 50 % . what was the price of a box of candy plus a can of soda before prices were raised ?
Options: a ) 11 . , b ) 12 . , c ) 13 . , d ) 14 . , e ) 16
Rationale: "price of candy before price increase = 15 / 1.25 = 12 price of soda before price increase = 6 / 1.5 = 4 total price = 12 + 4 = 16 e is the answer"
Answer: e
Question (physics): city a and city b are 140 miles apart . train c departs city a , heading towards city b , at 4 : 00 and travels at 40 miles per hour . train d departs city b , heading towards city a , at 4 : 20 and travels at 20 miles per hour . the trains travel on parallel tracks . at what time do the two trains meet ?
Options: a ) 5 : 00 , b ) 5 : 30 , c ) 6 : 00 , d ) 6 : 20 , e ) 7 : 00
Rationale: "train c has traveled 20 mi in the half hour before train d has started its journey . 140 - 20 = 120 40 + 20 = 60 mph 120 mi / 60 mph = 2 hrs 4 : 20 pm + 2 hrs = 6 : 20 pm answer : d . 6 : 20"
Answer: d
Question (general): a mathematics teacher tabulated the marks secured by 35 students of 8 th class . the average of their marks was 72 . if the marks secured by reema was written as 46 instead of 56 then find the correct average marks up to two decimal places .
Options: a ) 73.41 , b ) 72.28 , c ) 72.43 , d ) 73.43 , e ) can not be determined
Rationale: "total marks = 35 x 72 = 2520 corrected total marks = 2520 - 46 + 56 = 2530 correct average = 2530 / 35 = 72.28 answer : b"
Answer: b
Question (general): a number when divided by a divisor leaves a remainder of 21 . when twice the original number is divided by the same divisor , the remainder is 11 . what is the value of the divisor ?
Options: a ) 12 , b ) 13 , c ) 34 , d ) 37 , e ) 59
Rationale: "let the number is n , the divisor = d , i will make the two equations - n = xd + 21 2 n = yd + 11 where x and y are integers solving them : d ( y - 2 x ) = 34 as d is also integer and 34 is a prime number , the d should be 34 to satisfy the above equation . hence answer is ' d '"
Answer: d
Question (gain): last year a certain bond price with a face value of 5000 yielded 7 % of its face value in interest . if that interest was approx 6.5 of the bond ' s selling price approx what was the bond ' s selling price ?
Options: a ) 4063 , b ) 5325 , c ) 5385 , d ) 6000 , e ) 6154
Rationale: "interest = 0.07 * 5000 = 0.065 * selling price - - > selling price = 0.07 * 5000 / 0.065 - - > selling price = ~ 5,385 answer : c ."
Answer: c
Question (geometry): the length and the breadth of a rectangle are in the ratio of 3 : 2 respectively . if the sides of the rectangle are extended on each side by 1 metre , the ratio of length to breadth becomes 10 : 7 . find the area of the original rectangle in square metres .
Options: a ) 256
b ) 150
c ) 280
d ) data inadequate
e ) none of these
Rationale: let the length and breadth be l and b respectively . l ⁄ b = 3 ⁄ 2 or l = 3 ⁄ 2 b . . . . . ( i ) l + 1 / b + 1 = 10 / 7 or 7 l - 10 b = 3 . . . . . ( ii ) from eq . ( i ) 10.5 b – l 0 b = 6 or , 0.5 b = 3 or , b = 6 and l = 9 area = l × b = 6 × 9 = 54 m 2 answer e
Answer: e
Question (geometry): 32 meters of wire is available to fence off a flower bed in the form of a circular sector . what must the radius of the circle in meters be , if we wish to have a flower bed with the greatest possible surface area ?
Options: a ) 2 √ 2
b ) 2 √ 5
c ) 5
d ) 4 √ 2
e ) 8
Rationale: area of sector , a = x / 360 * pi * r ^ 2 circumference of the sector = 32 = > x / 360 * 2 * pi * r + 2 r = 32 = > 2 a / r + 2 r = 32 = > a = r 16 - r ^ 2 = r 16 - r ^ 2 we will now max using derivations max value of a will found at a = 0 i . e 16 - 2 r = 0 r = 8 e
Answer: e
Question (physics): a 300 m long train crosses a platform in 54 sec while it crosses a signal pole in 18 sec . what is the length of the platform ?
Options: a ) 287 , b ) 350 , c ) 600 , d ) 277 , e ) 122
Rationale: "speed = 300 / 18 = 50 / 3 m / sec . let the length of the platform be x meters . then , ( x + 300 ) / 54 = 50 / 3 3 x + 900 = 2700 = > x = 600 m . answer : c"
Answer: c
Question (geometry): compute the perimeter of a square with area 36 .
Options: a ) 24
b ) 27
c ) 25
d ) 26
e ) 29
Rationale: if the length of the square is s , then s 2 = 36 so s = 6 . the perimeter is therefore 4 s = 24 . correct answer a
Answer: a
Question (physics): a can run 4 times as fast as b and gives b a start of 72 m . how long should the race course be so that a and b might reach in the same time ?
Options: a ) 70 m , b ) 60 m , c ) 80 m , d ) 65 m , e ) 96 m
Rationale: "speed of a : speed of b = 4 : 1 means in a race of 4 m a gains 3 m . then in a race of 72 m he gains 72 * ( 4 / 3 ) i . e 96 m answer : e"
Answer: e
Question (general): evaluate : 30 - 12 ÷ 3 × 2 = ?
Options: a ) 20 , b ) 22 , c ) 24 , d ) 26 , e ) 28
Rationale: "according to order of operations , 12 ÷ 3 × 2 ( division and multiplication ) is done first from left to right 12 ÷ 3 × 2 = 4 × 2 = 8 hence 30 - 12 ÷ 3 × 2 = 30 - 8 = 22 correct answer b ) 22"
Answer: b
Question (other): a certain telephone company offers two plans , a and b . under plan a , the company charges a total of $ 0.60 for the first 5 minutes of each call and $ 0.06 per minute thereafter . under plan b , the company charges $ 0.08 per minute of each call . what is the duration of a call , in minutes , for which the company charges the same amount under plan a and under plan b ?
Options: a ) 2 , b ) 9 , c ) 15 , d ) 21 , e ) 30
Rationale: "let the duration , in minutes , for which the company charges the same under plan a and plan b be t minutes . then under plan a the cost would be $ 0.6 + 0.06 ( t - 5 ) and under plan b the cost would be $ 0.08 t . we want these amount to be equal : 0.6 + 0.06 ( t - 5 ) = 0.08 t - - > 60 + 6 ( t - 5 ) = 8 t - - > t = 15 . answer : c ."
Answer: c
Question (physics): an employer pays rs . 30 for each day a worker works , and forfeits rs . 5 for each day he is idle . at the end of 60 days , a worker gets rs . 500 . for how many days did the worker remain idle ?
Options: a ) 52 , b ) 27 , c ) 99 , d ) 61 , e ) 11
Rationale: explanation : suppose the worker remained idle for m days . then , he worked for ( 60 - m ) days . 30 ( 60 - m ) – 5 m = 500 1800 – 25 m = 500 25 m = 1300 m = 52 so , the worker remained idle for 52 days . answer : a
Answer: a
Question (physics): a can finish a piece of work in 5 days . b can do it in 15 days . they work together for two days and then a goes away . in how many days will b finish the work ?
Options: a ) 3 days , b ) 5 days , c ) 4 days , d ) 6 days , e ) 7 days
Rationale: "2 / 5 + ( 2 + x ) / 15 = 1 = > x = 7 days answer : e"
Answer: e
Question (physics): find the area of trapezium whose parallel sides are 20 cm and 18 cm long , and the distance between them is 16 cm
Options: a ) 304 cm 2 , b ) 179 cm 2 , c ) 285 cm 2 , d ) 167 cm 2 , e ) 197 cm 2
Rationale: "area of a trapezium = 1 / 2 ( sum of parallel sides ) * ( perpendicular distance between them ) = 1 / 2 ( 20 + 18 ) * ( 16 ) = 304 cm 2 answer : a"
Answer: a
Question (physics): a policeman noticed a criminal from a distance of 180 km . the criminal starts running and the policeman chases him . the criminal and the policeman run at the rate of 8 km and 9 km per hour respectively . what is the distance between them after 5 minutes ?
Options: a ) 96.7 m , b ) 120 m , c ) 130 m , d ) 150 m , e ) none of these
Rationale: "explanation : solution : relative speed = ( 9 - 8 ) = 1 km / hr . distance covered in 3 minutes = ( 1 * 5 / 60 ) km = 1 / 12 km = 83.3 m . . ' . distance between the criminal and policeman = ( 180 - 83.3 ) m = 96.7 m . answer : a"
Answer: a
Question (general): 8269 ã — 9998 = ?
Options: a ) 85432864 , b ) 82673462 , c ) 86985434 , d ) 68954365 , e ) 65486954
Rationale: "8269 ã — ( 10000 - 2 ) 82690000 - 16538 = 82673462 answer b"
Answer: b
Question (general): let f ( x ) = x ^ 2 + bx + c . if f ( 1 ) = 0 and f ( - 8 ) = 0 , then f ( x ) crosses the y - axis at what y - coordinate ?
Options: a ) - 8 , b ) - 1 , c ) 0 , d ) 1 , e ) 8
Rationale: "when x = 1 and when x = - 8 , the expression f ( x ) = x ² + bx + c equals 0 . then f ( x ) = ( x - 1 ) ( x + 8 ) f ( 0 ) = - 8 the answer is a ."
Answer: a
Question (other): two numbers are in the ratio of 5 : 7 . if 12 is subtracted from each number , they are in the ratio of 11 : 17 . what are the two numbers ?
Options: a ) 45 , 63 , b ) 50 , 70 , c ) 55 , 77 , d ) 60 , 84 , e ) 65 , 91
Rationale: "( 5 x - 12 ) : ( 7 x - 12 ) = 11 y : 17 y 5 x - 12 = 11 y 7 x - 12 = 17 y 84 - 60 = 85 y - 77 y 24 = 8 y y = 3 5 x - 12 = 33 x = 9 the two numbers are 5 x and 7 x which are 45 and 63 . the answer is a ."
Answer: a
Question (gain): the sale price sarees listed for rs . 600 after successive discount is 10 % and 5 % is ?
Options: a ) 227 , b ) 513 , c ) 342 , d ) 787 , e ) 191
Rationale: "600 * ( 90 / 100 ) * ( 95 / 100 ) = 513 answer : b"
Answer: b
Question (general): in an election between two candidates a and b , the number of valid votes received by a exceeds those received by b by 15 % of the total number of votes polled . if 20 % of the votes polled were invalid and a total of 6720 votes were polled , then how many valid votes did b get ?
Options: a ) 1888 , b ) 2999 , c ) 2834 , d ) 2777 , e ) 2184
Rationale: "let the total number of votes polled in the election be 100 k . number of valid votes = 100 k - 20 % ( 100 k ) = 80 k let the number of votes polled in favour of a and b be a and b respectively . a - b = 15 % ( 100 k ) = > a = b + 15 k = > a + b = b + 15 k + b now , 2 b + 15 k = 80 k and hence b = 32.5 k it is given that 100 k = 6720 32.5 k = 32.5 k / 100 k * 6720 = 2184 the number of valid votes polled in favour of b is 2184 . answer : e"
Answer: e
Question (general): harold works at a resort from the beginning of march to the end of september . during the month of august this past year , he made 5 times the average ( arithmetic mean ) of his monthly totals in tips for the other months . his total tips for august were what fraction of his total tips for all of the months he worked ?
Options: a ) 1 / 3 , b ) 2 / 5 , c ) 3 / 7 , d ) 4 / 7 , e ) 5 / 11
Rationale: "the time from beginning of march to the end of september is 7 months . if x is the average monthly tip for all months other than august then his august month tip will be 5 * x his total tip for the 7 months = 6 * ( average tip for the months other than august ) + 5 x = 11 x august tips as a fraction of total tips = 5 x / 11 x = 5 / 11 . so e"
Answer: e
Question (general): a clock store sold a certain clock to a collector for 45 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 25 percent of what the collector had paid . the shop then sold the clock again at a profit of 55 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 $ 180 , for how much did the shop sell the clock the second time ?
Options: a ) $ 149.55 , b ) $ 134.56 , c ) $ 175.43 , d ) $ 158.65 , e ) $ 255.45
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 45 % profit . this means the clocks ' selling price was c ( 1.45 ) 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 25 % the price at which the collector bought it . thus , you get = 1.45 * 0.25 * c = 0.3625 c furthermore , the store sells the clock for the second time for 55 % profit and thus the selling price of the clock becomes = cost price of the clock for the store at buy - back * 1.55 = 1.55 * 0.3625 c finally given that c - 0.3625 c = 180 - - - - > c = 282.35 $ thus , the cost of the clock the second time around = 1.55 * 0.3625 c = 1.55 * 0.3625 * 282.35 = 158.65 $ . hence d is the correct answer ."
Answer: d
Question (general): in a hostel there were 100 students . to accommodate some more students the average budget is decreased by rupees 10 . but total expenditure increased by rs . 400 . if the total expenditure of the hostel now 5400 , find the number of student joined ?
Options: a ) 30 , b ) 20 , c ) 35 , d ) 32 , e ) 40
Rationale: let average is x 100 x + 400 = 5400 x = 50 let the number of student joined is y ( 100 + y ) * ( 50 - 10 ) = 5400 y = 35 answer : d
Answer: d
Question (physics): 54 men working 8 hours per day dig 30 m deep . how many extra men should be put to dig to a depth of 50 m working 6 hours per day ?
Options: a ) 33 , b ) 66 , c ) 18 , d ) 100 , e ) 281
Rationale: "( 54 * 8 ) / 30 = ( x * 6 ) / 50 = > x = 120 120 – 54 = 66 answer : b"
Answer: b
Question (probability): what is the probability of getting sum 10 with the help of three dice ?
Options: a ) 1 / 4 , b ) 1 / 8 , c ) 1 / 16 , d ) 1 / 24 , e ) 1 / 32
Rationale: "( 1 , 3,6 ) 3 ! = 6 ( 2 , 2,6 ) = 3 ! / 2 = 3 ( 1 , 4,5 ) 3 ! = 6 ( 2 , 4,4 ) = 3 ( 2 , 3,5 ) 3 ! = 6 ( 3 , 3,4 ) = 3 prob . of getting sum 10 = ( 6 + 6 + 6 + 3 + 3 + 3 ) / 216 = 1 / 8 ans answer : b"
Answer: b
Question (other): a certain fraction has the same ratio to 1 / 18 , as 2 / 5 does to 7 / 9 . what is this certain fraction ?
Options: a ) 1 / 20 , b ) 1 / 25 , c ) 1 / 30 , d ) 1 / 35 , e ) 1 / 40
Rationale: "x / ( 1 / 18 ) = ( 2 / 5 ) / ( 7 / 9 ) x = 2 * 9 * 1 / 18 * 5 * 7 = 1 / 35 the answer is d ."
Answer: d
Question (general): a batsman makes a score of 87 runs in the 17 th inning and thus increases his average by 4 . find his average after 17 th inning .
Options: a ) 36 , b ) 39 , c ) 23 , d ) 45 , e ) none of the above
Rationale: "let the average after 17 th inning = x . then , average after 16 th inning = ( x – 4 ) . ∴ 16 ( x – 4 ) + 87 = 17 x or x = ( 87 – 64 ) = 23 . answer c"
Answer: c
Question (geometry): . if the sides of two cubes are in the ratio 3 : 1 the ratio of their total surface area is ?
Options: a ) 3 : 1
b ) 8 : 1
c ) 9 : 1
d ) 12 : 1
e ) 9 : 1
Rationale: a 1 : a 2 = 3 : 1 6 a 12 : 6 a 22 = 9 : 1 answer : c
Answer: c
Question (general): the sum of the first n positive perfect squares , where n is a positive integer , is given by the formula n ^ 3 / 3 + c * n ^ 2 + n / 6 , where c is a constant . what is the sum of the first 16 positive perfect squares ?
Options: a ) 1,010 , b ) 1,164 , c ) 1,240 , d ) 1,316 , e ) 1,496
Rationale: "first we need to find the constant ' c ' . the easiest way to find this is for the sum of the first two perfect squares for 1 and 2 = 1 and 4 respectively . hence lhs = 1 + 4 and plug n = 2 for rhs and simplify to get c = 1 / 2 . plug values of n = 16 and c = 1 / 2 into the equation and simplify to get the answer 1496 option e ."
Answer: e
Question (general): when the positive integer x is divided by 9 , the remainder is 5 . what is the remainder when 6 x is divided by 9 ?
Options: a ) 0 , b ) 1 , c ) 3 , d ) 4 , e ) 6
Rationale: "i tried plugging in numbers x = 9 q + 5 x = 14 6 x = 84 6 x / 9 = 9 * 9 + 3 remainder is 3 . answer is c ."
Answer: c
Question (general): set a : 3 , r , 8 , 10 set b : 4 , g , 9 , 11 the terms of each set above are given in ascending order . if the median of set a is equal to the median of set b , what is the value of g – r ?
Options: a ) - 2 , b ) - 1 , c ) 0 , d ) 1 , e ) 2
Rationale: so we have even no . of elements in the set so median is the average of middle two numbers ( r + 8 ) / 2 = ( g + 9 ) / 2 g - r = - 1 answer b
Answer: b
Question (general): how many integers from 40 to 200 , inclusive , are divisible by 3 but not divisible by 7 ?
Options: a ) 20 , b ) 31 , c ) 35 , d ) 40 , e ) 45
Rationale: "we should find # of integers divisible by 3 but not by 3 * 7 = 21 . # of multiples of 21 in the range from 40 to 200 , inclusive is ( 189 - 42 ) / 21 + 1 = 8 ; 53 - 8 = 45 . answer : e ."
Answer: e
Question (physics): water boils at 212 ° f or 100 ° c and ice melts at 32 ° f or 0 ° c . if the temperature of a pot of water is 45 ° c , what is the temperature of the pot of water in ° f ?
Options: a ) 92 ° f , b ) 97 ° f , c ) 104 ° f , d ) 113 ° f , e ) 118 ° f
Rationale: "let f and c denote the temperature in fahrenheit and celsius respectively . ( f - 32 ) / ( 212 - 32 ) = ( c - 0 ) / ( 100 - 0 ) f = 9 c / 5 + 32 f = 9 ( 45 ) / 5 + 32 = 113 ° f the answer is d ."
Answer: d
Question (gain): a sum of money at simple interest amounts to rs . 415 in 2 years and to rs . 514 in 4 years . the sum is ?
Options: a ) rs . 316 , b ) rs . 251 , c ) rs . 154 , d ) rs . 294 , e ) rs . 200
Rationale: "explanation : s . i . for 2 years = ( 514 - 415 ) = rs . 99 s . i . for 1 year = 99 / 2 principal = ( 415 - 99 ) = rs . 316 . answer is a"
Answer: a
Question (gain): a man can row his boat with the stream at 26 km / h and against the stream in 4 km / h . the man ' s rate is ?
Options: a ) 1 kmph , b ) 7 kmph , c ) 98 kmph , d ) 11 kmph , e ) 4 kmph
Rationale: "ds = 26 us = 4 s = ? s = ( 26 - 4 ) / 2 = 11 kmph answer : d"
Answer: d
Question (physics): a and b can complete a work in 30 days and 15 day . they started doing the work together but after 5 days b had to leave and a alone completed the remaining work . the whole work was completed in ?
Options: a ) 10 days , b ) 12 days , c ) 20 days , d ) 18 days , e ) 25 days
Rationale: a + b 1 day work = 1 / 30 + 1 / 15 = 1 / 10 work done by a and b in 10 days = 1 / 10 * 5 = 1 / 2 remaining work = 1 - 1 / 2 = 1 / 2 now 1 / 30 work is done by a in 1 day 1 / 2 work will be done by a in 30 * 1 / 2 = 15 days total time taken = 15 + 5 = 20 days answer is c
Answer: c
Question (physics): karen places a bet with tom that she will beat tom in a car race by 4 miles even if karen starts 4 minutes late . assuming that karen drives at an average speed of 60 mph and tom drives at an average speed of 45 mph , how many e miles will tom drive before karen wins the bet ?
Options: a ) 15 , b ) 18 , c ) 21 , d ) 24 , e ) 27
Rationale: let k and t be the speeds of karen and tom respectively . t be the time that karen will travel - - - - > t + 4 / 60 will be the total time tom will travel by the time the distance between karen and tom is 4 miles . thus , per the question , k ( t ) - t ( t + 4 / 60 ) = 4 - - - > t = 7 / 15 hours thus the distance traveled by tom when karen is 4 miles ahead of him e : t * ( t + 4 / 60 ) = 45 ( 7 / 15 + 4 / 60 ) = 24 miles . d is the correct answer .
Answer: d
Question (general): the sum of two numbers is 73 and their difference is 28 . find the difference between their squares .
Options: a ) 101 , b ) 45 , c ) 2044 , d ) 2048 , e ) 2064
Rationale: "explanation : let x and y be the two given numbers ( x + y ) = 73 ; ( x – y ) = 28 ( x 2 – y 2 ) = ( x + y ) ( x – y ) = 73 * 28 = 2044 answer : c"
Answer: c
Question (physics): a large tank can filled by a and b in 60 minutes and 40 minutes respectively . how many minutes will it take to fill the tanker from empty state if b is used for half the time and a and b fill it together for the other half ?
Options: a ) 10 min , b ) 15 min , c ) 30 min , d ) 25 min , e ) 42 min
Rationale: part filled by a + b in 1 minute = 1 / 60 + 1 / 40 = 1 / 24 suppose the tank is filled in x minutes then , x / 2 ( 1 / 24 + 1 / 40 ) = 1 x / 2 * 1 / 15 = 1 x = 30 min answer is c
Answer: c
Question (physics): in order to fence a square manish fixed 48 poles . if the distance between two poles , is 1 metres then what will be the area of the square so formed ?
Options: a ) 144 cm 2 , b ) 260 cm 2 , c ) 2500 cm 2 , d ) 302 cm 2 , e ) none of these
Rationale: "let the side of the square be x m . ∴ perimeter of the square = 48 × 1 = 4 x ∴ x = 12 m ∴ area = ( 12 ) 2 = 144 cm 2 answer a"
Answer: a
Question (other): the ratio , by volume , of bleach to detergent to water in a certain solution is 4 : 40 : 100 . the solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved . if the altered solution will contain 300 liters of water , how many liters of detergent will it contain ?
Options: a ) 80
b ) 70
c ) 60
d ) 40
e ) 50
Rationale: b : d : w = 4 : 40 : 100 bnew / dnew = ( 1 / 3 ) * ( 4 / 40 ) = ( 1 / 30 ) dnew / wnew = ( 1 / 2 ) * ( 40 / 100 ) = ( 1 / 5 ) wnew = 300 dnew = wnew / 5 = 300 / 5 = 60 so , answer will be c
Answer: c
Question (other): two vessels contains equal number of mixtures milk and water in the ratio 8 : 2 and 9 : 1 . both the mixtures are now mixed thoroughly . find the ratio of milk to water in the new mixture so obtained ?
Options: a ) 1 : 3 , b ) 9 : 13 , c ) 5 : 11 , d ) 11 : 3 , e ) 17 : 3
Rationale: "the ratio of milk and water in the new vessel is = ( 8 / 10 + 9 / 10 ) : ( 2 / 10 + 1 / 10 ) = 17 / 10 : 3 / 10 = 17 : 3 answer is e"
Answer: e
Question (general): for any integer n greater than 1 , # n denotes the product of all the integers from 1 to n , inclusive . how many prime numbers r are there between # 6 + 2 and # 6 + 6 , inclusive ?
Options: a ) none , b ) one , c ) two , d ) three , e ) four
Rationale: "none is the answer . a . because for every k 6 ! + k : : k , because 6 ! : : k , since k is between 2 and 6 . a"
Answer: a
Question (general): tickets numbered 1 to 20 are mixed up and then a ticked is drawn at random . what is the probability that the ticket drawn bears a number which is a multiple of 3 ?
Options: a ) 3 / 10 , b ) 3 / 20 , c ) 2 / 5 , d ) 1 / 2 , e ) 1 / 3
Rationale: s = { 1 , 23 , … . 20 } e = { 3 , 6 , 912 , 1518 } p ( e ) = 6 / 20 = 3 / 10 option a
Answer: a
Question (other): find the ratio between whole surfaces of a sphere and a hemisphere ?
Options: a ) 4 : 3
b ) 3 : 4
c ) 3 : 2
d ) 5 : 2
e ) 4 : 6
Rationale: 4 ï € r 2 : 3 ï € r 2 = > 4 : 3 answer a
Answer: a
Question (gain): some of 10 % - intensity red paint is replaced with 20 % solution of red paint such that the new paint intensity is 15 % . what fraction of the original paint was replaced ?
Options: a ) 2 / 5 , b ) 2 / 3 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 5
Rationale: "let total paint = 1 let amount replaced = x 10 ( 1 - x ) + 20 x = 15 x = 1 / 2 answer : c"
Answer: c