Cheukting/mathqa huggingface dataset:
Question (general): an alloy of copper and zinc contains copper and zinc in the ratio 8 : 2 . another alloy of copper and zinc contains copper and zinc in the ratio 4 : 6 . in what ratio should the two alloys be mixed so that the resultant alloy contains equal proportions of copper and zinc ?
Options: a ) 5 : 1 , b ) 4 : 1 , c ) 3 : 1 , d ) 6 : 1 , e ) 8 : 1
Rationale: "let alloy _ 1 be x units , and let alloy _ 2 be y units . so , fraction of copper in alloy _ 1 = 8 x / 10 , and fraction of zinc in alloy _ 1 = 2 x / 10 similarly , fraction of copper in alloy _ 2 = 4 y / 10 , and fraction of zinc in alloy _ 2 = 6 y / 10 . mixing them , we get copper = 8 x / 10 + 4 y / 10 ; zinc = 2 x / 10 + 6 y / 10 so , 8 x + 4 y = 2 x + 6 y - > 6 x = 2 y - > x / y = 6 / 2 = 3 / 1 so , they must be mixed in the ratio 3 : 1 answer : c"
Answer: c
Question (general): the average monthly income of p and q is rs . 5050 . the average monthly income of q and r is rs . 6250 and the average monthly income of p and r is rs . 5200 . the monthly income of p + q + r is :
Options: a ) 16100 , b ) 15700 , c ) 17500 , d ) 16000 , e ) 16500
Rationale: "explanation : let p , q and r represent their respective monthly incomes . then , we have : p + q = ( 5050 x 2 ) = 10100 . . . . ( i ) q + r = ( 6250 x 2 ) = 12500 . . . . ( ii ) p + r = ( 5200 x 2 ) = 10400 . . . . ( iii ) adding ( i ) , ( ii ) and ( iii ) , we get : 2 ( p + q + r ) = 33000 or p + q + r = 16500 . . . . ( iv ) ( p + q + r ) ' s monthly income = rs . 16500 . answer : e"
Answer: e
Question (general): if 1 / ( x + 1 ) + 1 / ( x - 1 ) = 1 / ( x - 1 ) , what is the value of x ?
Options: a ) 2 , b ) - 2 , c ) 1 , d ) - 1 , e ) 5
Rationale: if we solve the question , we get x = 1 . option : c
Answer: c
Question (general): evaluate 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 = ?
Options: a ) 3043 , b ) 5050 , c ) 5176 , d ) 9356 , e ) 4890
Rationale: b 5050 you must have noticed that 50 pairs of n ^ 2 – ( n - 1 ) ^ 2 exist . n ^ 2 – ( n - 1 ) ^ 2 = n + ( n – 1 ) in such case , we may as well write 100 ^ 2 - 99 ^ 2 + 98 ^ 2 - 97 ^ 2 + 96 ^ 2 - 95 ^ 2 + . . . + 2 ^ 2 - 1 ^ 2 as 100 + 99 + 98 + . . . + 2 + 1 = ( 100 x 101 ) / 2 = 5050
Answer: b
Question (gain): what percent of 14 is 14 percent of 1 ?
Options: a ) 0.001 , b ) 0.01 , c ) 0.1 , d ) 101 , e ) 1
Rationale: "14 % of 1 = ( 14 / 100 ) * 1 = 14 / 100 to determine what percentage of 14 this is : [ 14 ] [ / 100 * 14 ] * 100 = 1 % ans : e"
Answer: e
Question (general): the annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years r in which the population would be doubled assuming there is no emigration or immigration is
Options: a ) 20 , b ) r = 25 , c ) r = 30 , d ) r = 35 , e ) 40
Rationale: "suppose the population of the country in current year is 1000 . so annual increase is 1000 + 39.4 - 19.4 = 1020 hence every year there is an increase of 2 % . 2000 = 1000 ( 1 + ( 2 / 100 ) ) ^ n n = 35 answer is d ."
Answer: d
Question (probability): there are 15 balls in a jar . you take out 3 blue balls without putting them back inside , and now the probability of pulling out a blue ball is 1 / 3 . how many blue balls were there in the beginning ?
Options: a ) 12 . , b ) 9 . , c ) 8 . , d ) 7 . , e ) 6 .
Rationale: "7 = 3 blue balls + 12 / 3 answer : d"
Answer: d
Question (general): the average ( arithmetic mean ) of 8 numbers is 43.1 . if the sum of half of these numbers is 158.4 , what is the average of the other half ?
Options: a ) 12.8 , b ) 24.2 , c ) 46.6 , d ) 72.1 , e ) 96.8
Rationale: arithmetic mean = sum / total numbers sum = 43.1 * 8 = 344.8 sum of half of these numbers is 158.4 . so , 4 numbers sum is 158.4 . rest 4 numbers sum = 344.8 - 158.4 = 186.4 arithmetic mean of the 4 nos = 186.4 / 4 = 46.6 hence , c is the answer .
Answer: c
Question (general): 12.5 * 6.2 * 8.8 = ?
Options: a ) 352 , b ) 435 , c ) 224 , d ) 682 , e ) 742
Rationale: "d 682 ? = 12.5 * 6.2 * 8.8 = 682"
Answer: d
Question (other): if 5 and 8 are factors of 60 n , what is the minimum value of n ?
Options: a ) 2 , b ) 3 , c ) 7 , d ) 14 , e ) 56
Rationale: "60 n / 7 * 8 should be integer = > 2 * 2 * 3 * 5 * n / 5 * 2 * 2 * 2 = 3 * n / 2 must be an integer for this to be true n must multiple of 2 , thus min of n = 2 hence a"
Answer: a
Question (probability): what is the probability of getting exactly 2 heads in a single throw of four fair coins ?
Options: a ) 1 / 2 , b ) 3 / 4 , c ) 3 / 8 , d ) 3 / 16 , e ) 5 / 16
Rationale: "one possible case is hhtt . p ( hhtt ) = 1 / 2 * 1 / 2 * 1 / 2 * 1 / 2 = 1 / 16 there are 4 c 2 = 6 possible cases . p ( 2 heads ) = 6 * 1 / 16 = 3 / 8 the answer is c ."
Answer: c
Question (physics): the speed of a car increases by 2 kms after every one hour . if the distance travelling in the first one hour was 45 kms . what was the total distance traveled in 12 hours ?
Options: a ) 252 kms , b ) 152 kms , c ) 672 kms , d ) 752 kms , e ) 152 kms
Rationale: explanation : total distance travelled in 12 hours = ( 45 + 47 + 49 + . . . . . upto 12 terms ) this is an a . p with first term , a = 45 , number of terms , n = 12 , d = 2 . required distance = 12 / 2 [ 2 x 45 + { 12 - 1 ) x 2 ] = 6 ( 112 ) = 672 kms . answer : c
Answer: c
Question (general): n denotes the number obtained when n is rounded to the nearest tenth . for example 4.31 = 4.3 0.089 - 1.135 =
Options: a ) 1.05 , b ) 1.04 , c ) - 1.05 , d ) - 1.0 , e ) - 0.1
Rationale: here let the first quantity be a = > a rounded to nearest tenths = > 0.1 similarly let the second quantity be b = > b rounded to nearest tenths = > 1.1 = > a - b = 0.1 - 1.1 = - 1 hence a - b = - 1 answer : d
Answer: d
Question (general): if x , y , and z are positive real numbers such that x + y - z = 50 , y - z + x = 60 , and z - x + y = 80 , then find the z value ?
Options: a ) 10 , b ) 20 , c ) 5 , d ) 15 , e ) 25
Rationale: "x + y - z = 50 , - - - - - - 1 ) y - z + x = 60 , - - - - - - 2 ) z - x + y = 80 - - - - - - 3 ) from ( 1 ) & ( 2 ) 2 z = 10 z = 5 correct option is c"
Answer: c
Question (other): initially , the men and women in a room were in the ratio of 4 : 5 . then , 2 men entered the room and 3 women left the room . then , the number of women doubled . now there are 14 men in the room . how many w women are currently in the room ?
Options: a ) 12 , b ) 14 , c ) 15 , d ) 24 , e ) 36
Rationale: "the number of women doubled means that they have become 24 from 12 . . and we have to tell the current strength so 24 is the answer . . let the number be 4 x and 5 x . . given 4 x + 2 = 14 . . so x = 3 . . women number = 5 * 3 - 3 = 12 , then doubled = 24 . . ans d"
Answer: d
Question (general): 12.5 * 3.2 * 7.8 = ?
Options: a ) 312 , b ) 435 , c ) 224 , d ) 646 , e ) 742
Rationale: "a 312 ? = 12.5 * 3.2 * 7.8 = 312"
Answer: a
Question (general): a certain protective additive increases from 30 days to 45 days the time between required maintenance checks on an industrial vehicle . by what percent is the time between maintenance checks increased by using the additive ?
Options: a ) 25 % , b ) 33 1 / 3 % , c ) 50 % , d ) 66 2 / 3 % , e ) 75 %
Rationale: general formula for percent increase or decrease , ( percent change ) : percent = change / original ∗ 100 so , the time between maintenance checks increased by 45 − 30 / 30 ∗ 100 = 50 answer : c .
Answer: c
Question (general): an optometrist charges $ 150 per pair for soft contact lenses and $ 85 per pair for hard contact lenses . last week she sold 5 more pairs of soft lenses than hard lenses . if her total sales for pairs of contact lenses last week were $ 1,220 , what was the total number of pairs of contact lenses that she sold ?
Options: a ) 9 , b ) 13 , c ) 15 , d ) 17 , e ) 19
Rationale: "( x + 5 ) * 150 + x * 85 = 1220 = > x = 2 total lens = 2 + ( 2 + 5 ) = 9 answer a"
Answer: a
Question (physics): a bus trip of 660 miles would have taken 1 hour less if the average speed v for the trip had been greater by 5 miles per hour . what was the average speed v , in miles per hour , for the trip ?
Options: a ) 40 , b ) 45 , c ) 50 , d ) 55 , e ) 60
Rationale: "the time is the distance / speed . the time difference is 1 hour . 660 / v - 660 / ( v + 5 ) = 1 660 ( v + 5 ) - 660 v = ( v ) ( v + 5 ) 3300 = ( v ) ( v + 5 ) 55 * 60 = ( v ) ( v + 5 ) v = 55 mph the answer is d ."
Answer: d
Question (physics): a man can row downstream at 35 kmph and upstream at 25 kmph . find the speed of the man in still water and the speed of stream respectively ?
Options: a ) 35 , 3 , b ) 25 , 5 , c ) 35 , 4 , d ) 5 , 30 , e ) 30 , 5
Rationale: "let the speed of the man in still water and speed of stream be x kmph and y kmph respectively . given x + y = 35 - - - ( 1 ) and x - y = 25 - - - ( 2 ) from ( 1 ) & ( 2 ) 2 x = 60 = > x = 30 , y = 5 . answer : e"
Answer: e
Question (general): in an examination , 300 students appeared . out of these students ; 30 % got first division , 54 % got second division and the remaining just passed . assuming that no student failed ; find the number of students who just passed .
Options: a ) 33 , b ) 37 , c ) 54 , d ) 99 , e ) 48
Rationale: the number of students with first division = 30 % of 300 = 30 / 100 × 300 = 9000 / 100 = 90 and , the number of students with second division = 54 % of 300 = 54 / 100 × 300 = 16200 / 100 = 162 therefore , the number of students who just passed = 300 – ( 90 + 162 ) = 48 answer : e
Answer: e
Question (probability): if two dice are thrown together , the probability of getting an even number on one die and an odd number on the other is ?
Options: a ) 1 / 9 , b ) 1 / 2 , c ) 1 / 1 , d ) 1 / 5 , e ) 1 / 8
Rationale: "the number of exhaustive outcomes is 36 . let e be the event of getting an even number on one die and an odd number on the other . let the event of getting either both even or both odd then = 18 / 36 = 1 / 2 p ( e ) = 1 - 1 / 2 = 1 / 2 . answer : b"
Answer: b
Question (general): 5 men are equal to as many women as are equal to 8 boys . all of them earn rs . 45 only . men â € ™ s wages are ?
Options: a ) 6 rs , b ) 7 rs , c ) 8 rs , d ) 4 rs , e ) 3 rs
Rationale: "5 m = xw = 8 b 5 m + xw + 8 b - - - - - 45 rs . 5 m + 5 m + 5 m - - - - - 45 rs . 15 m - - - - - - 45 rs . = > 1 m = 3 rs . answer : e"
Answer: e
Question (physics): one pipe can fill a tank three times as fast as another pipe . if together the two pipes can fill the tank in 34 minutes , then the slower pipe alone will be able to fill the tank in
Options: a ) 144 mins , b ) 140 mins , c ) 136 mins , d ) 132 minw , e ) none of these
Rationale: "explanation : let the slower pipe alone fill the tank in x minutes then faster will fill in x / 3 minutes . part filled by slower pipe in 1 minute = 1 / x part filled by faster pipe in 1 minute = 3 / x part filled by both in 1 minute = 1 / x + 3 / x = 1 / 34 = > 4 / x = 1 / 34 x = 34 ∗ 4 = 136 mins option c"
Answer: c
Question (other): two dice are rolled . what is the probability that the sum on the top face of both the dice will be greater than 9 ?
Options: a ) 3 / 8 , b ) 2 / 3 , c ) 1 / 2 , d ) 1 / 3 , e ) 1 / 6
Rationale: total number of outcomes possible when a die is rolled = 6 ( ∵ any one face out of the 6 faces ) hence , total number of outcomes possible two dice are rolled , n ( s ) = 6 × 6 = 36 e = getting a sum greater than 9 when the two dice are rolled = { ( 4 , 6 ) , { 5 , 5 } , { 5 , 6 } , { 6 , 4 } , { 6 , 5 } , ( 6 , 6 ) } hence , n ( e ) = 6 p ( e ) = n ( e ) / n ( s ) = 6 / 36 = 1 / 6
Answer: e
Question (physics): let a be the event that a randomly selected two digit number is divisible by 3 and let b be the event that a randomly selected two digit number is divisible by 10 . what is p ( a and b ) ?
Options: a ) 1 / 30 , b ) 1 / 15 , c ) 1 / 5 , d ) 1 / 3 , e ) 1 / 2
Rationale: "p ( a and b ) = 1 / 3 * 1 / 10 = 1 / 30 the answer is a ."
Answer: a
Question (general): if x is 12 percent greater than 80 , then x =
Options: a ) 89.6 , b ) 91.0 , c ) 88.0 , d ) 70.9 , e ) 71.2
Rationale: "12 % of 80 = ( 80 * 0.12 ) = 9.6 12 % greater than 80 = 80 + 9.6 = 89.6 answer is clearly a ."
Answer: a
Question (physics): a and b complete a work in 6 days . a alone can do it in 8 days . if both together can do the work in how many days ?
Options: a ) 3.75 days , b ) 3.43 days , c ) 2.99 days , d ) 2.98 days , e ) 2.44 days
Rationale: "1 / 6 + 1 / 8 = 7 / 24 24 / 7 = 3.43 days answer : b"
Answer: b
Question (general): the avg weight of a , b & c is 84 kg . if d joins the group , the avg weight of the group becomes 80 kg . if another man e who weights is 8 kg more than d replaces a , then the avgof b , c , d & e becomes 79 kg . what is the weight of a ?
Options: a ) 25 , b ) 35 , c ) 75 , d ) 80 , e ) 90
Rationale: "a + b + c = 3 * 84 = 252 a + b + c + d = 4 * 80 = 320 - - - - ( i ) so , d = 68 & e = 68 + 8 = 76 b + c + d + e = 79 * 4 = 316 - - - ( ii ) from eq . ( i ) & ( ii ) a - e = 320 â € “ 316 = 4 a = e + 4 = 76 + 4 = 80 d"
Answer: d
Question (other): 130 kg of an alloy a is mixed with 160 kg of alloy b . if alloy a has lead and tin in the ratio 2 : 3 and alloy b has tin and copper in the ratio 3 : 4 , then the amount of tin in the new alloy is ?
Options: a ) 140.6 kg , b ) 145.3 kg , c ) 146.5 kg , d ) 110.8 kg , e ) 114 kg
Rationale: "quantity of tin in 130 kg of a = 130 * 3 / 5 = 78 kg quantity of tin in 160 kg of b = 160 * 3 / 7 = 68.5 kg quantity of tin in the new alloy = 78 + 68.5 = 146.5 kg answer is c"
Answer: c
Question (gain): if each side of a square is increased by 325 % in length , find the percentage change in its area ?
Options: a ) 54 % , b ) 957 % , c ) 956.25 % , d ) 958.25 % , e ) 959.50 %
Rationale: "let each side of the square be a , then area = a x a new side = 325 a / 100 = 13 a / 4 new area = ( 13 a x 13 a ) / ( 4 x 4 ) = ( 25 a ² / 16 ) increased area = = ( 169 a ² / 16 ) - a ² increase % = [ ( 153 a ² / 16 ) x ( 1 / a ² ) x 100 ] % = 956.25 % answer : c"
Answer: c
Question (gain): martin bought 10 concert tickets , some at the full price of $ 2.00 per ticket , and some at a discounted price of $ 1.60 per ticket . if he spent a total of $ 18.80 , how many discounted tickets did he buy ?
Options: a ) 3 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "let x be the number of tickets he bought at $ 2 per ticket . then 2 x + ( 10 - x ) 1.6 = 18.8 0.4 x = 2.8 = > x = 7 discounted tickets = 10 - x = 3 ans : a"
Answer: a
Question (physics): a can do a piece of work in 10 days and b can do it in 15 days and c can do it 20 days . they started the work together and a leaves after 5 days and b leaves after 3 days from the beginning . how long will work lost ?
Options: a ) 2 , b ) 4 , c ) 5 , d ) 6 , e ) 7
Rationale: "5 / 10 + 3 / 15 + x / 20 = 1 x = 18 / 3 = 6 answer : d"
Answer: d
Question (general): at the end of year x , automobile installment credit accounted for 35 % of all outstanding consumer installment credit . at that time automobile finance companies extended $ 40 billion of credit , or 1 / 3 of the automobile installment credit . how many billion dollars of consumer installment credit was outstanding at that time ?
Options: a ) 120 , b ) 300 , c ) 401.36 , d ) 350.15 , e ) 342.86
Rationale: "system of equations a = ( 35 / 100 ) c ( 1 / 3 ) a = 40 - - > a = 120 substitution 120 = ( 35 / 100 ) c c = ( 100 / 35 ) 120 answer - 120 / 35 * 100 the correct answer is e . - 342.86"
Answer: e
Question (other): two numbers are in the ratio 3 : 5 . if 9 be subtracted from each , they are in the ratio of 2 : 3 . the first number is :
Options: a ) a ) 27 , b ) b ) 98 , c ) c ) 34 , d ) d ) 35 , e ) e ) 62
Rationale: "( 3 x - 9 ) : ( 5 x - 9 ) = 2 : 3 x = 9 = > 3 x = 27 answer : a"
Answer: a
Question (physics): the length of the bridge , which a train 130 metres long and travelling at 54 km / hr can cross in 30 seconds , is :
Options: a ) 200 m , b ) 225 m , c ) 320 m , d ) 250 m , e ) 240 m
Rationale: "speed = [ 54 x 5 / 18 ] m / sec = [ 15 / 1 ] m / sec time = 30 sec let the length of bridge be x metres . then , ( 130 + x ) / 30 = 15 = > ( 130 + x ) = 450 = > x = 450 - 130 = 320 m answer : c"
Answer: c
Question (general): two kinds of vodka are mixed in the ratio 1 : 2 and 2 : 1 and they are sold fetching the profit 10 % and 40 % respectively . if the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4 / 3 and 5 / 3 times respectively , then the mixture will fetch the profit of
Options: a ) 18 % , b ) 20 % , c ) 21 % , d ) 40 % , e ) can not be determined
Rationale: answer : d .
Answer: d
Question (general): what is 3 2 / 3 - 2 1 / 4 divided by 6 / 7 - 2 / 5 ?
Options: a ) 17 / 36 , b ) 36 / 17 , c ) 17 / 64 , d ) 15 / 4 , e ) 14 / 4
Rationale: "3 2 / 3 - 2 1 / 4 = 11 / 3 - 9 / 4 = ( 44 - 27 ) / 12 = 17 / 12 6 / 7 - 2 / 5 = ( 30 - 14 ) / 35 = 16 / 35 so 17 / 12 / 16 / 3 = 17 / 12 * 3 / 16 = 17 / 64 answer - c"
Answer: c
Question (general): the sum of the ages of 5 children born at the intervals of 3 year each is 50 year . what is the age of the youngest child ?
Options: a ) 4 year , b ) 8 year , c ) 10 year , d ) none of these , e ) 9 year
Rationale: "solution let the ages of the children be x , ( x + 3 ) , ( x + 6 ) , ( x + 9 ) and ( x + 12 ) year . then , x + ( x + 3 ) + ( x + 6 ) + ( x + 9 ) + ( x + 12 ) = 50 ⇔ 5 x = 20 ⇔ x = 4 . ∴ age of the youngest child = x = 4 years . answer a"
Answer: a
Question (other): sara bought both german chocolate and swiss chocolate for some cakes she was baking . the swiss chocolate cost $ 2.5 per pound , and german chocolate cost $ 1.5 per pound . if the total the she spent on chocolate was $ 30 and both types of chocolate were purchased in whole number of pounds , how many total pounds of chocolate she purchased ?
Options: a ) 7 , b ) 18 , c ) 10 , d ) 12 , e ) 11
Rationale: "if there were all the expensive ones 2.5 . . . . there would be 30 / 2.5 or 12 of them but since 1.5 $ ones are also there , answer has to be > 12 . . . . if all were 1.5 $ ones , there will be 30 / 1.5 or 20 . . . so only 18 is left ans b . ."
Answer: b
Question (general): the total age of a and b is 16 years more than the total age of b and c . c is how many year younger than
Options: a ) 14 years , b ) 12 years , c ) 56 years , d ) 16 years , e ) 55 years
Rationale: "given that a + b = 16 + b + c = > a â € “ c = 16 + b â € “ b = 16 = > c is younger than a by 16 years answer : d"
Answer: d
Question (geometry): the area of sector of a circle whose radius is 12 metro and whose angle at the center is 30 ° is ?
Options: a ) 35 m 2
b ) 36 m 2
c ) 37 m 2
d ) 38 m 2
e ) 40 m 2
Rationale: 30 / 360 * 22 / 7 * 12 * 12 = 37 m 2 answer : c
Answer: c
Question (general): find large number from below question the difference of two numbers is 1360 . on dividing the larger number by the smaller , we get 6 as quotient and the 15 as remainder
Options: a ) 1254 , b ) 1376 , c ) 1456 , d ) 1555 , e ) 1629
Rationale: "let the smaller number be x . then larger number = ( x + 1360 ) . x + 1360 = 6 x + 15 5 x = 1345 x = 269 large number = 269 + 1360 = 1629 e"
Answer: e
Question (general): solve the equation 2 – x = 2 b – 2 ax , where a and b are real parameters . find for which values of a the equation has for solution a natural number , if b = 7
Options: a ) 0 , b ) 1 , c ) 2 , d ) 3 , e ) 4
Rationale: solution : we write the given equation like this ( 2 a - 1 ) x = 2 ( b - 1 ) the following cases are possible : if 2 a - 1 ≠ 0 , i . e . a ≠ 1 / 2 , the equation has single solution x = 2 ( b - 1 ) / ( 2 a - 1 ) if a = 1 / 2 and b = 1 , the equation gets the kind 0 . x = 0 and every x is solution if a = 1 / 2 and b ≠ 1 , we get 0 . x = 2 ( b - 1 ) , where 2 ( b - 1 ) ≠ 0 in this case the equation has no solution . if b = 7 and a ≠ 1 / 2 the single solution is x = 2 ( 7 - 1 ) / ( 2 a - 1 ) = 12 / ( 2 a - 1 ) if a is whole number , then 2 a - 1 is also whole number and the solution x = 12 / ( 2 a - 1 ) is natural number when 2 a - 1 is positive divisor of 12 . to have a as whole number , the divisor of 12 mu be odd . but the only whole positive odd numbers divisible by 12 are 1 and 3 . therefore 2 a - 1 = 3 < = > a = 2 or 2 a - 1 = 1 < = > a = 1 a = 2 or 2 a - 1 = 1 < = > a = 1 answer b
Answer: b
Question (general): in a caravan , in addition to 50 hens there are 45 goats and 8 camels with some keepers . if the total number of feet be 224 more than the number of heads , find the number of keepers .
Options: a ) 25 , b ) 20 , c ) 15 , d ) 13 , e ) 14
Rationale: let the number of keepers be x then , total number of heads = ( 50 + 45 + 8 + x ) = ( 103 + x ) . total number of feet = ( 45 + 8 ) x 4 + ( 50 + x ) x 2 = ( 312 + 2 x ) . ( 312 + 2 x ) - ( 103 + x ) = 224 = = > x = 15 . hence , number of keepers = 15 . answer c .
Answer: c
Question (physics): a motorcyclist goes from bombay to pune , a distance of 160 kms at an average of 32 kmph speed . another man starts from bombay by car 2 ½ hours after the first , and reaches pune ½ hour earlier . what is the ratio of the speed of the motorcycle and the car ?
Options: a ) 1 : 2 , b ) 2 : 5 , c ) 1 : 4 , d ) 1 : 1 , e ) 1 : 6
Rationale: "t = 160 / 32 = 5 h t = 5 - 3 = 2 time ratio = 5 : 2 = 5 : 2 speed ratio = 2 : 5 answer : b"
Answer: b
Question (geometry): what will be the percentage increase in the area of the cube ' s surface if each of the cube ' s edges grows by 40 % ?
Options: a ) 95 % , b ) 90 % , c ) 85 % , d ) 96 % , e ) 25 %
Rationale: "the question is very easy . my logic is the following : a surface = 6 * a ^ 2 after 40 % increase a surface = 6 * ( ( 1.4 a ) ^ 2 ) = 6 * 1.96 * a ^ 2 the increase in the surface area = ( 6 * 1.96 * a ^ 2 - 6 * a ^ 2 ) / 6 * a ^ 2 = ( 6 * a ^ 2 ( 1.96 - 1 ) ) / ( 6 * a ^ 2 ) = 1.96 - 1 = 0.96 = 96 % answer : d"
Answer: d
Question (physics): how many shots of 1 cm radius can be prepared from a sphere of 5 cm radius ?
Options: a ) 33 , b ) 88 , c ) 27 , d ) 125 , e ) 199
Rationale: 4 / 3 ï € * 5 * 5 * 5 = 4 / 3 ï € * 1 * 1 * 1 * x x = 125 answer : d
Answer: d
Question (general): in a village there are 150 men and 90 women in present time . if in next year population will be p = ( a ^ 2 + b ^ 2 ) ^ 1 / 2 , and in every year men are reduces 10 % . what is population of after 2 year .
Options: a ) 140 , b ) 141 , c ) 142 , d ) 143 , e ) 144
Rationale: next year total population = [ 150 ^ 2 + 90 ^ 2 ] ^ . 5 = 174.92 = 175 man decreased by 10 % so total man = 150 * . 9 = 135 women will be = 175 - 135 = 40 so population after two years = [ 135 ^ 2 + 40 ^ 2 ] ^ . 5 = 140.80 = 141 so population after two year = 141 answer : b
Answer: b
Question (physics): a train 124 m long running at 68 kmph crosses a platform in 19 sec . what is the length of the platform ?
Options: a ) 338 , b ) 234 , c ) 240 , d ) 881 , e ) 271
Rationale: "d = 68 * 5 / 18 = 19 = 358 – 124 = 234 answer : b"
Answer: b
Question (other): the hcf of two numbers is 42 and the other two factors of their lcm are 11 and 12 . what is the largest number .
Options: a ) 462 , b ) 450 , c ) 480 , d ) 504 , e ) 555
Rationale: "explanation : hcf of the two numbers = 42 hcf will be always a factor of lcm 42 is factor of lcm other two factors are 11 & 12 then the numbers are ( 42 11 ) and ( 42 x 12 ) = 462 and 504 answer : option d"
Answer: d
Question (general): given f ( x ) = 3 x – 5 , for what value of x does 2 * [ f ( x ) ] + 8 = f ( 3 x – 6 )
Options: a ) 0 , b ) 4 , c ) 6 , d ) 7 , e ) 13
Rationale: "answer = d = 7 f ( x ) = 3 x – 5 2 * [ f ( x ) ] + 8 = f ( 3 x – 6 ) 2 ( 3 x - 5 ) + 8 = 3 ( 3 x - 6 ) - 5 6 x - 2 = 9 x - 23 x = 7"
Answer: d
Question (physics): sheila works 8 hours per day on monday , wednesday and friday , and 6 hours per day on tuesday and thursday . she does not work on saturday and sunday . she earns $ 468 per week . how much does she earn in dollars per hour ?
Options: a ) 2 , b ) 8 , c ) 9 , d ) 11 , e ) 13
Rationale: "explanation : total hours worked = 8 x 3 + 6 x 2 = 36 total earned = 468 . hourly wage = 468 / 36 = 13 answer : e"
Answer: e
Question (gain): a trader bought a car at 20 % discount on its original price . he sold it at a 50 % increase on the price he bought it . what percent of profit did he make on the original price ?
Options: a ) 17 % , b ) 72 % , c ) 20 % , d ) 82 % , e ) 16 %
Rationale: "original price = 100 cp = 80 s = 80 * ( 150 / 100 ) = 120 100 - 120 = 20 % answer : c"
Answer: c