mathewhe/aqua_rat huggingface dataset:
Question: Two boys starting from the same place walk at a rate of 5kmph and 5.5kmph respectively. What time will they take to be 9km apart, if they walk in the same direction?
(A) 15 hours
(B) 16 hours
(C) 17 hours
(D) 18 hours
(E) 19 hours
Rationale: The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 9 km
Time = Distance/Speed
Time= 9km / 0.5 kmph = 18 hrs
answer :D
Answer: (D) 18 hours
Question: X can finish a work in 15 days. Y can finish the same work in 20 days. Y worked for 12 days and left the job. how many days does X alone need to finish the remaining work?
(A) 5
(B) 3
(C) 4
(D) 7
(E) 8
Rationale: Work done by X in 1 day = 1/15
Work done by Y in 1 day = 1/20
Work done by Y in 12 days = 12/20 = 3/5
Remaining work = 1 – 3/5 = 2/5
Number of days in which X can finish the remaining work = (1/3) / (1/15) = 5
A
Answer: (A) 5
Question: solve the given equation 9^y = 3^12, what is y?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 3^2y = 3^12
2y=12, therefore y=6
E
Answer: (E) 6
Question: 100 identical coins each with probability "p" showing up heads & tossed. If 0 then show the number of heads?
(A) 33/100
(B) 41/101
(C) 51/101
(D) 87/101
(E) 98/101
Rationale: Let aa be the number of coins showing heads
Then, P(A=50)=P(A=51)P(A=50)=P(A=51)
⇒100C50×P50×(1−P)50⇒100C51×P51×(1−P)49⇒100C50×P51×(1−P)50=100C51×P⇒51(1âˆ′P)=50P⇒P=51/101
C
Answer: (C) 51/101
Question: Abby, Brandon, Cedric, and Deirdre are planning to attend a concert. If their friend Kim also goes with them, they will get a group discount on their tickets. If the total price of the tickets with the group discount is the same as the total price of the tickets without the group discount, how much is the discount?
(A) 5%
(B) 10%
(C) 20%
(D) 25%
(E) 33%
Rationale: Let A,B,C and D individual tickets be X and total tickets is 4X..
Now with Kelly they get a discount , total tickets here is 5x.
We are told that group discount is same as total price without discount..
When we need to solve 5X till we get 4X..
Take options..5X - 5%(5X) = 5x - (0.05)(5X) = 5x - 0.25X = 4.75X...not same as 4X..
(B) 5X - 10% of 5x => 5x - (0.1)(5x) = 4.5X, which is again not equal to 4x. So, this is not the correct option.
(C) 5X - 20% of 5x => 5x - (0.2)(5x) = 4X, this is same as 4X...no need to do other options..
Answer: option C is correct answer.
Answer: (C) 20%
Question: Simran started a software business by investing Rs. 50,000. After six months, Nanda joined her with a capital of Rs. 80,000. After 3 years, they earned a profit of Rs. 5600. What was Simran share in the profit?
(A) s 9500
(B) s 2400
(C) s 10500
(D) s 11000
(E) s 1400
Rationale: Simran : Nanda = (50000 x 36) : (80000 x 30) = 3 : 4.
Simran's share = Rs. 5600 x	3/7	= Rs. 2,400
ANSWER :B
Answer: (B) s 2400
Question: What is the area of a square field whose diagonal of length 28 m?
(A) 288
(B) 289
(C) 200
(D) 112
(E) 392
Rationale: d2/2 = (28 * 28)/2
= 392
Answer: E
Answer: (E) 392
Question: The second of two numbers is two less than three times the first. Find the numbers if there sum is
26.
(A) 7-19
(B) 8-20
(C) 10-16
(D) 15-9
(E) 20-6
Rationale: We are looking for two numbers.
#1 - x
#2 - 3x – 2
The sum is 26. #1 + #2 = 26
Substituting x + 3x – 2 = 26
4x – 2 = 26
4x = 28
x = 7
The first number is 7, the second number is two less than three times 7 or 19.
correct answer A
Answer: (A) 7-19
Question: A money lender lent a total of $1600 to two of his customers. He charged at the rate of 5%p.a. to one of them and 6% p.a. to the other. If he earned an average of 5.67% on $1600, how much did he lend to each of the two customers?
(A) 700; 1100
(B) 1072; 528
(C) 1000; 800
(D) 1200; 800
(E) None of the above
Rationale: The method given above is the one given in the book.
However the method I used was
(1*x*5)/100 + (1600-x)*6/100 = 1600*5.67/100
Simplifying we get x= 528
B
Answer: (B) 1072; 528
Question: In a certain neighborhood, there are half as many beige houses as white houses, and six times as many white houses as brown houses. What is the ratio of the number of brown houses to the number of beige houses?
(A) 1:3
(B) 1:9
(C) 2:5
(D) 5:3
(E) 6:1
Rationale: The ratio of beige:white:brown = 3:6:1
The answer is A.
Answer: (A) 1:3
Question: A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 260 m long?
(A) 34 Seconds
(B) 22 Seconds
(C) 41 Seconds
(D) 24 Seconds
(E) 29 Seconds
Rationale: D
24 Seconds
Distance travelled = 140 + 260m = 400m
Speed = 60 * 5/8 = 50/3m
Time = 400 * 3/50 = 24 Seconds
Answer: (D) 24 Seconds
Question: Machine P and Machine Q are each used to manufacture 440 sprockets. It takes Machine P 10 hours longer to produce 440 sprockets than Machine Q. Machine Q produces 10% more sprockets per hour than Machine A. How many sprockets per hour does Machine A produce?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: P makes x sprockets per hour.
Then Q makes 1.1x sprockets per hour.
440/x = 440/1.1x + 10
1.1(440) = 440 + 11x
11x = 44
x = 4
The answer is B.
Answer: (B) 4
Question: A fruit vendor purchased 20 dozens of bananas at Rs. 15 per dozen. But one-fourth of the bananas were rotten and had to be thrown away. He sold two-third of the remaining bananas at Rs. 22.50 per dozen. At what price per dozen should he sell the remaining bananas to make neither a profit nor a loss?
(A) 17
(B) 15
(C) 11
(D) 16
(E) 12
Rationale: CP of 20 dozen of bananas = 15 * 20 = Rs. 300
Number of bananas which are rotten = 1/4 * 20 = 5 dozen.
SP of two-third of remaining bananas = (2/3 * 15) * 22.5 = Rs. 225
SP of remaining 5 dozens of bananas to make no profit and no loss =(300 - 225) = Rs. 75.
SP of 1 dozen bananas = 75/5 = Rs. 15.
Answer: B
Answer: (B) 15
Question: Lake A has a duck population of 30 females and 36 males. Lake B’s duck population consists of the same ratio of females to males. If 4 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?
(A) 144
(B) 105
(C) 78
(D) 75
(E) 36
Rationale: Lake A has a duck population of 30 females and 36 males --> the ratio is F:M = 30:36 = 5:6.
Lake B’s duck population consists of the same ratio of females to males --> F:M = 5:6.
D
Answer: (D) 75
Question: In how many ways Chief Minister and Minister be elected froma team of 12 members?
(A) 120
(B) 124
(C) 132
(D) 135
(E) 139
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: (C) 132
Question: When positive integer x is divided by positive integer y, the result is 59.32. What is the sum R of all possible 2-digit remainders for x/y?
(A) 560
(B) 616
(C) 672
(D) 728
(E) 784
Rationale: ans B 616...
remainders = .32=32/100=8/25=16/50 and so on..
so two digit remainders are 16+24+32+....+96..
R=8(2+3+4....+12)=616.B
Answer: (B) 616
Question: An amount of money was lent for 3 years. What will be the difference between the simple and the compound interest earned on it at the same rate?
I.	The rate of interest was 8 p.c.p.a.
II.	The total amount of simple interest was Rs. 1200.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: EXPLANATION
Given: T = 3 years.
I. gives: R = 8% p.a.
II. gives: S.I. = Rs. 1200.
Thus, P = Rs. 5000, R = 8% p.a. and T = 3 years.
Difference between C.I. and S.I. may be obtained.
answer is (E).
Answer: (E) Both I and II are necessary to answer
Question: When positive integer v is multiplied by positive integer n, the units digit of the product is 3. Which of the following are factors of n?
I. 8
II. 15
III. 30
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) None of the above
Rationale: ans E..
we can tell the ans w/o using examples..
the units digit of product v*n is 3..
this means v and n are odd positive integers..
therefore n cannot have an even factor so 8 and 30 are out..
n cannot have a factor ending in 5 because in that case the units digit has to be 5 or 0... so 15 is also out
Answer: (E) None of the above
Question: A certain store sold pens for $0.35 each and pencils for $0.25 each. If a customer purchased both pens and pencils from the store for a total of $1.60, what total number of pens and pencils did the customer purchase?
(A) 6
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Answer: Algebraically, the question looks like this: 2.5 = 0.35x + 0.25y. There are six possible numbers of pencils that fit that requirement:
1 pen: $0.35 and 5 pencils for $0.25 each. That's 1 pens and 5 pencils for a total of 6 pens and pencils. Choice (A) is correct.
Answer: (A) 6
Question: In the formula A = 22/7*b^2, if b is halved, then A is multiplied by
(A) 4
(B) 1/8
(C) 1/4
(D) 8
(E) 1/2
Rationale: Say b=2 => A1 = 88/7
when r=1; A2 = 22/7
A2 = 1/4*A1.
Answer : C
Answer: (C) 1/4
Question: From a pack of 52 cards, one card is drawn at random. Find the probability that the drawn card is a club or a jack?
(A) 17/52
(B) 8/13
(C) 4/13
(D) 1/13
(E) 2/13
Rationale: Solution:
n(S) = 52
n(E) = 16
P(E) = n(E) / n(S) = 16/ 52
= 4/13
ANSWER IS C
Answer: (C) 4/13
Question: If the price of an article went up by 40%, then by what percent should it be brought down to bring it back to its original price?
(A) 16 2/3%
(B) 16 4/3%
(C) 16 7/3%
(D) 16 6/3%
(E) 28 4/7%
Rationale: Let the price of the article be Rs. 100.
40% of 100 = 40.
New price
= 100 + 40 = Rs. 140
Required percentage
= (140 - 100)/140 * 100
= 40/140 * 100
= 200/7
= 28 4/7%.
Answer:E
Answer: (E) 28 4/7%
Question: Running at the same constant rate,6 identical machines can produce a total of 270 bottles per minute.At this rate,how many bottles could 10 such machines produce in 4 minutes ?
(A) 648
(B) 1800
(C) 2700
(D) 10800
(E) None of these
Rationale: Solution
Let the required number of bottles be x.
More machines,More bottles (Direct Proportion)
More minutes,More bottles (Direct Proportion)
∴ 6 × 1 × x = 10 × 4 × 270 ⇔ x = 10x4x270/6= 1800 . Answer B
Answer: (B) 1800
Question: The sum of the fourth and twelfth term of an arithmetic progression is 20. What is the sum of the first 12 terms of the arithmetic progression?
(A) 300
(B) 120
(C) 150
(D) 170
(E) 270
Rationale: n th term of A.P. is given by a+(n-1)d
4 th term = a+3d
12 th term = a+11d
Given a+3d+a+11d=20 --> 2a+14d=20 --> a+7d = 10
Sum of n term of A.P = n/2[2a+(n-1)d]
subsitiuing n = 12 ...we get 12/2[ 2a + 14d] = 15 [a+7d] = 12*10 = 120...
Answer is B...
Answer: (B) 120
Question: In a practice paper at 2iim.com, questions were given from 5 topics. Out of the appearing students, 10% passed in all topics while 10% did not pass in any. Of the remaining, 20% passed in one topic only and 25% in two topics only. If 24% of the total students passed 4 topics only and 500 students passed in 3 topics only, find the total number of students who appeared in the examination?
(A) 2500
(B) 2000
(C) 1600
(D) 4545
(E) 6565
Rationale: DETAILED SOLUTION
Let the number of appearing students be 100.
Pass only in 0 topic – 10
1 – 16 (20% of 80)
2 – 20 (25% of 80)
3 – 20% (100 – (16+20+24+20))
4 – 24%
5 – 20%
Therefore, 20% of x = 500 = ) x = 2500
Correct Answer: A
Answer: (A) 2500
Question: In the junior basketball league there are 18 teams, 2/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad?
(A) 4.
(B) 6.
(C) 7.
(D) 8.
(E) 10
Rationale: otal teams =18
bad teams=(2/3)*18=12
rich teams=9
so maximum value that the both rich and bad can take will be 9. so E= 10 can not be that value.
ANSWER:E
Answer: (E) 10
Question: A money lender lends Rs.2500 for six months at 20% p.a. rate. It the interest is reckoned quarterly than find the amount given after time limit?
(A) 2205
(B) 1978
(C) 2834
(D) 2827
(E) 2756.25
Rationale: A = 2500(21/20)2
= 2756.25
Answer: E
Answer: (E) 2756.25
Question: If a, b, c and g are non-zero integers, 3 ≥ c ≥ – 9 , 5 ≥ a ≥ –2 , 10 ≥b ≥ –1 , 4 ≥ g ≥ 1, then which of the following expresses the smallest possible value of ag/(bc)?
(A) –90
(B) –20
(C) –10
(D) 1/90
(E) 15/4
Rationale: ag have to be greatest from its range && bc to be smallest with -ve sign to became ag/bc smallest
A)-90 never possible case.(all nos. are integers and ag has max. 20 value)
B)-20 a=5,b=4 and b=1,c=-1 then it is possible
Option C,D,E are > -20....
Ans B
Answer: (B) –20
Question: The value of (4x10^7)(7x10^8) is closest to which of the following?
(A) 10^15
(B) 10^12
(C) 10^13
(D) 10^14
(E) 10^17
Rationale: multiplying these we get,
28 x 10^7 x 10^8
= 2.8x 10^16
which is closer to 10^17
Answer: E
Answer: (E) 10^17
Question: The area of the floor of a room is 20 m2 that of a longer wall 15 m2 and of the shorter wall 12 m2, find the edge of the new cube?
(A) 450 m3
(B) 100 m2
(C) 60 m3
(D) 400 m3
(E) 500 m3
Rationale: lb = 20 ; lh = 15 ; fh = 12
(lbh)2 = 20 * 15 * 12 => lbh = 60 m3
ANSWER:C
Answer: (C) 60 m3
Question: Two men Amar and Bhuvan have the ratio of their monthly incomes as 6 : 5. The ratio of their monthly expenditures is 3 : 2. If Bhuvan saves one-fourth of his income, find the ratio of their monthly savings?
(A) 3 : 5
(B) 3 : 10
(C) 3 : 8
(D) 1 : 2
(E) 2:1
Rationale: Let the monthly incomes of Amar and Bhuvan be 6x and 5x respectively.
Let the monthly expenditure of Amar and Bhuvan be 3y and 2y respectively.
Savings of Bhuvan every month = 1/4(5x)
= (His income) - (His expenditure) = 5x - 2y.
=> 5x = 20x - 8y => y = 15x/8.
Ratio of savings of Amar and Bhuvan
= 6x - 3y : 1/4(5x) = 6x - 3(15x/8) : 5x/4 = 3x/8 : 5x/4
= 3 : 10.
ANSWER:B
Answer: (B) 3 : 10
Question: Griffin has a bag of marbles that contains 6 black marbles and 6 red marbles. If he removes 3 marbles at random without replacing any of the marbles, what is the probability that all 3 marbles selected will be red?
(A) 1/11
(B) 2/33
(C) 3/44
(D) 4/55
(E) 5/66
Rationale: P(3 red marbles) = 6/12*5/11*4/10 = 1/11
The answer is A.
Answer: (A) 1/11
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
(A) 5 : 6
(B) 3 : 4
(C) 7 : 8
(D) 8 : 9
(E) None of these
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
ANSWER:C
Answer: (C) 7 : 8
Question: In the class of 40 students, 30 speak Tamil and 20 speak Telugu. What is the lowest possible number of students who
speak both the languages?
(A) 8
(B) 10
(C) 20
(D) 30
(E) 32
Rationale: let the student who speaks hindi-x
let the student who speaks english-y
as (xuy)-(xny)=total
30+20-(xny)=40
=10
B)
Answer: (B) 10
Question: 24 oz of juice P and 25 oz of juice W are mixed to make smothies X and Y . The ratio of p to W in smothie X is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie X?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Easy way to solve this question is start from the answer and then conform the information provided in the question.
we can start from option D i.e 20 ... as a quantity of juice P in X because it is the only one option that gets divided by 4 is 20 ... since in the X the juice P to W ratio is 4:1
this gives us that quantity of juice P in X = 20 therefore quantity of Juice W will be 5 ... hence ratio = 4:1
This will lead to quantity of juice P in X = 4 and quantity of Juice W = 20 ... hence ratio 1:5
if we calculate total Juice P = 24 and total of juice W = 25
it fits because totals are same as what mentioned in the question ...
thus ans is D
Answer: (D) 20
Question: The Carson family will purchase three used cars. There are two models of cars available, Model A and Model B, each of which is available in eight colors: blue, black, red, and green. How many different combinations of three cars can the Carsons select if all the cars are to be different colors?
(A) 24
(B) 32
(C) 48
(D) 60
(E) 321
Rationale: I have no idea how you got 8C8, 7C6 and 4C1.
I could have understood 8C1*6C1*4C1 (I have explained why this doesn't work in the post above)
The best way to solve it is by first selecting 3 colors out of the given 4 in 4C3 ways. (say, you got black, red and green)
Now for each color, you have 2 choices - model A or B
So you select a model in 2 ways.
No of ways of selecting the 3 cars = 6C3 * 2 * 2 * 2 = 321
Well, my logic was
The number of ways of selecting r objects from n different objects is nCr.
We have 8 options and can select either of the 8 as the first - 8C8
One car is gone and one becomes a forbidden choice so we have 7 options and need to select either of the 6 as the first - 7C6
Two cars are gone and two becomes a forbidden choice so we have 6 options and need to select either of the 4 as the first - 6C4
E
Answer: (E) 321
Question: A bag contains an equal number of one rupee, 50 paise and 25 paise coins respectively. If the total value is 35, how many coins of each type are there?
(A) 20 coins
(B) 30 coins
(C) 28 coins
(D) 25 coins
(E) None of these
Rationale: Let number of each type of coin = x. Then,
1 × x + .50 × x + .25x = 35
⇒ 1.75x = 35 ⇒ x = 20 coins
Answer A
Answer: (A) 20 coins
Question: In the youth summer village there are 125 people, 50 of them are not working, 25 of them have families and 75 of them like to sing in the shower. What is the largest possible number of people in the village, which are working, that don't have families and that are singing in the shower?
(A) 75
(B) 80
(C) 85
(D) 100
(E) 90
Rationale: total =125
not working =50
having family=25
like to sing in shower = 75
working=125-50=75
not having family = 125-25=100
like to sing in shower = 100
largest possible number is the lowest possible among the above
Thus 75
A
Answer: (A) 75
Question: Average of five consecutive even numbers is 35. Find the greatest number in these five numbers?
(A) 37
(B) 38
(C) 39
(D) 41
(E) 42
Rationale: 39
Option 'C'
Answer: (C) 39
Question: The compound interest accrued on an amount of Rs.44000 at the end of two years is Rs.1193.60. What would be the simple interest accrued on the same amount at the same rate in the same period?
(A) Rs.10,840
(B) Rs.10,720
(C) Rs.10,560
(D) Rs.10,280
(E) None of these.
Rationale: Let the rate of interest be R% p.a.
4400{[1 + R/100]2 - 1} = 11193.60
[1 + R/100]2 = (44000 + 11193.60)/44000
[1 + R/100]2 = 1 + 2544/1000 = 1 + 159/625
[1 + R/100]2 = 784/625 = (28/25)2
1 + R/100 = 28/25
R/100 = 3/25
Therefore R = 12 SI on Rs.44000 at 12% p.a. for two years = 44000(2)(12)/100
=Rs.10560
ANSWER:C
Answer: (C) Rs.10,560
Question: How many perfect squares are divisors of the product (1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!)?
(A) 504
(B) 672
(C) 864
(D) 936
(E) 1008
Rationale: N=(1!)(2!)(3!)(4!)(5!)(6!)(7!)(8!)(9!)
1!=1
2!=1*2
3!=1*2*3
4!=1*2*3*4
5!=1*2*3*4*5
6!=1*2*3*4*5*6
7!=1*2*3*4*5*6*7
8!=1*2*3*4*5*6*7*8
9!=1*2*3*4*5*6*7*8*9
N=(2^8)(3^7)(4^6)(5^5)(6^4)(7^3)(8^2)(9^1)
=(2^30)(3^13)(5^5)(7^3)
To find the number of perfect squares each exponent in the prime factorization must be even .
Comparing to the form (2^p)(3^q)(5^r)(7^s).
In this case,
p can take values from 0 to 30
q can take values from 0 to 13
r can take values from 0 to 5
s can take values from 0 to 3
Number of even exponents
p=16
q=7
r=3
s=2
Number of perfect squares= 16*7*3*2 = 672
Answer B
Answer: (B) 672
Question: In a dance competition the points in each round for the first,second,third and fourth position were 100,50,20,10 . No other points were given. Ashita participated in several rounds in the competition and the product of her score was 50000. In How many rounds did she participate?
(A) 3
(B) 2
(C) 1
(D) 5
(E) Cannot be determined
Rationale: Correct answer is E because we are given that there won't be any points awarded for rounds other than 1st four position.
Thus, it may happen that she played 15 rounds out of only 5 rounds were there in which she was awarded some points.
Answer: (E) Cannot be determined
Question: A rectangular tiled patio is composed of 48 square tiles. The rectangular patio will be rearranged so that there will be 2 fewer columns of tiles and 4 more rows of tiles. After the change in layout, the patio will still have 48 tiles, and it will still be rectangular. How many rows are in the tile patio before the change in layout?
(A) 5
(B) 6
(C) 10
(D) 13
(E) 28
Rationale: Suppose there are c columns and there are r rows
Original Situation
So, Number of tiles = c*r = 48
Also. Reach column has r tiles and each row has c tiles
New Situation
Number of tiles in each column is r-2 and number of tiles in each row is c+4
So, number of rows = r-2 and number of columns is c+4
So, Number of tiles = (r-2)*(c+4) = 48
Comparing both of them we get
c*r = (r-2)*(c+4)
=> 4r -2c = 8
c = 2r - 4
Putting it in c*r=48
(2r-4)*r = 48
2r^2 - 4r - 48=0
r cannot be negative so r = 6
and c = 8
So, Answer will be B
Answer: (B) 6
Question: 7 people, A, B, C, D, E, F and H, go to a movie and sit next to each other in 8 adjacent seats in the front row of the theatre. In how many different arrangements will there be at least one person between A and F?
(A) 8! - 7!2
(B) 5! - 7!2
(C) 6! - 7!2
(D) 8! - 6!2
(E) 8! - 9!2
Rationale: We need to find at least one person between A and F which is equal to Total ways - No one between A and F
Eight people can be arranged in 8! ways.
No one between A and F is equal to 7!*2! (consider A and F as one. 7 people can be arranged in 7! and A and F in 2!)
So, total ways = 8! - 7!2
ANS:A
Answer: (A) 8! - 7!2
Question: A man and a boy complete a work together in 24 days. If for the last 6 days man alone does the work then it is completed in 26 days. How long the boy will take to complete the work alone?
(A) 72 days
(B) 20 days
(C) 24 days
(D) 36 days
(E) 34 days
Rationale: Explanation:
(man + boy)’s 1 day’s work = 1/24
Their 20 day’s work = 1/24 × 20 = 5/6
The remaining 1/6 work is done by the man in 6days
Therefore, the man alone will finish the work in 6 × 6 days = 36 days
Man’s 1 day’s work = 1/36
Therefore, boy’s 1 day’s work = 1/24 – 1/36 = 3 – 2 /72 = 1/72
Therefore, the Boy alone will finish the work in 72 days.
Answer: Option A
Answer: (A) 72 days
Question: Albert is 2 times Mary’s age and 4 times as old as Betty. Mary is 22 years younger than Albert. How old is Betty?
(A) 8
(B) 9
(C) 11
(D) 15
(E) 18
Rationale: A = 2M = M+22
M = 22
A = 44
A = 4B, and so B = 11
The answer is C.
Answer: (C) 11
Question: The average (arithmetic mean) of four numbers is 4x + 1. If one of the numbers is x, what is the average of the other three numbers?
(A) x + 1
(B) 3x + 3
(C) 5x + 4/3
(D) 5x + 4
(E) 15x + 12
Rationale: If the average of four numbers is 4x + 1, then the sum of all four numbers if 4 * (4x + 1) = 16x + 12. If one of the numbers is x, then the average of the remaining three numbers would be: (16x + 4 - x)/3 = (15x + 4)/3 = 5x + 4/3.
Answer is C.
Answer: (C) 5x + 4/3
Question: In a college, 70% of total 100 Arts students are Locals. 50% of students from 200 Science students are locals and 85% of total 120 Commerce students are locals. What is the total percentage of locals from Arts, Science and Commerce.
(A) 56
(B) 86.7
(C) 25.7
(D) 66
(E) 64.7
Rationale: locals from Arts = 70% of 100 = 70
locals from Science = 50% of 200 = 100
locals from Commerce = 85% of 120 = 102
total local percentage = (70+100+102)/(100+200+120) = 272/420 = 0.647
E
Answer: (E) 64.7
Question: In an election a candidate who gets 60% of the votes is elected by a majority of 1300 votes. What is the total number of votes polled?
(A) A)4500
(B) B)5200
(C) C)6900
(D) D)7520
(E) E)6500
Rationale: Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 1300
20x/100 = 1300
x = 1300*100/20 = 6500
Answer is E
Answer: (E) E)6500