mathewhe/aqua_rat huggingface dataset:
Question: In what ratio should water and wine be mixed so that after selling the mixture at the cost price a profit of 33.33% is made?
(A) 9:3
(B) 2:1
(C) 1:3
(D) 2:3
(E) 2:5
Rationale: 33.33% profit means there is one part water and 3 part is pure wine. so the required ratio of water and wine in the mixture is 1:3
Answer: Option C
Answer: (C) 1:3
Question: In a throw of dice what is the probability of geÆ«ng number greater than 2
(A) 1/2
(B) 2/3
(C) 1/5
(D) 1/6
(E) None of these
Rationale: Explanation:
Number greater than 2 is 3, 4, 5 & 6, so only 4 number
Total cases of dice = [1,2,3,4,5,6]
So probability = 4/6 = 2/3
Answer: B
Answer: (B) 2/3
Question: Three competing juice makers conducted a blind taste test with mall shoppers. The shoppers could choose to taste any number of the three brands of juices but had to select at least one juice that they liked. If 100 shoppers liked brand J, 200 shoppers liked brand K, 700 shoppers liked brand L, 350 shoppers liked exactly 2 juices, and 50 shoppers liked all three juices, how many shoppers took the taste test?
(A) 1,300
(B) 1,000
(C) 900
(D) 700
(E) 550
Rationale: Given: Atleast 1 juice was liked by the participants. --> Neither = 0
Assume, I -->No overlap between the sets
II --> Overlap between 2 sets
III --> Overlap between 3 sets
I + 2*(II) + 3*(III) = 100 + 200 + 700
I + 2*(350) + 3*(50) = 1000
I = 150
Total number of shoppers who took the taste test = I + II + III = 150 + 350 + 50 = 550
Answer: E
Answer: (E) 550
Question: A man is riding a bike downhill at 18 Km/hr, and uphill at 4 Km/hr, what is his rate?
(A) 1 Km/Hr
(B) 3 Km/Hr
(C) 5 Km/Hr
(D) 7 Km/Hr
(E) 9 Km/Hr
Rationale: Dh = 18
Uh = 4
s=?
s=(18-4)/2 = 14/2 = 7
Answer = D
Answer: (D) 7 Km/Hr
Question: In an examination 40% failed in Hindi, 45% failed in English. If 25% students failed in both the subjects. Then the percentage of failed students is?
(A) 59%
(B) 50%
(C) 90%
(D) 60%
(E) 20%
Rationale: Male = 45,000* 5/9 = 25,000
Female = 45,000* 4/9 = 20,000
Married Male = 25,000* 40/100 = 10,000
Married Female = 10,000
20,000 ------------ 10,000
100 ------------- ? => 50%
Answer: B
Answer: (B) 50%
Question: If Jan 1, 2006 was a Sunday, What was the day of the week Jan 1, 2010?
(A) Friday
(B) Thursday
(C) Tuesday
(D) Saturday
(E) None of these
Rationale: Explanation :
Given that Jan 1 2006 was a Sunday
Number of odd days in the period 2006-2009
= 3 normal years + 1 leap year
= 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved)
Hence Jan 1 2010 = (Sunday + 5 odd days) = Friday.. Answer : Option A
Answer: (A) Friday
Question: The daytime telephone rate between two cities is 60 cents for the first 3 minutes and c cents for each additional minute. The total charge is reduced 50 percent on calls made after 10:00 P.M. The cost, in dollars, of a 35-minute call made at 10:30 P.M. between these two cities is:
(A)  0.4(0.60) + 35c
(B)  0.5(0.60 + 32c)
(C)  0.4(0.60 + 9c)
(D)  0.5(0.60 + 0.32c)
(E)  0.6(0.60 + 0.35c)
Rationale: For first three minutes = 60 cents
Remaining minutes = 35 -3 = 32
charge for 32 minutes = 32c
total cost (if the call was made in daytime) = 0.60 + 32c
50% chargereducedon night calls => 50% charge
=>0.5(0.60 + 32c)
Hence, Answer is D
Answer: (D)  0.5(0.60 + 0.32c)
Question: A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of times taken by them is 14 hours. Then, A's speed is equal to?
(A) 5 km/hr
(B) 3 km/hr
(C) 6 km/hr
(D) 9 km/hr
(E) 2 km/hr
Rationale: Let A's speed = x km/hr. Then, B's speed = (7 - x) km/ hr.
So, 24/x + 24/(7 - x) = 14
x2 - 98x + 168 = 0
(x - 3)(x - 4) = 0 => x = 3 or 4.
Since, A is faster than B, so A's speed = 4 km/hr and B's speed
= 3 km/hr.
Answer: B
Answer: (B) 3 km/hr
Question: A committee of 3 people is to be chosen from the president and vice president of four different companies. What is the number of different committees that can be chosen if two people who work for the same company cannot both serve on the committee?
(A) 16
(B) 24
(C) 28
(D) 32
(E) 40
Rationale: i just did the total number of possibilities first:
ab cd ef gh are the 4 companies for example
8c3. this will include the problem counts of a pres/vp of the same company
how many ways did we over count = How many ways can a president and VP of the same company be part of this group?
choose the group, 4c1, then take both the president and vp, 2c2, then a remaining member from one of the other 3, 6c1
4c1 * 2c2 * 6c1
4 * 1 * 6 = 24
8c3 - 24 = 56 - 24 = 32 answer is D
Answer: (D) 32
Question: A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.140 where as B does not. In what ratio should they divide the second year's profit?
(A) 8:7
(B) 7:5
(C) 1:3
(D) 8:7
(E) 9:10
Rationale: Explanation:
3: 4
A = 3/7*140 = 60
360: 400
39:40
Answer:E
Answer: (E) 9:10
Question: A, B and C rents a pasture for Rs.841. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should B pay?
(A) 270
(B) 279
(C) 348
(D) 371
(E) 372
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
12/29 * 841 = 348
Answer: C
Answer: (C) 348
Question: 2/5 of the fish in an aquarium is red and 1/4 of the fish is brown. 1/4of the red fish and 1/5 of the brown fish is male. If the rest of the fish in the aquarium is female, what is the probability that a fish randomly picked from the aquarium is male?
(A) 3/20
(B) 7/30
(C) 5/16
(D) 1/3
(E) 2/5
Rationale: Straight method....
1/4 of 2/5 + 1/5 of 1/4 = 2/20 +1/20 =3/20
ANSWER:A
Answer: (A) 3/20
Question: If a^2+b^2=177and ab=54 then find the value of a+b/a-b?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: (a+b)^2=a^2+b^2+2ab=117+2*24=225
a+b=15
(a-b)^2=a^2+b^2-2ab=117-2*54
a-b=3
a+b/a-b=15/3=5
Answer is C.
Answer: (C) 5
Question: The bankerâ€™s discount of a certain sum of money is Rs. 60 and the true discount on the same sum for the same time is Rs.54. The sum due is
(A) 210
(B) 280
(C) 360
(D) 720
(E) None
Rationale: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[60 *54 / 60 - 54] = Rs. [72 * 60 / 6] = Rs. 720
Answer D
Answer: (D) 720
Question: Among all sales staff at Listco Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Listco's sales staff. Listco employs 60 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?
(A) 46
(B) 42
(C) 56
(D) 70
(E) 58
Rationale: I'm going in on this one.
So let's say that we have the following
So we know that L1 = 60 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 60 = 140. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 30 = 70.
Thus D is the correct answer choice
Answer: (D) 70
Question: M, N and O can do a piece of work in 60, 30 and 20 days respectively. Inhow many days can M do the work if he is assisted by N and O on every third day?
(A) 10 days
(B) 12 days
(C) 15 days
(D) 25 days
(E) 30 days
Rationale: M's 2 day's work = 1	x 2 =	1	.
20	10
(M + N + O)'s 1 day's work = 1	+	1	+	1 =	6	=	1	.
20	30	60	60	10
Work done in 3 days = 1	+	1 =	1	.
10	10	5
Now,	1	work is done in 3 days.
5
Whole work will be done in (3 x 5) = 15 days.
C
Answer: (C) 15 days
Question: If f(a)=a^2, what is the value of (f(a+b)−f(a))/a ?
(A) a
(B) b
(C) 2b+b^2
(D) 2a + b
(E) 2b - a
Rationale: start with f(a+b) before start calculations: f(a+b)=(a+b)^2= a^2+2ab+b^2
a^2+2ab+b^2 - a^2/a = (simplify a^2)
2ab+b^2/b = (cancel b's)
= 2b+b^2
Ans : C
Answer: (C) 2b+b^2
Question: Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
(A) 2
(B) 1/2
(C) 2/2
(D) 3
(E) None
Rationale: Solution:
1/2
one of two is the possibility
1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.
2. If any of the first 99 people sit in Aishwarya's seat, Abhishek will get to sit in his seat.
Answer B
Answer: (B) 1/2
Question: A person with some money spends1/3 for cloths, 1/5 of the remaining for food and 1/4 of the remaining for travel.He is left with Rs 100/- How much did he have with him in the beginning ?
(A) 150
(B) 200
(C) 250
(D) 270
(E) 280
Rationale: x/3+ 2x/15 + 8x/60 + 100 = x
x/3 + 4x/15 = x-100
3x= 5x - 500
x = 250
ANSWER:C
Answer: (C) 250
Question: How many positive integers less than 5,000 are evenly divisible by neither 14 nor 21?
(A) 4,514
(B) 4,475
(C) 4,521
(D) 4,428
(E) 4,349
Rationale: integers less than 5000 divisible by 14 5000/14 =333.something , so 333
integers less than 5000 divisible by 21 5000/21 = 238.## , so 238
we have double counted some, so take LCM of 14 and 21 =105 and divide by 5000, we get 47. so all numbers divisible by 14 and 21 = 333 +238 -47 =524
now subtract that from 4999. 4999- 524 = 4349 answer E.
Answer: (E) 4,349
Question: Ajay can walk 6km in 1 hour. In how many hours he can walk 45km?
(A) 5hrs
(B) 10hrs
(C) 7.5hrs
(D) 20hrs
(E) 30hrs
Rationale: 1 hour he walk 6km
he walk 45km in = 45/6 * 1 = 7.5hours
Answer is C
Answer: (C) 7.5hrs
Question: The ratio of two numbers is 3:4 and their sum is 28. The greater of the two numbers is?
(A) 15
(B) 16
(C) 18
(D) 21
(E) 22
Rationale: 3:4
Total parts = 7
= 7 parts --> 28 (7 × 4 = 28)
= 1 part ---->4 (1 × 4 = 4)
= The greater of the two number is = 4
= 4 parts ----> 16 (4 × 4 = 16)
B
Answer: (B) 16
Question: Anup was asked to find the value of 7/12 of a sum of money Q. Instead of multiplying the same by 7/12,he divided it by 7/12 and his answer exceeded the correct answer by 95. The correct answer is:
(A)  48
(B)  89
(C)  84
(D)  69
(E)  49
Rationale: Q=12/7*x-7/12*x=95 --> x=84 --> 7/12*x=49.
So if bythe correct answerquestion means 7/12 of the amount then the answer should be E.
Answer: (E)  49
Question: In a business, A and C invested amounts in the ratio 2:1, whereas the ratio between amounts invested by A and B was 3:2. If Rs. 1,57,300 was their profit, how much amount did B receive ?
(A) 48400
(B) 23777
(C) 12387
(D) 48213
(E) 37882
Rationale: A : B = 3 : 2 => B : A = 2 : 3 = 4 : 6 and A : C = 2 : 1 = 6 : 3.
So, B : A : C = 4 : 6 : 3 or A : B : C = 6 : 4 : 3.
B's share = Rs. (157300 x 4/13 ) = Rs. 48400
Answer: A
Answer: (A) 48400
Question: The sides of a square region, measured to the nearest centimeter, are 10 centimeters long. The least possible value of the actual area of the square region is
(A) 96.25 sq cm
(B) 98.25 sq cm
(C) 92.25 sq cm
(D) 100.25 sq cm
(E) 90.25 sq cm
Rationale: Though there might be some technicalities concerning the termnearest(as 9.5 is equidistant from both 9 and 10) the answer still should be : 9.5^2=90.25.
Answer: E
Answer: (E) 90.25 sq cm
Question: A division of a company consists of five men and five women. If two of these employees are randomly selected as representatives of the division, what is the probability that both representatives will be female?
(A) 2/5
(B) 2/7
(C) 2/9
(D) 2/11
(E) 2/13
Rationale: Total number of ways to select 2 members = 10C2 = 45
Total number of ways to select 2 females = 5C2 = 10
P(two females) = 10/45 = 2/9
The answer is C.
Answer: (C) 2/9
Question: Let a be a positive integer. If w is divisible by 2^a and w is also divisible by 3^(2a), then it is possible that w is NOT divisible by
(A) 6
(B) 3 × 2^a
(C) 2 × 3^(2a)
(D) 6^a
(E) 6^(2a)
Rationale: Since, w is divisible by 2^a and 3^(2a), it must be divisible by 6. As least value of a = 1
Only for E, 6^(2a) doesn't satisfy, if a = 1 and w=18, it is not divisible by 6^2 (i.e 36)
Hence answer is E
Answer: (E) 6^(2a)
Question: Simplify: 839478 x 625
(A) 524673750
(B) 546273750
(C) 562473750
(D) 564273750
(E) None of them
Rationale: 839478 x 625 = 839478 x 5^4 = 8394780000/16 = 524673750.
Answer is A
Answer: (A) 524673750
Question: The probability of pulling a black ball out of a glass jar is 1/R. The probability of pulling a black ball out of a glass jar and breaking the jar is 1/Y. What is the probability of breaking the jar?
(A) 1/(XY)
(B) R/Y
(C) Y/X
(D) 1/(X+Y)
(E) 1/(X-Y)
Rationale: P of pulling a black ball out of a glass jar AND breaking the jar = 1/Y
P of pulling a black ball out of a glass jar is 1/R
Lets say P of breaking the jar = n
That means 1/R*n=1/Y
n= R/Y
B is the answer
Answer: (B) R/Y
Question: The average age of the mother and her six children is 13 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
(A) 40
(B) 41
(C) 42
(D) 43
(E) 44
Rationale: Total age of mother and 6 children = avg x n = 13 x (6+1)= 91
If mother is excluded new average is (13 - 5) = 8
so for 6 children = 6 x 8=48
so mother's age is 91 - 48 =43
Answer: Option D
Answer: (D) 43
Question: A+B+C = 500
A+C = 200
B+C = 350
--------------
A+B+2C = 550
A+B+C = 500
----------------
C = 50
Answer: A
(A) 50
(B) 27
(C) 26
(D) 28
(E) 24
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer: C
Answer: (C) 26
Question: An intelligence agency decides on a code of 2 digits selected from 0, 1, 2, …, 9. But on the slip on which the code is hand written allows confusion between top and bottom, because there are indistinguishable. Thus, for example, the code 91 could be confused with 16. How many codes are there such that there is no possibility of any confusion?
(A) 90
(B) Required numbers = 80
(C) 40
(D) 50
(E) 89
Rationale: Total digits that can be formed = 10C1 * 10C1 = 100.
The digits that still remain digits when turned upside down are 0, 1, 6, 8 and 9.
So codes that can create confusion are:
01, 06, 08, 09
10, 16, 18, 19
60, 61, 66, 68 (69 would still be 69 when inverted)
80, 81, 86, 89
90, 91, 98, 99 (96 would still be 96 when inverted)
There are 20 such numbers.
Required numbers = 100 - 20 = 80
ANSWER:B
Answer: (B) Required numbers = 80
Question: A rectangular circuit board is designed to have a width of W inches, a length of L inches, a perimeter of P inches, and an area of X square inches. Which of the following equations must be true?
(A) 2W^2 − PW + 2X = 0
(B) 2W^2 + PW + 2X = 0
(C) 2W^2 − PW − 2X = 0
(D) W^2 + PW + X = 0
(E) W^2 − PW + 2X = 0
Rationale: P = 2(L+W)-----------------1)
X= LW------------------------2)
option A is not possible why ?? because all the terms are positive.
lets try option B , put value of P and A from 1 and 2 we have,
2W^2-2(L+W)W + 2(LW)
2W^2 - 2LW - 2W^2 + 2LW=0.
hence answer is A.
Answer: (A) 2W^2 − PW + 2X = 0
Question: If x+y=4, x-y=36, for integers of x and y, x=?
(A) 20
(B) 15
(C) 25
(D) 13
(E) 42
Rationale: x+y = 4
x-y = 36
2x = 40
x = 20
Answer is A
Answer: (A) 20
Question: Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 50 and the turban. Find the price of the turban.
(A) 27
(B) 36
(C) 29
(D) 10
(E) 70
Rationale: Let the price of turban be x.
Thus, for one year the salary = (90 + x)
For 9 months he should earn 3434 (90 + x).
Now he gets one turban and Rs. 50.
Thus, 3434 (90 + x) = 50 + x or 270 + 3x = 200 + 4x or x = 70
Answer:E
Answer: (E) 70
Question: The length of a side of a hexagon is 4 inches. What is the perimeter?
(A) 22
(B) 23
(C) 24
(D) 25
(E) 26
Rationale: Hexagon. It means 6 equal sides.
p = 6(4) = 24 inches
Answer C
Answer: (C) 24
Question: For a positive integer n, let PnPn denote the product of the digits of nn and SnSn denote the sum of the digits of nn. The number of integers between 10 and 100 for which Pn+Sn=n
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: Let the two digit number be 'ab'
Given, a × b + a + b = 10a + b
a × b = 9a
b = 9
Therefore, for b = 9, the above condition satisfies. So all the two digit numbers for which units digit is 9 are our solutions. They range from 19 to 99. Total 9 numbers.
Answer:	A
Answer: (A) 9
Question: A small pool filled only with water will require an additional 800 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 800 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?
(A) 1000
(B) 1250
(C) 1300
(D) 2000
(E) 2250
Rationale: Since pumping in additional 800 gallons of water will increase the amount of water in the pool by 30%, then initially the pool is filled with 1,000 gallons of water.
So, we have that 1,000 + 800 = 0.8*{total} --> {total} = 2,250.
Answer: E.
Answer: (E) 2250
Question: In a new Engineering Hostels containing 100 rooms. Ankit Garg was hired to paint the numbers 1 to 100 on the doors.
How many times will Ankit have to paint the number eight ?
(A) 10 times
(B) 15 times
(C) 30 times
(D) 20 times
(E) 35 times
Rationale: D
20 times
8,18,28,38,48,58,68,78,98,80,81,82,83,84,85,86,87,88,88(2),89
Answer: (D) 20 times
Question: The profits of QRS company rose 20% from March to April, then dropped 20% from April to May, then rose 50% from May to June. What was the percent increase for the whole quarter, from March to June?
(A) 15%
(B) 32%
(C) 44%
(D) 62%
(E) 80%
Rationale: Assume 100 in march , then 120 in April as 20% increase , Then 96 in may as 20% decrease from April , and then 144 in june which is 150% of 96 .
So overall increase is from 100 to 144 is 44%
Answer C
Answer: (C) 44%
Question: A 100-litre mixture of milk and water contains 36 litres of milk. 'x' litres of this mixture is removed and replaced with an equal quantum of water. If the process is repeated once, then the concentration of the milk stands reduced at 16%. What is the value of x?
(A) 33.33 litres
(B) 36.67 litres
(C) 37.67 litres
(D) 36.5 litres
(E) 36 litres
Rationale: Working formula ...
Initial Concentration*Initial Volume=Final Concentration*Final Volume.
Let X is the part removed from 100 lts.
36%(1-X/100)^2 = 16% * 100%
(1-x/100)^2=16/36------>(1-x/100)^2=(4/6)^2
100-X=400/6
x=33.33...
Ans A
Answer: (A) 33.33 litres
Question: In a certain sequence of numbers, a1, a2, a3, ..., an, the average (arithmetic mean) of the first m consecutive terms starting with a1 is m, for any positive integer m. If a1=1, what is a13?
(A) 100
(B) 55
(C) 25
(D) 19
(E) 1
Rationale: As stated above, (a1+a2+a3......+a13)/13=13
therefore a1+a2+a3.......a13=169 (1)
using the same logic, we got a1+a2+a3..........+a12=144 (2)
(2)-(1) we got a13=25
C
Answer: (C) 25
Question: In a set of 5 black balls and 3 red balls, how many selections of 5 balls can bemade such that at least 3 of them are black balls?
(A) 24
(B) 26
(C) 46
(D) 49
(E) 50
Rationale: Selecting at least 3 black balls from a set of 5 black balls in a total selection of 5 balls can be
3 B and 2 R
4 B and 1 R and
5 B and 0 R balls.
Therefore, our solution expression looks like this.
5C3 * 3C2 + 5C4 * 3C1 + 5C5 * 3C0 = 46 ways.
C
Answer: (C) 46
Question: a sixth grade teacher asked her students to draw rectangles with positive integer length and a perimeter of 42.the difference between the largest and smallest possible ares of the rectangles that the students could have come up with is?
(A) 50 sq units
(B) 60 sq units
(C) 70 sq units
(D) 80 sq units
(E) 90 sq units
Rationale: sum of length and breadth will be 21 units . 42/2=21
area will be max when lxb = 11x10=110 sq units
area will be min when lxb = 20x1=20 sq units.
.the difference between the largest and smallest possible ares of the rectangles that the students could have come up with= 110-20=90 sq units
ANSWER:E
Answer: (E) 90 sq units
Question: Working at constant rate, pump X pumped out half of the water in a flooded basement in 2 hours. The pump Y was started and the two pumps, working independently at their respective constant rates, pumped out rest of the water in 3 hours. How many hours would it have taken pump Y , operating alone at its own constant rate, to pump out all of the water that was pumped out of the basement?
(A) a. 10
(B) b. 12
(C) c. 14
(D) d. 18
(E) e. 24
Rationale: rate of x=1/8
rate of x+y=1/6
rate of y=1/6-1/8=1/24
18 hours
D
Answer: (D) d. 18
Question: Donald duck can can swim his pool downstream(with the pool current helping time) in exact 40 seconds and upstream(against the pool current) in a pool in exact 60 seconds. The length of pool is 2 kilometers.
How long Donald duck can cover distance of one side at a still pool (with no current).
(A) 48 minutes.
(B) 58 minutes.
(C) 68 minutes.
(D) 88 minutes.
(E) 78 minutes.
Rationale: Solution:
48 minutes.
Donald duck's speed = X km/seconds
pool current speed = Y km/seconds
2/(X+Y) = 40
2/(X-Y) = 60
Solving the simultaneous equations gives X = 1/24
Therefore, to cover 2km will take 2/X = 48 seconds
Answer A
Answer: (A) 48 minutes.
Question: If the given two numbers are respectively 6% and 18% of a third number, then what percentage is the first of the second ?
(A) 20%
(B) 25%
(C) 18%
(D) 33 1/3%
(E) none of these
Rationale: Here, l = 6 and m = 18
Therefore, first number = l/m x 100% of second number = 6/18 x 100% of second number = 33 1/3% of second number
ANSWER:D
Answer: (D) 33 1/3%
Question: A invested Rs. 76,000 in a business. After few months, B joined him Rs. 57,000. At the end of the year, the total profit was divided between them in ratio 2 : 1. After bow many months did B join?
(A) 4
(B) 3
(C) 2
(D) 1
(E) None of them
Rationale: Suppose B joined after x months. Then, B's money was invested for (12 - x)
=(76000 x 12)/(57000 x (12-x) =2/1 =912000=114000(12-x)
=114 (12 - x) = 912=12-x=8=x=4
Hence, B joined after 4 months
Answer is A.
Answer: (A) 4
Question: If n is a positive integer, which of the following expressions must be even?
(A) (n − 1)( n + 3)
(B) (n − 6)( n + 1)
(C) (n − 2)( n + 6)
(D) (n − 3)( n + 3)
(E) (n − 3)( n + 7)
Rationale: Whether n is even or odd, (n-6)(n+1) will have one odd factor and one even factor.
The product will be even.
The answer is B.
Answer: (B) (n − 6)( n + 1)
Question: A train traveling at 100 kmph overtakes a motorbike traveling at 64 kmph in 40 seconds. What is the length of the train in meters?
(A) 1777 meters
(B) 1822 meters
(C) 400 meters
(D) 1111 mete
(E) None of these
Rationale: Answer
Concept : Distance covered by train when it crosses a moving object
When a train overtakes another object such as a motorbike, whose length is insignificant compared to the length of the train, the distance traveled by the train is equal to the length of the train.
Because the motorbike is also moving, we have to take the relative speed between the train and the motorbike and not just the speed of the train.
The length of the train = distance traveled by the train while overtaking the motorbike = relative speed between the train and the motorbike * time taken
In this case, as both the objects i.e., the train and the motorbike are moving in the same direction, the relative speed between them = difference between their respective speeds = 100 - 64 = 36 kmph.
Distance traveled by the train while overtaking the motorbike = 36 kmph * 40 seconds.
The final answer is in meters and the speed is given in kmph and the time in seconds.
So let us convert the given speed from kmph to m/sec.
1 kmph = 5/18 m/sec
Therefore, 36 kmph = 36 * 5/18 = 10 m/sec.
Relative speed = 10 m/sec. Time taken = 40 seconds.
Therefore, distance traveled = 10 * 40 = 400 meters.
Choice C
Answer: (C) 400 meters
Question: If x2−1/x+1, then, x = ?
(A) 1
(B) 0
(C) 2
(D) Can’t be determined
(E) None of these
Rationale: (x – 1) = 2 ⇒ x = 3
Answer E
Answer: (E) None of these
Question: Simplfy
b - [b -(a+b) - {b - (b - a+b)} + 2a]
(A) a
(B) 2a
(C) 4a
(D) 0
(E) 1
Rationale: Explanation:
b-[b-(a+b)-{b-(b-a+b)}+2a]
=b-[b-a-b-{b-(2b-a)}+2a]
=b-[-a-{b-2b+a}+2a]
=b-[-a-{-b+a}+2a]
=b-[-a+b-a+2a]
=b-[-2a+b+2a]
=b-b
=0
Option D
Answer: (D) 0