mathewhe/aqua_rat huggingface dataset:
Question: The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
(A) 14
(B) 144
(C) 777
(D) 992
(E) 221
Rationale: The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
Answer:B
Answer: (B) 144
Question: If 72/x is an integer and 108/x is an integer, which of the following must be true?
I. 9/x is an integer.
II. 12/x is an integer.
III. 36/x is an integer.
(A) III only
(B) I and II only
(C) I, II, and III
(D) II and III only
(E) I only
Rationale: The largest possible value of x is 36 (the greatest common factor of 72 and 108), and if x=36 then
A
Answer: (A) III only
Question: Which of the following equations has a solution in common with 2x^2 - 5x - 42?
(A) 2x^2 + 8x - 42 = 0
(B) x^2 - 14x + 24 = 0
(C) 2x^2 - 8x + 8 = 0
(D) x^2 + 13x + 13 = 0
(E) none of the above
Rationale: Given : 2x^2 - 5x - 42 => (2x + 7) (x - 6) = 0 => -7/2 and 6 are the roots..
A. 2x^2 + 8x - 42 = 0 => (2x - 6) (x + 7)
B. x^2 - 14x + 24 = 0 => (x - 6) (x - 8)
C. x^2 + 13x + 13 = 0 => (2x -7) ( x - 1)
D. x^2 + 13x + 13 = 0 => (x + 6) (x + 7)
None of the answer equations have exactly both the same roots as the question equation, but at least one of them does share one of the two roots.
So IMO "B" is correct answer... because it shares the one root (part of the solution), -3, from the (x+3) portion of its factoring
Answer: (B) x^2 - 14x + 24 = 0
Question: Look at this series: 7, 10, 8, 11, 9, 12, ... What number should come next?
(A) 7
(B) 10
(C) 12
(D) 13
(E) 14
Rationale: Explanation: This is a simple alternating addition and subtraction series. In the first pattern, 3 is added; in the second, 2 is subtracted.
Answer: Option B
Answer: (B) 10
Question: There are 48 students in a class. Find the numbers of ways in which a committee of 2 students is to be formed?
(A) 1128
(B) 1978
(C) 2546
(D) 3121
(E) 2400
Rationale: Required number of ways = 48C2 = 48*47 / 2 = 1128
Answer is A
Answer: (A) 1128
Question: A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
(A) 1:00 P.M.
(B) 2:00 P.M
(C) 1:30 P.M.
(D) 2:30 P.M.
(E) 12:30 P.M.
Rationale: (P + Q + R)'s 1 hour's work =	(	1	+	1	+	1	)	=	37	.
8	10	12	120
Work done by P, Q and R in 2 hours =	(	37	x 2	)	=	37	.
120	60
Remaining work =	(	1 -	37	)	=	23	.
60	60
(Q + R)'s 1 hour's work =	(	1	+	1	)	=	11	.
10	12	60
Now,	11	work is done by Q and R in 1 hour.
60
So,	23	work will be done by Q and R in	(	60	x	23	)	=	23	hours = 2 hours.
60	11	60	11
So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.
Option A
Answer: (A) 1:00 P.M.
Question: In a certain state, gasoline stations compute the price per gallon p, in dollars, charged at the pump by adding a 3 percent sales tax to the dealer's price per gallon d, in dollars, and then adding a gasoline tax of $0.18 per gallon. Which of the following gives the dealer's price per gallon d in terms of the price per gallon p charged at the pump?
(A) d = (p-0.03)/1.18
(B) d = p/1.21
(C) d= (p-0.18)/1.03
(D) d = p-0.20
(E) d = p/1.03 - 0.18
Rationale: Let dealers price (d) be 1. so adding 3% to dealers price is d+ 3% of d. i.e. 1 + 3% of 1 which is1 + 0.03. then add 0.18 to the value.
Now 1.03 + 0.18. this is now 1.21. you have the gasoline stations price (p) as 1.21 dollars.
Now sub 1.21 in the options to know which option gave you d = 1. d must equal 1 because you earlier picked 1 as the value of d in the question.
PS: always remember to start from E upwards.
Answer : C
Answer: (C) d= (p-0.18)/1.03
Question: How many squares are there between 2011 to 2300 ????
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: nos. are 2025, 2116, 2209
Answers is 3
ANSWER:A
Answer: (A) 3
Question: A man sold 10 eggs for 5 rupees and gained 20%. How many eggs did he buy for 5 rupees?
(A) 10 eggs
(B) 12 eggs
(C) 14 eggs
(D) 16 eggs
(E) None of these
Rationale: S.P. for 1 egg = 5⁄10 = 1⁄2
∴ C.P. for 1 egg = 100/(100+20)×12=512
⇒ He bought 12 eggs for 5 rupees.
Answer B
Answer: (B) 12 eggs
Question: (√27+√243)/√75=?
(A) 2√2
(B) 2√3
(C) 3√2
(D) 3√3
(E) 12/5
Rationale: (√27+√243)/√75
=(3√3+9√3)/5√3
=12√3/5√3
=12/5.
Hence, the correct answer is E
Answer: (E) 12/5
Question: Two sets of 4 consecutive positive even integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set?
(A) 14
(B) 7
(C) 18
(D) 24
(E) it cannot be determined from the information given.
Rationale: A=(2,4,6,8), sum of this=20
B=(8,10,12,14), sum of this=44,
The differenct between 44-20=24
Hence,24 is the answer i.e.D
Answer: (D) 24
Question: In order to fulfill a local school’s request for a cakes, B parents agreed to each bake an equal number of cakes. If p of the parents did not bake any cakes, which of the following represents the additional number of cakes that each of the other parents had to bake in order for the school’s request for a cakes to be fulfilled?
(A) pa/(B(B-p))
(B) pa/2
(C) pa/B
(D) p/B-p
(E) pa/B
Rationale: No of cakes each parent has to bake : a/B
No of parents did not bake cake = p
No of cakes that were not baked by p parents = p*a/B
No of parents has to bake additional cakes = B-p
additional number of cakes that each of the other parents had to bake in order for the school’s request for a cakes = pa/(B(B - P))
Answer A
Answer: (A) pa/(B(B-p))
Question: How many 1/2s are there in 37 1/2?
(A) 75
(B) 150
(C) 300
(D) 600
(E) 700
Rationale: Required number = (75/2)/(1/2)
= (75/2 x 2/1)
= 75
ANSWER:A
Answer: (A) 75
Question: Find the odd one out:
125, 106, 86, 76, 65, 58, 53
(A) 33
(B) 86
(C) 26
(D) 18
(E) 222
Rationale: Explanation:
This sequence represents a series in which from the reverse order a prime number is added:
53+5=58
58+7=65
65+11=76
76+13=89
89+17=106
106+19=125
Hence 86 is the answer.
ANSWER: B
Answer: (B) 86
Question: FIND THE ODD NUMBER:
1,5,11,17,23,29
(A) 1
(B) 3
(C) 4
(D) 6
(E) 7
Rationale: Explanation:
All the given numbers are prime numbers.
1 is not a prime number because it is divisible by only one factor that is 1.
ANSWER: A
Answer: (A) 1
Question: How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)?
(A) 360
(B) 817
(C) 145
(D) 346
(E) 342
Rationale: The given digits are six.
The number of four digit numbers that can be formed using six digits is ⁶P₄
= 6 * 5 * 4 * 3
= 360.
Answer: A
Answer: (A) 360
Question: The sum of all the integers k such that –25 < k < 24 is
(A) 0
(B) -2
(C) -25
(D) -49
(E) -47
Rationale: -24------------------0-----------------23
values upto+23 cancels outwe are left with only -24-23 sum of which is - 47. hence option D.
E
Answer: (E) -47
Question: Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 50% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?
(A) $20
(B) $40
(C) $50
(D) $80
(E) $100
Rationale: Deargoodyear2013,
I'm happy to help.This is a relatively straightforward problem, not very challenging. BTW,Crazy Eddiewas the actually name of an electronics chain on the East Coast of the USA back in the 1970s.
Manufacturing now is $50. They now are making a 50% profit, so the selling price must be $100.
They had this same selling price, $100, before they made the change, and had a profit of 50%, so the manufacturing must have been $50. Answer = (C).
Answer: (C) $50
Question: In the biology lab of "Jefferson" High School there are 0.036*10^5 germs, equally divided among 45000*10^(-3) Petri dishes. How many germs live happily in a single dish?
(A) 10
(B) 20
(C) 30
(D) 60
(E) 80
Rationale: 0.036*10^5 can be written as 3600
45000*10^(-3) can be written as 45
Required= 3600/45= 80
ANSWER:E
Answer: (E) 80
Question: A shepherd has 1 million sheep at the beginning of Year 2010. The numbers grow by xx during the yr. A famine hits his village in the next year & many of his sheep die. The sheep population decreases by yy during 2001 and at the beginning of 2011 the shepherd finds that he is left with 1 million sheep. Which of the following is correct?
(A) x<y
(B) x>y
(C) x=y
(D) x<=y
(E) x>=y
Rationale: Let us assume the value of xx to be 10%10%.
Therefore, the number of sheep in the herd at the beginning of year 2001 (end of 2000) will be 1 million + 10%10% of 1 million = 1.1 million
In 2001, the numbers decrease by y%y% and at the end of the year the number sheep in the herd = 1 million.
i.e., 0.1 million sheep have died in 2001.
In terms of the percentage of the number of sheep alive at the beginning of 2001,
it will be (0.1/1.1)×100%=9.09%(0.1/1.1)×100%=9.09%.
From the above illustration it is clear that x>y
B
Answer: (B) x>y
Question: If x is an integer, which of the following is a possible value of W=(x^2 +2x – 7)/9?
(A) -2.4
(B) 0.268
(C) 1.166 repeating
(D) 4.555 repeating
(E) 8.125
Rationale: x is an integer, which of the following is a possible value of W= (x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.125
when this is multiplied by 9, x is not an integer
Answer choice D seems to fit.D
Answer: (D) 4.555 repeating
Question: if Juan takes 14 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
(A) 14x/y
(B) 11y/x
(C) x/11y
(D) 11/xy
(E) xy/11
Rationale: Answer is A.
The rate of running hards: 14 minutes per y hards.
Thus the time for running x hards = x hards * 14 minutes/y hards = 14x/y
Answer: (A) 14x/y
Question: A cylinder is sliced by a plane to form the solid
shown. The base edge of the solid is a circle
of radius 3. The top edge is an ellipse. The
highest point on the ellipse is 6 units above the
base. The lowest point on the ellipse is 2 units
above the base. What is the volume, in cubic
units, of the solid?
(A) 24π
(B) 30π
(C) 36π
(D) 42π
(E) 48π
Rationale: The plane parallel to the base passing through the center of the ellipse will cross the ellipse
along its minor axis. If we cut the solid along this plane and flip the top piece that is sliced off 180
degrees around the minor axis, the solid becomes a cylinder with the base of area 9 and height
(2 + 6)/2 = 4. The volume is therefore 36π.
correct answer C
Answer: (C) 36π
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 20000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is
(A) 20
(B) 49
(C) 22
(D) 23
(E) NONE
Rationale: Sol.
Let the total number of workers be x. Then,
8000x = (20000 × 7) + 6000 ( x – 7)
‹=› 2000x = 98000
‹=› x = 49.
Answer B
Answer: (B) 49
Question: A small company is planning to rent either computer A or computer B to print customer mailing lists. Both computer A and computer B must be rented on an hourly basis. The rental fee is based only on the amount of time the computer is turned on. It will cost 40 percent more per hour to rent computer A than to rent computer B. Computer B would, however, require 20 hours more than computer A to do the job. If either computer A, or computer B were rented the total cost to rent the computer would be $650.00. What would be the approximate hourly charge to rent computer B?
(A) $9.28
(B) $11.30
(C) $13.20
(D) $17.80
(E) $22.10
Rationale: Pa = price of A
Pb = price of B
Ta = time for A to complete the job
Tb = time for B to complete the job
Given
Pa = 1.4 Pb
Ta+20 = Tb
Pa*Ta = Pb*Tb=650
1.4Pb * (Tb-20) = Pb*Tb
1.4 Pb Tb - Pb Tb = 1.4 Pb * 20
0.4PbTb = 28Pb
Tb = 28/0.4 = 70
Pb=650/70 ~ 9.28
A
Answer: (A) $9.28
Question: Mr. Gangadhar, Mr. Ramesh and Mr. Shridhar together earned 19800. The ratio of earnings between Mr. Gangadhar and Mr. Ramesh is 2 : 1 while that between Mr.Ramesh and Mr. Shridhar is 3 : 2. How much did Mr. Ramesh earn?
(A) 3600
(B) 5400
(C) 1800
(D) 6300
(E) None of these
Rationale: Ratio of investment = 6 : 3 : 2
∴ Share of Mr. Ramesh = 3⁄11 × 19800 = 5400
Answer B
Answer: (B) 5400
Question: A tea expert claims that he can easily find out whether milk or tea leaves were added first to water just by tasting the cup of tea. In order to check this claims 12 cups of tea are prepared, 6 in one way and 6 in other. Find the different possible ways of presenting these 12 cups to the expert.
(A) 252
(B) 240
(C) 300
(D) 924
(E) None
Rationale: Solution:
Since, there are 6 cups of each kind, prepared with milk or tea leaves added first, are identical hence, total number of different people ways of presenting the cups to the expert is,
[12!/(6!x 6!)]= 924
Answer: Option D
Answer: (D) 924
Question: when W is divided by 13, the reminder is 0. if W is one more than it value and when divided by 10 its remainder is 0. what is the value of W ?
(A) 39
(B) 26
(C) 14
(D) 13
(E) 52
Rationale: W is divided by 13 so that is multiple of 14 as 13,26,39...
W+1 is divided by 10 the remainder is 0 so it is divisible by 10. Consider from option let us take the number is 39 it is divisible by 13 but 39+1 is divisible by 10 so ans is A
Answer: (A) 39
Question: A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 40% impurities to the product. Find the net profit percentage of the dealer?
(A) 94%
(B) 87.5%
(C) 55%
(D) 56.25%
(E) 36%
Rationale: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.
It means that he is selling $4 worth of product for $5.
The dealer then further added 50% impurities to the product.
It means that he is selling $5 worth of product for $7.5.
So his profit is $7.5-$4 = $3.5
and his profit percent is
(3.5/4)*100 = 87.5%
Answer:- B
Answer: (B) 87.5%
Question: If A exceeds B by 40%, B is less than C by20%, then A : C is :
(A) 28:25
(B) 26:25
(C) 3:2
(D) 3:1
(E) 28:27
Rationale: A = B + 40% of B
A = 140/100 * B
Now,
A/B = 14/10
B = C - 20% of C
B = 80/100 *C
B/C = 8/10
SO,
A/C = (A/B) * (B/C) = (14 *8) / (10 *10) = 28 : 25.
answer - Option A
Answer: (A) 28:25
Question: How many 4-digit Z numbers (ABCD) can be formed such that |A – D| = 2?
(A) 2,000
(B) 1,900
(C) 1,800
(D) 1,600
(E) 1,500
Rationale: 1) A=0 and D-8
2) A and D as 1 and 9..so 3*100= 300 extra ways ans 1800-300 = 1500.
we are looking for |A-D|=2 so any of the two can be bigger..
these two can have values (1,3) ; (2,4) so on till (7,9) so total 7*2 = 14..
another arrangement could be A as 2 and D as 0... D as 2 and A as 0 is not possible as number will become 3 digits..
so the ways A and D can be placed = 14+1=15 ways..
B and C can be placed in 10*10 ways..
Total Z= 15*10*10=1500.E
Answer: (E) 1,500
Question: If f(x) =4* (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?
(A) f(x)
(B) -f(x)
(C) -4*f(x)
(D) -1/f(x)
(E) 2*f(x)
Rationale: 4*f(1/x) = 4*((1/x)^4 - 1) / ((1/x)^2)
= 4*((1/x^4) - 1) / (1/x^2)
= 4*((1-x^4)/(x^4)) / (1/x^2)
=4* (1-x^4)/(x^2)
= - 4*( (x^4) -1) / (x^2)
= -4f(x)
Answer is C.
Answer: (C) -4*f(x)
Question: A cheetah can at 65 mph but only for a maximum of 6 minutes before it exhausts itself. How many miles can the cheetah run before tiring out? Round to the nearest hundredths place.
(A) 5 miles
(B) 5.50 miles
(C) 6 miles
(D) 6.50 miles
(E) 7 miles
Rationale: 65 mph x (6/60)= 6.5 miles
Answer D
Answer: (D) 6.50 miles
Question: A man took a loan from a bank at the rate of 8% p.a. simple interest.After 3 years he had to pay Rs. 5400 interest only for the period.The principal amount borrowed by him was :
(A) Rs. 2000
(B) Rs. 10,500
(C) Rs. 15,500
(D) Rs. 22,500
(E) None
Rationale: Solution
Principal = Rs.(100x5400/8x3)= Rs.22,500.
Answer D
Answer: (D) Rs. 22,500
Question: Six bells commence tolling together and toll at intervals of 1,2,3,4,5,6 seconds respectively. In 30 minutes, how many times do they toll together?
(A) 44
(B) 31
(C) 15
(D) 16
(E) 17
Rationale: L.C.M of 1,2,3,4,5,6 is 180. i.e after each 1 min they will toll together.So in 30 min they will toll 30 times.As they have initially tolled once,The answer will be 30+1=31.
ANSWER:B
Answer: (B) 31
Question: The ratio between the speeds of two trains is 7 : 8. If the second train runs 400 km in 4 hours, then the speed of the first train is:
A.
B.
C.
D.
Answer: Option D
Explanation:
(A) 70 km/hr
(B) 75 km/hr
(C) 87.5 km/hr
(D) 84 km/hr
(E) 75.6 km/hr
Rationale: Let the speed of two trains be 7x and 8x km/hr.
Then, 8x =	400/4	= 100
x =	100/8 = 12.5
8 Speed of first train = (7 x 12.5) km/hr = 87.5 km/hr.
answer :C
Answer: (C) 87.5 km/hr
Question: How many positive integers less than 26 are prime numbers, odd multiples of 5, or the sum of a positive multiple of 2 and a positive multiple of 4?
(A) 27
(B) 21
(C) 24
(D) 22
(E) 20
Rationale: 9 prime numbers less than 28: {2, 3, 5, 7, 11, 13, 17, 19, 23}
3 odd multiples of 5: {5, 15, 25}
10 numbers which are the sum of a positive multiple of 2 and a positive multiple of 4: {6, 8, 10, 12, 14, 16, 18, 20, 22, 24}
Notice, that 5 is in two sets, thus total # of integers satisfying the given conditions is 9+3+10-1=21.
Answer: B.
Answer: (B) 21
Question: If the Average of 10 consecutive integers is 23.5 then the 10th integer is :-
(A) 15
(B) 20
(C) 23
(D) 28
(E) 25
Rationale: The average falls between the 5th and 6th integers,
integer 5 = 23, integer 6 = 24.
Counting up to the tenth integer
we get 28.
ANSWER:D
Answer: (D) 28
Question: 3,9,12,15,18,__
(A) 19
(B) 20
(C) 22
(D) 21
(E) 41
Rationale: 9=3*3
12=3*4
15=3*5
18=3*6
21=3*7
ANSWER:D
Answer: (D) 21
Question: How many 4's are there preceded by 7 but not followed by 3?
5 9 3 2 1 7 4 2 6 9 7 4 6 1 3 2 8 7 4 1 3 8 3 2 5 6 7 4 3 9 5 8 2 0 1 8 7 4 6 3
(A) 4
(B) 5
(C) 6
(D) 8
(E) 9
Rationale: 7 4 2
7 4 6
7 4 1
7 4 6
Only at these placees 4 is preceded by 7 but not followed by 3
Answer: A
Answer: (A) 4
Question: Alex has 4 pens worth of {22, 25, 30, 40}, what is the total mean and median of the worth of pens ?
(A) 3.42
(B) 6.16
(C) 8.32
(D) 2.0
(E) 1.75
Rationale: This is a good question to understand the difference between mean and median.
Mean: Average of all the numbers. (Sum of all the elements divided by the number of elements)
Median: Arrange the elements of the set in increasing order. If the number of terms is odd, the middle term is the median. If the number of terms is even, the average of middle two terms is the median
Coming to this question,
Mean = (22+ 25+ 30+ 40)/4 = 29.25
Median = (25 + 30)/2 = 27.5
Total = 1.75
Option E
Answer: (E) 1.75
Question: oy started cycling along the boundaries of a square field from corner point A. After half an hour he reached the corner point C, diagonally opposite to A. If his speed was 8km/hr, the area of the filed in square km is?
(A) 64
(B) 4
(C) 16
(D) 9
(E) 5
Rationale: Explanation :
Distance covered by Roy in 1/2hr = 4 kmTherefore, side of the square =4/2=2 kmHence, Area=2×2= 4 square km
Answer : B
Answer: (B) 4
Question: Two pots are in side-by-side. One pot, which is 20 inches tall, casts a shadow that is 10
inches long. The other pot is 40 inches tall. Compute, in inches, the length of the shadow that
the taller pot casts.
(A) 25
(B) 30
(C) 10
(D) 15
(E) 20
Rationale: The ratio of shadow to height is constant, so if x is the length of the shadow, then
20/10 = 40/x and x = 20 .
correct answer E
Answer: (E) 20
Question: 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?
(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 = 9C/5 + 32
F = 9(45)/5 + 32 = 113°F
The answer is D.
Answer: (D) 113°F
Question: Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 10 years old. At what age did the father get married ?
(A) 23 years
(B) 25 years
(C) 33 years
(D) 35 years
(E) 37 years
Rationale: Explanation:
Ayush's present age = 10 years.
His mother's present age = (10 + 20) years = 30 years.
Ayush's father's present age = (30 + 5) years = 35 years.
Ayush's father's age at the time of Ayush's birth = (35 - 10) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years.
Answer: A) 23 year
Answer: (A) 23 years
Question: A man saves 25% of his monthly salary. If an account of dearness of things he is to increase his monthly expenses by 10%, he is only able to save Rs. 175 per month. What is his monthly salary?
(A) Rs.1000
(B) Rs.2000
(C) Rs.1500
(D) Rs.3000
(E) Rs.3100
Rationale: Income = Rs. 100
Expenditure = Rs. 75
Savings = Rs. 25
Present Expenditure 75+75*(10/100) = Rs.82.5
Present Savings = 100 – 82.50 =Rs. 17.50
If savings is Rs. 17.50, salary = Rs. 100
If savings is Rs.175, salary = 100/17.5*175 = 1000
Answer : A
Answer: (A) Rs.1000
Question: All the milk in container A which was filled to its brim was poured into two containers B and C. The quantity of milk in container B was 62.5% less than the capacity of container A. If 158 liters was now transferred from C to B, then both the containers would have equal quantities of milk. What was the initial quantity of milk in container A?
(A) 1264
(B) 1723
(C) 1129
(D) 2613
(E) 1372
Rationale: A
B has 62.5% or (5/8) of the milk in A. Therefore, let the quantity of milk in container A(initially) be 8k.
Quantity of milk in B = 8k - 5k = 3k.
Quantity of milk in container C = 8k - 3k = 5k
Container: A B C
Quantity of milk: 8k 3k 5k
It is given that if 158 liters was transferred from container C to container B, then both the containers would have equal quantities of milk.
5k - 158 = 3k + 158 => 2k =316 => k = 158
The initial quantity of milk in A = 8k = 8 * 158 = 1264 liters.
Answer: (A) 1264
Question: In the formula Y = 1/(2x+2)^3, if x is halved, then Y is multiplied by
(A) 27
(B) 27/8
(C) 8/27
(D) 8
(E) 1/27
Rationale: Say x=2 => Y1 = 1/108
when x=1; Y2 = 1/32
Y2 = 27/8*Y1.
Answer : B
Answer: (B) 27/8
Question: Find the no.of ways of arranging the boy and 7 guests at a circular table so that the boy always sits in a particular seat?
(A) 3!
(B) 8!
(C) 7!
(D) 9!
(E) 11!
Rationale: Ans.(C)
Sol. Total number of persons = 8 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 7 places in 7P7 = 7! Ways ... The number of required arrangements = 7! x 1= 7! = 7! ways
Answer: (C) 7!
Question: If W is a positive integer, and W/15 = 8.2, what is the remainder when W is divided by 15?
(A) A.1
(B) B.2
(C) C.3
(D) D.4
(E) E.8
Rationale: If W were a multiple of 15, the quotient W/15 would be an integer. The fact that it's a decimal tells us that 15 goes into W eight whole times and some decimal part of a time. This decimal part, 0.2 is the remainder divided by the divisor. Let R be the remainder.
R/15 = 0.2 = 1/5
R = (15)*(1/5) = 3
Answer =(C)
Answer: (C) C.3
Question: How many positive integers less than 50 are multiples of 3 but NOT multiples of 5?
(A) 4
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: IMO the answer is C (8 numbers)
The LCM of 3 and 5 is 15.
If x <50 and x is divisible by 3 not by 5 --> x is NOT divisible by 15.
From 1--> 50, we have 3 numbers which is divisible by 15: 15, 30, 45.
From 1-->50, we have (45-3)/3 +1 =15 numbers divisible by 3.
Therefore, our answer is 15-3 = 12 numbers.
E
Answer: (E) 12
Question: Find the surface area of a 10 cm x 4 cm x 2 cm brick.
(A) 136 cu cm
(B) 124 cu cm
(C) 164 cu cm
(D) 180 cu cm
(E) None
Rationale: Sol.
Surface area = [2(10 x 4 + 4 x 2 + 10 x 2)]
= (2 x 68)
= 136 cu cm
Answer A
Answer: (A) 136 cu cm