mathewhe/aqua_rat huggingface dataset:
Question: Solve the equation:
|(2x + 1)2 - 4x2 - 2| - 3|4x – 1| = - 6
(A) -1/2
(B) 1/2
(C) -3/4
(D) 3
(E) None
Rationale: Solution:
|(2x + 1)2 - 4x2 - 2| – 3|4x -1| = - 6 <=>
|4x2 + 4x + 1 - 4x2 - 2 | - 3|4x - 1| = - 6 <=>
|4x – 1| - 3|4x – 1| = - 6 <=> -2|4x – 1| = - 6 <=>
|4x – 1| = 3 <=> 4x - 1 = 3 or 4x - 1 = -3
Therefore x = 1 or x = -1/2
Answer A
Answer: (A) -1/2
Question: How many positive integers less than 500 can be formed using the numbers 1,2,3,and 5 for digits, each digit being used only once.
(A) 22
(B) 34
(C) 73
(D) 26
(E) 11
Rationale: Single digit numbers = 4
Double digit numbers = 4 x 3 = 12
Three digit numbers = 3 x 3 x 2 x 1 = 18
Total = 34
Answer:B
Answer: (B) 34
Question: A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ?
(A) 144
(B) 265
(C) 177
(D) 156
(E) 199
Rationale: Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
B's share = Rs. (378 * 8/21) = Rs. 144.
Answer: A
Answer: (A) 144
Question: The LCM of two numbers is 2310 and HCF is 61. If one of the numbers is 210. Then what is the other number ?
(A) 715
(B) 671
(C) 330
(D) 582
(E) 465
Rationale: First number * Second Number = LCM * HCF
Other number = 2310 * 61 / 210 = 11*61 = 671
ANSWER :B
Answer: (B) 671
Question: Three integers are at random chosen between 0 and 9 inclusive. What is the probability Q that each number is different ?
(A) A.18/25
(B) B.4/5
(C) C.81/100
(D) D.9/10
(E) E.1
Rationale: Number of ways of choosing the 3 integers without restriction = 10 * 10 * 10
Number of ways of choosing the 3 integers so that the 3 integers are different = 10 * 9 * 8
Probability Q= 10 * 9 * 8/10 * 10 * 10 = 72/100 = 18/25
Answer: A
Answer: (A) A.18/25
Question: If n = 3^10 – 2^10 which of the following is NOT a factor of n?
(A) 43
(B) 437
(C) 23
(D) 19
(E) 373
Rationale: 3^10 - 2^10
= (3^5)^2 - (2^5)^2
=(3^5 + 2^5)(3^5- 2^4)
=(405+32(405-32)
=437*373
=19*23*373
Therefore, 43 is Not a factor of n.
A
Answer: (A) 43
Question: A flagpole 18 meters high casts a shadow of length 45 meters. If a building under similar conditions casts a shadow of length 60 meters, what is the height of the building (in meters)?
(A) 20
(B) 24
(C) 28
(D) 32
(E) 36
Rationale: The height:length ratio will be equal in both cases.
18 / 45 = x / 60
x = 24
The answer is B.
Answer: (B) 24
Question: If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:
(A) 3:1
(B) 3:2
(C) 3:5
(D) 3:7
(E) None of these
Rationale: Explanation:
Let the edges be a and b of two cubes, then
a3/b3=27/1
=>(a/b)3=(3/1)3
a/b=3/1
=>a:b=3:1
Option A
Answer: (A) 3:1
Question: The length of a train and that of a platform are equal. If with a speed of 72 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
(A) 600
(B) 799
(C) 719
(D) 750
(E) 712
Rationale: Speed = [72 * 5/18] m/sec = 20 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 20 Ã¨ x = 20 * 60 / 2 = 600
Answer: A
Answer: (A) 600
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 11km apart, if they walk in the same direction?
(A) 15 hours
(B) 16 hours
(C) 17 hours
(D) 20 hours
(E) 22 hours
Rationale: The relative speed of the boys = 5.5kmph â€“ 5kmph
= 0.5 kmph
Distance between them is 11 km
Time = Distance/Speed
Time=11km / 0.5 kmph = 17 hrs
answer :E
Answer: (E) 22 hours
Question: A certain kind of fuel is 1515high octane and 4545regular octane. If high octane costs three times as much as regular octane, what fraction of the cost of the fuel is due to the high octane?
(A) 1/5
(B) 2/3
(C) 3/7
(D) 3/5
(E) 4/5
Rationale: let x be the amount of fuel
high octane = x/5
regular = 4x/5
price of regular = y
price of high octante = 3y
cost of high octane in the fuel = 3y * x/5
total cost = 3y * x/5 + 4x/5 * y
% = cost of high octante / total cost
= 3/7
Answer is C
Answer: (C) 3/7
Question: One robot builds a robot in 1 hour, another one builds a robot in 2 hours. The 2 robots work together and when a new robot is complete, it joins the others, working at a constant rate of one robot in 2 hours. How much time will it take until there are 8 robots altogether, if the robots build only one robot at a time?
(A) 70 min
(B) 94 min
(C) 110 min
(D) 131 1/7 min
(E) 146 1/7 min
Rationale: First the 2 robots work at the rate of
1 + 1/2 = 3/2
so they complete one robot in 2/3 rd of an hour = 40 minutes - (1)
Now the 3 robots work together at the rate of
1 + 1/2 + 1/2 = 4/2 = 2/1
so they complete one robot in 1/2 an hour,i.e 30 minutes - (2)
Now the 4 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 = 5/2
so they complete one robot in 2/5th of an hour - (3)
Now the 5 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2+1/2 = 3
so they complete one robot in 1/3th of an hour - (4)
Now the 6 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=7/2
so they complete one robot in 2/7th of an hour - (5)
Now the 7 robots work together at the rate of
1 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2 + 1/2=9/2
so they complete one robot in 2/9th of an hour - (6)
And now we have 8 robots
So Total = (1) + (2) + (3)+(4)+(5) + (6) = 146 1/7minutes
Answer - E
Answer: (E) 146 1/7 min
Question: Rice weighing 35/2 pounds was divided equally and placed in 4 containers. How many ounces of rice were in each container? (Note that 1 pound = 16 ounces)
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: 35/2 ÷ 4 = 35/8 pounds in each container
35/8 pounds * 16 ounces / pound = 70 ounces in each container
The answer is D.
Answer: (D) 70
Question: Oil cans x and y are right circular cylinders and the height and radius of y are each twice those of x. If the oil in can x filled to capacity sells for $3, how much does the oil in y sell for if y is only half filled?
(A) $11
(B) $12
(C) $13
(D) $14
(E) $18
Rationale: formula for vol of a cyl is PI*r^2*h
so Vy = 8*Vy
y when half filled will cost 4 times x so ans is B
Answer: (B) $12
Question: What is the area of a square field whose diagonal of length 22 m?
(A) 287
(B) 269
(C) 270
(D) 242
(E) 230
Rationale: d2/2 = (22 * 22)/2
= 242
Answer:D
Answer: (D) 242
Question: If the average of t, b, c, 14 and 15 is 12. What is the average value of t, b, c and 29
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: t+b+c+14+15 = 12*5 = 60
=>t+b+c = 60-29 = 31
t+b+c+29 = 31+29= 60
Average = 60/4 = 15
Answer D
Answer: (D) 15
Question: Two sides of a triangle have length 6 and 8. Which of the following are possible areas of the triangle?
I. 2
II. 22
III. 24
(A) I, II, and III
(B) I and II only
(C) II and III only
(D) I and III only
(E) I only
Rationale: Answer = A. I, II, and III
With dimensions of only 2 sides given (for a triangle), this becomes an open ended question
Any area is possible out of the three
Answer: (A) I, II, and III
Question: A table is bought for Rs.400/- and sold at Rs.500/- find gain or loss percentage?
(A) 25%
(B) 30%
(C) 35%
(D) 43%
(E) 45%
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (500 - 400)/400 = 25% gain
A)
Answer: (A) 25%
Question: y = 100 - 398x
Which of the following values of x gives the greatest value of y in the equation above?
(A)  200
(B)  -4
(C)  0.5
(D)  0
(E)  1
Rationale: Clearly, the negative value of x will result in maximum value of y.
Answer is B
Answer: (B)  -4
Question: Two pipes P and Q can fill a cistern in 12 and 10 minutes respectively. Both are opened together, but at the end of 3 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 1/8
(B) 1/2
(C) 2/4
(D) 1/4
(E) 1/4
Rationale: 3/12 + x/10
= 1
x= 8 1/2
Answer: B
Answer: (B) 1/2
Question: 25 percent of the women in a college class are science majors, and the non-science majors make up 80% of the class. What percentage of the men are science majors if 40% of the class are men?
(A) 2%
(B) 12.5%
(C) 28%
(D) 30%
(E) 45%
Rationale: 2.5/k + 2/m = 6/t
Assuming total # is 100 :
[Science - Women] will have - 0.25 * 60 = 15
[Non-Science-Women] will have - 45
[Science-Men] will have = 20-15 = 5
S0 5/40 * 100 = 12.5%
Answer - B
Answer: (B) 12.5%
Question: The number of new words that can be formed by rearranging the letters of the word 'TOO' is
(A) 5
(B) 10
(C) 11
(D) 2
(E) 3
Rationale: Explanation:
Number of words which can be formed = 3! - 1 = 6 - 1 = 5.
Answer: A
Answer: (A) 5
Question: A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 4
(B) 6
(C) 7
(D) 4
(E) 2
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 110 * 3/55
= 6 sec.
Answer: B
Answer: (B) 6
Question: If "BEACH" is given a code of 19, then what is the difference between "SANDCASTLE" and "WAVES"?
(A) 15
(B) 28
(C) 30
(D) 168
(E) 22
Rationale: Case – Codes : A - 1, B - 2, C - 3, D - 4, E - 5, F - 6, G - 7, H - 8, I - 9, J - 10, K - 11, L - 12, M - 13, N - 14, O - 15, P - 16, Q - 17, R - 18, S - 19, T - 20, U - 21, V - 22, W - 23, X - 24, Y - 25, Z - 26
SANDCASTLE: 98
WAVES: 70
Answer: B
Answer: (B) 28
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 50 white marbles. How many red marbles could be in bag A?
(A) 1
(B) 5
(C) 4
(D) 6
(E) 8
Rationale: 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4k
W =50 = 6K+4k
=> k= 5
Total Red's in bag A will be 2K = 10
B
Answer: (B) 5
Question: How much time is required to cover the distance of 910 Km by a car driver, if he start with the initial speed of 40 Km/hr. and increases the speed by 5 Km/hr for every next hour ?
(A) 11 hours
(B) 12 hours
(C) 13 hours
(D) 14 hours
(E) 15 hours
Rationale: IT is AP series problem where
a= 40, d=5 , sum = 910
and n=?
910 = (n/2)*(2*40+(n-1)*5)
5n^2+75n-1820=0
n^2+15n-364=0
solving it, we get
n=13
so 13 hours
ANSWER:C
Answer: (C) 13 hours
Question: Sandy purchased 20 dozen toys at the rate of $360 per dozen. Sandy sold each toy at the rate of $31.50. What was the percentage profit?
(A) 3%
(B) 5%
(C) 7%
(D) 9%
(E) 11%
Rationale: A dozen toys cost $360, so each toy cost $30.
selling price / cost price = 31.50 / 30 = 1.05
The percentage profit is 5%.
The answer is B.
Answer: (B) 5%
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 25 seconds. Find the length of the faster train?
(A) 270
(B) 250
(C) 187
(D) 257
(E) 271
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 25 sec = 25 * 10 = 250 m.
The length of the faster train = 250 m.
Answer: B
Answer: (B) 250
Question: A departmental store charges the commission of 15 percent on the first sale of items worth $50,000 and then an additional 10 percent on any sale price that exceeds the initial $50,000. If the department store earned $24,000 in commissions for the sale of a series of diamonds, what was the sale price of the diamond set?
(A) $215,000
(B) $365,000
(C) $115,000
(D) $240,000
(E) $160,000
Rationale: Lets start with looking at the options. All options are above 50,000 -> Thus the total commission will be the sum of 15% of 50,000 and 10% of the rest of the amount.
Let's start with calculating 15% of 50,000 = 7,500.
So out of the total commission of 24000, 7500 was earned on the first 50,000. Commission remaining = 24,000 - 7500 = 16,500
16,500 is actually the 10% of the rest of the amount => 165,000
So total sales = 50,000 + 165,000 = 215,000
ANSWER:A
Answer: (A) $215,000
Question: Two trains of equal length 120 metres move in the same direction. The faster train completely
overtakes the slower one in 15 seconds. If the slower train were to move at half its speed, the over
taking would take in 10 seconds. At what speeds are the 2 trains moving (faster and slower respectively
in m/s)
(A) 24, 22
(B) 32, 16
(C) 30, 18
(D) 28, 14
(E) None of these
Rationale: The total distance covered for over taking = length of the two trains = 120 +120 = 240
Speed of faster train be x m/s and slower train be y m/s
In the first case Relative speed = x-y
Relative Speed = Distance / Time taken = x-y = 240/15 = 16 m/s………(1)
In the second case, the slower train moves at half its speed
Relative Speed = x-0.5y = 240/10 = 24 m/s …………………..(2)
Solving equation 1 & 2 we get x = 32 and y = 16 .
:. The speed of the faster and slower trains are 32 m/s and 16 m/s respectively
Answer: B
Answer: (B) 32, 16
Question: 35 percent of the women in a college class are science majors, and the non-science majors make up 70% of the class. What percentage of the men are science majors if 40% of the class are men?
(A) 20%
(B) 25%
(C) 22.5%
(D) 30%
(E) 45%
Rationale: 3.5/k + 2/m = 6/t
Assuming total # is 100 :
[Science - Women] will have -> 0.35 * 60 = 21
[Non-Science-Women] will have -> 39
[Science-Men] will have = 30-21 = 9
S0 9/40 * 100 = 22.5%
Answer -C
Answer: (C) 22.5%
Question: Ratio of Rani's and Kamal's age is 3:5. Ratio of Kamal's and Pooja's age is 2:3.If Rani's age is two-fifth of Pooja's age, what is Rani's age?
(A) 10 years
(B) 15 years
(C) 24 years
(D) Cannot be determined
(E) None of these
Rationale: Solution:Here in this question only ratio is given.No other information like sum ,difference or product is given.So given data is inadequate to find a solution.
Answer D
Answer: (D) Cannot be determined
Question: If the operation @ is defined for all a and b by the equation a@b =(a^b)/2,then (3@2)=?
(A) 4
(B) 2
(C) 9/2
(D) -9/2
(E) -8/2
Rationale: work within the parenthesis first so solve (3@2) first
(3@2)=(3^2)/2=9/2
so 9/2 is the answer....this question is merely testing order of operations
remember PEMDAS
Answer:C
Answer: (C) 9/2
Question: The length of the bridge, which a train 180 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 876 m
(B) 157 m
(C) 195 m
(D) 156 m
(E) 167 m
Rationale: Speed = [45 X 5/18] m/sec
= [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (180 + x)/30 = 25/2
=> 2(180 + x) = 750 => x
= 195 m.
Answer: C
Answer: (C) 195 m
Question: Albert invested Rs. 8000 in a scheme for 2 years at compound interest rate 5% p.a. How much amount will Albert get on maturity of the fixed deposit?
(A) Rs.8829
(B) Rs.8820
(C) Rs.8822
(D) Rs.8289
(E) Rs.8820
Rationale: Amount = [8000 * (1 + 5/100)2]
= 8000 * 21/20 * 21/20
= Rs.8820
Answer:E
Answer: (E) Rs.8820
Question: The average age of a husband and a wife is 25 years when they were married nine years ago but now the average age of the husband, wife and child is 23 years(the child was born during the interval). What is the present age of the child?
(A) 2 years
(B) 5 years
(C) 9 years
(D) 4 years
(E) 1 years
Rationale: 34 * 2 = 68
23 * 3 = 69
-----------
1 years
Answer:E
Answer: (E) 1 years
Question: An alchemist discovered that the formula expressing the correct proportions needed to turn ordinary metal into gold is G = 3/2M + 25, where G is the number of gold bars and M is the number of metal bars. If a metal bar weighs twice as much as a gold bar, how many metal bars will yield an equal weight of gold?
(A) a.	A - 10
(B) b.	B - 15
(C) c.	C – 22.5
(D) d.	D – 30
(E) e.	E – 67.5
Rationale: A --- 30/2 + 15 = 40 --- wrong
B --- 45/2 + 15 = not an integer --- wrong
C --- 22.5(3/2) + 15 = not an integer --- wrong
D --- 90/2+15 = 70 --- CORRECT
This is one of those problems that will probably be easiest to solve by plugging in numbers. The algebra is do-able, but it's not worth the effort (in my opinion). I was able to solve it in under 30 seconds total with this method.
A
Answer: (A) a.	A - 10
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 176 sec
(B) 30 sec
(C) 766 sec
(D) 165 sec
(E) 186 sec
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer:B
Answer: (B) 30 sec
Question: Sum of 24 odd numbers is?
(A) 572
(B) 573
(C) 574
(D) 575
(E) 576
Rationale: sum of 1st n odd no.s = 1+3+5+7+... = n^2
so, Sum of 1st 24 odd numbers = 24^2 = 576
ANSWER:E
Answer: (E) 576
Question: A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered.If the area of the field is 680 sq.ft, how many feet of fencing will be required ?
(A) 88 feet
(B) 86 feet
(C) 84 feet
(D) 82 feet
(E) None of these
Rationale: Explanation:
We are given with length and area, so we can find the breadth.
as Length * Breadth = Area
=> 20 * Breadth = 680
=> Breadth = 34 feet
Area to be fenced = 2B + L = 2*34 + 20
= 88 feet
Option A
Answer: (A) 88 feet
Question: In a dance competition the points in each round for the first,second,third and fourth position were 1000,500,200,100 . No other points were given. Reney participated in several rounds in the competition and the product of her score was 100000. In How many rounds did she participate?
(A) 4
(B) 2
(C) 5
(D) Cannot be determined
(E) 20
Rationale: Correct answer is D 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 50 rounds out of only 7 rounds were there in which she was awarded some points.
Answer: (D) Cannot be determined
Question: What is the area of square field whose side of length 8 m?
(A) 225
(B) 64
(C) 772
(D) 882
(E) 21
Rationale: 8 * 8
= 64 sq m
Answer:B
Answer: (B) 64
Question: What distance will be covered by a bus moving at 54 kmph in 30 seconds?
(A) 287
(B) 900
(C) 289
(D) 276
(E) 207
Rationale: 54 kmph = 54 * 5/18
= 30 mps
D = Speed * time = 30 * 30
= 900 m.
Answer:B
Answer: (B) 900
Question: A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?
(A) 8
(B) 9
(C) 6
(D) 4
(E) 2
Rationale: Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.
Answer:D
Answer: (D) 4
Question: x, y and z are consecutive positive integers such that x < y < z; which of the following must be true?
1. xyz is divisible by 8
2. (z-x)(y-x+1) = 4
3. xy is odd
(A) I and II
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: Since x, y and z are consecutive integers such that x < y < z, we can say x = y-1 and Z = y+1
Statement 1 would be true as at least one of the three numbers is divisible by 2 and one by 4 so xyz would be divisible by 8.
Statement 2 can be simplified if we write everything in terms of y as ((y+1)-(y-1))*(y-(y-1)+1) = 2*2 = 4 So, always true
Statement 3 talks about xy Since x and y are consecutive integers one of them is odd and other is even so product would always be even and hence not true.
So, I and II are always true and hence answer
A
Answer: (A) I and II
Question: When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 19?
(A) 7
(B) 21
(C) 13
(D) 47
(E) 55
Rationale: Số thẻ number given is N = 143Q + 45
If this number is divided by 13, the remainder would be R[(143Q + 45)/13]
Since 143 is divisible by 13 , the product 143Q gives no remainder
This means the remainder of 45/13 should be the remainder of the entire number N
which is 6
To make it divisible by 13 , the smallest number that can be added = 19 - 6 =13
Correct Option : C
Answer: (C) 13
Question: (3164 + 6160) / 28
(A) 380
(B) 350
(C) 333
(D) 310
(E) None of these
Rationale: Explanation:
As per BODMAS rule, first we will solve the equation in bracket then we will go for division
= (9324)/28 = 333
Option C
Answer: (C) 333
Question: There are 193 items that are members of set U. Of these items, 47 are members of set B, 59 are not members of either of set A or set B, and 23 are members of both sets A and B. How many of the members of set U are members of set A ?
(A) 72
(B) 85
(C) 94
(D) 106
(E) 108
Rationale: You had the answer almost right. The x = 83 refers to ONLY set A.
However what's being asked is how many members are part of set A. This will include:
1. Only Set A
2. Set A and Set B
So the answer is Set A = 85 + Set AB = 83+23 = 106
D
Answer: (D) 106
Question: A batsman in his 12th innings makes a score of 75 and thereby increases his average by 1 runs. What is his average after the 12th innings if he had never been ‘not out’?
(A) 42
(B) 43
(C) 44
(D) 64
(E) 46
Rationale: Let ‘x’ be the average score after 12 th innings
⇒ 12x = 11 × (x – 1) + 75
∴ x = 64
Answer D
Answer: (D) 64
Question: One morning after sunrise, Suresh was standing facing a pole. The shadow of the pole fell exactly to his right. To which direction was he facing?
(A) East
(B) West
(C) South
(D) North
(E) 2891
Rationale: Explanation:
Sun rises in the east in the morning. Since the shadow of Suresh falls to his right. So he is facing South.
Answer: C) South
Answer: (C) South
Question: A certain drink of type A is prepared by mixing 4 parts milk with 3 parts fruit juice. Another drink of type B is prepared by mixing 4 parts of fruit juice and 3 parts of milk. How many liters of fruit juice must be added to 105 liters of drink A to convert it to drink B?
(A) 14
(B) 21
(C) 28
(D) 35
(E) 42
Rationale: In 105 liters of drink A, there are 60 liters of milk and 45 liters of juice.
With 60 liters of milk, we need a total of 80 liters of juice to make drink B.
We need to add 35 liters of juice.
The answer is D.
Answer: (D) 35
Question: Given positive even integer x, which of the following CAN NOT be evenly divisible by x?
(A) x + 1
(B) x + 2
(C) 2x + 4
(D) 3x − 2
(E) 7x
Rationale: This can be easily solved by substituting values:
Assume x to be 2
A. x + 1: 3 is not evenly divisible by 2
B. x + 2: 4 is evenly divisible by 2
C. 2x + 4: 8 is evenly divisible by 2
D. 3x − 2: 4 is evenly divisible by 2
E. 7x: 14 is evenly divisible by 2
Option A
Answer: (A) x + 1
Question: 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 3 kg more than D Replaces A, Then the avgof B,C,D&E becomes 79 kg. What is the weight of A?
(A) 56
(B) 65
(C) 75
(D) 89
(E) 90
Rationale: A + B + C = 3 *84 = 252
A + B + C + D = 4 * 80 = 320 ---- (i)
So, D = 68& E = 68 + 3 = 71
B + C + D +E = 79 * 4 = 316 --- (ii)
From Eq. (i) & (ii)
A-E = 320 – 316 = 4
A = E +4 = 71 + 4 = 75
C
Answer: (C) 75
Question: A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in:
(A) 4 days
(B) 6 days
(C) 8 days
(D) 10 days
(E) 12 days
Rationale: Suppose A, B and C take x,x/2 and x/3	days respectively to finish the work.
Then,	1/x+2/x+3/x=1/2
6/x = 1/2
x = 12.
So, B takes (12/2) = 6 days to finish the work.
answer :B
Answer: (B) 6 days
Question: My grandson is about as many days as my son in weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 150 years. Can you tell my son age in years?
(A) 63 years
(B) 60 years
(C) 50 years
(D) 53 years
(E) 46 years
Rationale: Let m be my age in years. If s is my son's age in years, then my son is 52s weeks old. If g is my grandson's age in years, then my grandson is 365g days old. Thus,365g = 52s.Since my grandson is 12g months old,12g = m.Since my grandson, my son and I together are 150 years,g + s + m = 100.The above system of 3 equations in 3 unknowns (g, s and m) can be solved as follows:52s / 365 + s + 12 x (52s / 365) = 150 or52s + 365s + 365 x (624s / 365) = 365 x 150 ors = 54,750 / 1,041 = 53 yearsAnswer = D
Answer: (D) 53 years