GRE Questions and Answers with Explanation

Q:

Two solutions have milk & water in the ratio 7:5 and 6:11. Find the proportion in which these two solutions should Be mixed so that the resulting solution has 1 part milk and 2 parts water ?

A) 7 : 12	B) 8 : 13
C) 9 : 4	D) 2 : 5

Answer & Explanation Answer: B) 8 : 13

Explanation:

To get the solution that contains 1 part of milk and two parts of water,
they must be mixed in the ratio as
7x+6x/5y+11y = 1/2
26x = 16y
x/y = 16/26
x/y = 8/13

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Filed Under: Ratios and Proportions
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19 12382

Q:

What comes once in a year, twice in a week and never in a day?

A) Sunday	B) New moon day
C) E	D) All of the above

Answer & Explanation Answer: C) E

Explanation:

YEAR - 1 E

WEEK - 2 E

DAY - 0 E

Hence, the letter 'E', comes once in a year, twice in a week and never in a day.

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Filed Under: Logic Puzzles
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9 12381

Q:

One-quarter of one-seventh of a land is sold for Rs. 30,000. What is the value of an four fifteenth of land ?

A) Rs.1,92,000	B) Rs.2,24,000
C) Rs.1,26,000	D) Rs.3,42,000

Answer & Explanation Answer: B) Rs.2,24,000

Explanation:

One-quarter of one-seventh = 1/4 x 1/7
= 1/28
Now, 1/28 of a land costs = Rs. 30,000
Thus, 8/35 of the land will cost = 30,000 x 28 x 4/15
= Rs. 2,24,000.

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Filed Under: Percentage
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15 12375

Q:

If $a^{2} + b^{2} = c^{2}$ , then $\frac{1}{l o g_{c + a} (b)} + \frac{1}{l o g_{c - a} (b)} = ?$

A) 1	B) 2
C) 4	D) 8

Answer & Explanation Answer: B) 2

Explanation:

Given $a^{2} + b^{2} = c^{2}$

Now $\frac{1}{\log_{c + a} (b)} + \frac{1}{\log_{c - a} (b)}$

= $\log_{b} (c + a) + \log_{b} (c - a)$

= $\log_{b} (c^{2} - a^{2})$

= $2 \log_{b} (b) = 2$

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Filed Under: Logarithms
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32 12374

Q:

Two Fathers and Two Sons walk into a ice cream parlour. They each buy something for Rs. 50 but they only spent Rs. 150. How is that possible?

Answer

One grandfather, One father and One son makes two fathers and two sons.

Workspace

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Subject: Logic Puzzles Exam Prep: AIEEE , Bank Exams , CAT , GATE , GRE , TOEFL
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87 12346

Q:

Third proportion of 10 and 20 is

A) 30	B) 40
C) 25	D) 20

Answer & Explanation Answer: B) 40

Explanation:

The third proportional of two numbers p and q is defined to be that number r such that

p : q = q : r.

Here, required third proportional of 10 & 20, and let it be 'a'

=> 10 : 20 = 20 : a

10a = 20 x 20

=> a = 40

Hence, third proportional of 10 & 20 is 40.

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Filed Under: Average
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Q:

If the given two numbers are respectively 7% and 28% of a third number, then what percentage is the first of the second ?

A) 24%	B) 29%
C) 34%	D) 25%

Answer & Explanation Answer: D) 25%

Explanation:

Here, k = 7 and l = 28
Therefore, first number = $\frac{k}{l}$ x100 % of second number = 7/28 x 100% of second number = 25% of second number.

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Filed Under: Percentage
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Q:

Amy has to visit towns B and C in any order. The roads connecting these towns with her home are shown on the diagram. How many different routes can she take starting from A and returning to A, going through both B and C (but not more than once through each) and not travelling any road twice on the same trip?

A) 10	B) 8
C) 6	D) 4

Answer & Explanation Answer: B) 8

Explanation:

Amy can travel clockwise or anticlockwise on the diagram.

Clockwise, she has no choice of route from A to B, a choice of one out of two routes from B to C, and a choice of one out of two routes from C back to A. This gives four possible routes.

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