XAT 2015 Quant & DI: Number Properties

This question appeared as a part of the quantitative reasoning and data interpretation section of the XAT 2015. A total of 33 questions appeared in this section in XAT 2015. This one is a medium level difficulty question and the concept tested is that of your ability to reason when the value of an expression will be maximum and find that value. Question 14 of 33.

Question

If a, b, c and d are four different positive integers selected from 1 to 25, then the highest possible value of \\frac{(a + b) + (c + d)}{(a + b) + (c - d)}\\) would be:

1. 47
2. 49
3. 51
4. 96
5. None of the above

  Correct Answer            Choice C. The highest possible value is 51.

Explanatory Answer

Key Inference

In order to get the highest possible value for a fraction:

1. Numerator has to be as high as possible
2. Denominator must be as low as possible.

Approach

Given a, b, c, d are distinct positive integers.
The least possible value of denominator ((a + b) + (c - d)) can be only 1.

We have to maximize the value of the numerator ((a + b) + (c + d)) simultaneously.

We can observe that in numerator 'd' is added and in denominator 'd' is subtracted.

So, if d is given the highest value we can simultaneously maximize the numerator and minimize the denominator.

The obvious choice for is d = 25

If d = 25 and from the denominator we know ((a + b) + (c - d)) = 1
(a + b) + c = 26

Substituting (a + b) + c = 26 and d = 25 in the numerator
we get ((a + b) + (c + d)) = 26 + 25 = 51

Maximum value of the numerator is 51 and the minimum value of the denominator is 1.
\\frac{(a + b) + (c + d)}{(a + b) + (c - d)}\\) = \\frac{51}{1}\\) = 51

  The correct answer is Choice C.

Video Explanation

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