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Gurome's Quant Blog Series - Fractions, Decimals and Percentages A13


The correct answer along with the explanation to yesterday's question in the Quant Blog series is as follows:


Explanation:

It is given that c is the hypotenuse and a is one of the perpendicular sides. Let us assume the other perpendicular side to be b.

By Pythagoras Theorem, b = √(c2 - a2)

Area of the triangle = 0.5 × a × b = 0.5 × a × √(c2 - a2)

When c is increased by 25%, it becomes c + 0.25c = 1.25c = 5c/4.

Hence, the new area is 0.5 × a × √(25c2/16 - a2)

So, percentage change in area =

[0.5 × a × √(25c2/16 - a2) - 0.5 × a × √(c2 - a2)] × 100 / [0.5 × a × √(c2/a2 - 1)]

Note: A simple way to calculate the above expression is to cancel 0.5 × a from both numerator and denominator and then dividing both of them by a.

So, we get percentage change in area = [√(25c2/16a2 - 1) - √(c2/a2 - 1)] × 100 / [√(c2/a2 - 1)]

Now, to know percentage change we need to know both c and a individually or their ratios.

(1)  Hypotenuse c = 3. The value of c is given but not of a.

So, (1) is NOT SUFFICIENT to answer the question.

(2)  c/a = 5 implies c2/a2 = 25.

Percentage change = [√(25 × 25)/16 - 1] - [√(25 - 1)] × 100 / [√(25 - 1)]  

Note: The above expression can be easily calculated to get a definite value. But no need to calculate it as this is a data sufficiency question.

So, (2) is SUFFICIENT to answer the question.

The correct answer is (B). Statement (2) alone is sufficient, but statement (1) is not sufficient.


Difficulty Level: 600


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Posted by kalyani at Sep 3, 2010 3:33:13 PM
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