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Gurome's Quant Blog Series - Arithmetic Q6


So far we have covered Algebra in our Quant Blog Series to help you with your GMAT test prep. From this week onwards, we will be looking at few questions and tips on Arithmetic. Here is the question for this week. You can check the correct answers and the explanation on Friday.

If x = z/(x + y) and xy = 3, which of the following values can z take?

(A)  -2.5

(B)  -2

(C)  -1

(D)  2

(E)   4

Solution

If x = z/(x + y) then x2 + xy = z or x2 = z - xy

Since a perfect square is always positive, z - xy ≥ 0

Or zxy

Since z cannot be less than xy, if xy is 3, z cannot take values -2.5, -2, -1 or 2.

But it can take the value 4.

The correct answer is (E).


Note:

Ø  In these types of questions, the answer is easy to find if we use the given information in the question appropriately. So, always try to make use of all the given expressions in the question.

Ø  In the above case, we cross-multiplied the terms so that we get a perfect square on one of the sides and we know a perfect square is always positive.

Ø  When we put the left hand side to be greater than equal to zero, the right hand side also will be greater than equal to zero, that is zxy and the value of xy is given to us. So, z ≥ 3 and 4 is the only option from the given answer choices.

Difficulty level: 500


Gurome's Quant Blog Series is a repository of Free GMAT Questions which focuses primarily on the Quantitative section of GMAT. To receive regular updates about our Quant Blog Series, follow us on Facebook and Twitter.



Posted by Ryan Cooper at Jul 7, 2010 10:58:15 AM
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