GRE® Quantitative Comparison | Algebra Q3

The GRE maths sample question given below is a Quantitative comparison problem in Algebra.

Question 3 : x, y ≠ 0 and x > y

Quantity A	Quantity B
\\frac{1}{\frac{x}{y} + \frac{y}{x}})	\\frac{1}{\frac{x}{y} - \frac{y}{x}})

1. Quantity A is greater
2. Quantity B is greater
3. The two quantities are equal
4. Cannot be determined

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Video Explanation

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Explanatory Answer

Step 1 of solving this GRE Algebra Question: Evaluate both the quantities

Quantity A: \\frac{1}{\frac{x}{y} + \frac{y}{x}}) = \\frac{1}{\frac{x^2 + y^2}{xy}})

= \\frac{xy}{x^2 + y^2})

Quantity B: \\frac{1}{\frac{x}{y} - \frac{y}{x}}) = \\frac{1}{\frac{x^2 - y^2}{xy}})

= \\frac{xy}{x^2 - y^2})

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Step 2 of solving this GRE Algebra Question: Compare Using Counter Examples

Example: x = 4, y = 2; x > y

Quantity A: \\frac{xy}{x^2 + y^2}) = \\frac{4 × 2}{4^2 + 5^2}) = \\frac{8}{20})

Quantity B: \\frac{xy}{x^2 - y^2}) = \\frac{4 × 2}{4^2 - 5^2}) = \\frac{8}{12})

Quantity B > Quantity A

Counter Example: x = 4, y = −2; x > y

Quantity A: \\frac{xy}{\text{x^2 + y^2})}) = \\frac{4 × (-2)}{4^2 + (-2)^2}) = \\frac{-8}{20})

Quantity B: \\frac{xy}{x^2 - y^2}) = \\frac{4 × (-2)}{4^2 - (-2)^2}) = \\frac{-8}{12})

Quantity A > Quantity B

A Counter Example exists. Therefore, we will not be able to deduce which of the two quantities is greater.

Choice D is the correct answer