# GRE® Quantitative Comparison | Algebra Q3

#### GRE Sample Questions | Polynomial Comparison

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
$$frac{1}{\frac{x}{y} + \frac{y}{x}}$ $\frac{1}{\frac{x}{y} - \frac{y}{x}}$ 1. Quantity A is greater 2. Quantity B is greater 3. The two quantities are equal 4. Cannot be determined ## Get to 170 in GRE Quant #### Online GRE Courses From INR 2999 ### Video Explanation ## GRE Live Online Classes #### Starts Fri, August 26, 2022 ### Explanatory Answer #### Step 1 of solving this GRE Algebra Question: Evaluate both the quantities Quantity A: $\frac{1}{\frac{x}{y} + \frac{y}{x}}$ = $\frac{1}{\frac{x^2 + y^2}{xy}}$ = $\frac{xy}{x^2 + y^2}$ Quantity B: $\frac{1}{\frac{x}{y} - \frac{y}{x}}$ = $\frac{1}{\frac{x^2 - y^2}{xy}}$ = $\frac{xy}{x^2 - y^2}$ #### Step 2 of solving this GRE Algebra Question: Compare Using Counter Examples Example: x = 4, y = 2; x > y Quantity A: $\frac{xy}{x^2 + y^2}$ = $\frac{4 × 2}{4^2 + 5^2}$ = $\frac{8}{20}$ Quantity B: $\frac{xy}{x^2 - y^2}$ = $\frac{4 × 2}{4^2 - 5^2}$ = $\frac{8}{12}$ Quantity B > Quantity A Counter Example: x = 4, y = −2; x > y Quantity A: $\frac{xy}{\text{x^2 + y^2}$}) = $\frac{4 ×$-2$}{4^2 + (-2)^2}) = $$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 #### GRE Online Course - QuantTry it free! Register in 2 easy steps and Start learning in 5 minutes! #### Already have an Account? #### GRE Live Online Classes Next Batch August 26, 2022 ##### Where is Wizako located? Wizako - GMAT, GRE, SAT Prep An Ascent Education Initiative 14B/1 Dr Thirumurthy Nagar 1st Street Nungambakkam Chennai 600 034. India Work @ Wizako ##### How to reach Wizako? Mobile:$91) 93800 48484
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