GRE® Quantitative Comparison Q2

Algebra | GRE Sample Questions | Quadratic Equations

This GRE quant sample question is a Quantitative Comparison question in Algebra. Concept tested: Comparison of quadratic equations.

Question 2 : $$frac{x}{y}$ < 0 Quantity A Quantity B$4x + 3y)(x – 6y) 4x2 + 16xy – 18y2

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

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Explanatory Answer | GRE Quantitative Comparison Q2

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

Quantity A: (4x + 3y)(x – 6y) = 4x2 - 24xy + 3xy – 18y2
= 4x2 - 21xy – 18y2

Quantity B: 4x2 + 16xy – 18y2

Step 2 of solving this GRE Algebra Question: Comparison both the Quantities

Quantity A: 4x2 - 21xy – 18y2
Quantity B: 4x2 + 16xy – 18y2

The comparison is essentially between -21xy and 16xy.
We know $$frac{x}{y}$ < 0 i.e., one of x or y is positive and the other is negative. Therefore, we can infer that xy < 0 If xy is negative, then -21xy will be positive and 16xy will be negative. A positive value is greater than a negative value. Hence, Quantity A > Quantity B. Choice A 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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