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

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