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 |
Quantity A: (4x + 3y)(x – 6y) = 4x2 - 24xy + 3xy – 18y2
= 4x2 - 21xy – 18y2
Quantity B: 4x2 + 16xy – 18y2
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.
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