Is xy < 6 (1) x < 3 and y < 2 (2) 1/2 < x < 2

[BTGmoderatorDC]

Is \(xy < 6\) ?

(1) \(x < 3\) and \(y < 2\)

(2) \(\frac{1}{2} < x < \frac{2}{3}\) and \(y^2 < 64\)




OA B

Source: Official Guide

[Brent@GMATPrepNow]

Is \(xy < 6\) ?

(1) \(x < 3\) and \(y < 2\)

(2) \(\frac{1}{2} < x < \frac{2}{3}\) and \(y^2 < 64\)

Target question: Is xy < 6?

Statement 1: x < 3 and y < 2
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 0. In this case, xy = (0)(0) = 0. So, the answer to the target question is YES, xy IS less than 6
Case b: x = -5 and y = -5. In this case, xy = (-5)(-5) = 25. So, the answer to the target question is NO, xy is NOT less than 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 1/2 < x < 2/3 and y² < 64
Let's see if we can find the greatest possible value of xy.
Since we can see that x is POSITIVE, the maximum value of xy will be achieved when y is also POSITIVE
From the inequality y² < 64, we can conclude that y < 8
He also know that x < 2/3
(8)(2/3) = 16/3 = 5 1/3 (which is less than 6)

Since x < 2/3 and y < 8, we can be certain that xy is less than 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent