sacmanitin wrote:
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 6Case 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 6Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: 1/2 < x < 2/3 and y² < 64Let'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 6Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
_________________
Brent Hanneson – Creator of gmatprepnow.com
Before you spend another second preparing for the GMAT, check out my article series, Are you doing it wrong?.
You’ll learn what the GMAT actually tests, and why memorizing a ton of formulas actually makes you less effective.