BTGModeratorVI wrote: ↑Wed Feb 26, 2020 4:12 pm
Is xy < 6 ?
(1) x < 3 and y < 2
(2) 1/2 < x < 2/3 and y² < 64
Answer:
B
Source: Official Guide
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
