BTGModeratorVI wrote: ↑

Thu Aug 20, 2020 7:16 am

Is x < y?

(1) 1/x < 1/y
(2) x/y < 0

Answer: C
Source: Manhattan prep

Target question: Is x < y?

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

Statement 2: x/y < 0
This tells us that x and y have OPPOSITE signs, but we don't have any information about which variable is positive and which variable is negative.
So, there's no way to tell whether x < y
Since we can't answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that x and y have OPPOSITE signs
Statement 1 tells us that 1/x < 1/y. If x and y have OPPOSITE signs, then we can be certain that x is NEGATIVE and y is POSITIVE.

Take: 1/x < 1/y
Multiply both sides by x to get: 1 > x/y [since we multiplied both sides by a NEGATIVE value, we REVERSED the direction of the inequality symbol]
Multiply both sides by y to get: y > x
Perfect! The answer to the target question is YES, x is less than y
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent