BTGModeratorVI wrote: ↑Tue May 12, 2020 2:13 pm
If xy > 0, does (x - 1)(y - 1) = 1?
(1) x + y = xy
(2) x = y
Answer:
A
Source: Official guide
Given: xy > 0
Target question: Does (x - 1)(y - 1) = 1?
This is a good candidate for
rephrasing the target question
Take the equation:
(x - 1)(y - 1) = 1
Use FOIL to expand the left side to get:
xy - x - y + 1 = 1
Subtract 1 from both sides to get:
xy - x - y = 0
REPHRASED target question: Does xy - x - y = 0?
Statement 1: x + y = xy
Take the REPHRASED target question and replace xy with x+y to get:
Does (x + y) - x - y = 0?
Simplify the left side to get:
Does 0 = 0?
Great! The answer to the REPHRASED target question is
YES, it IS the case that xy - x - y = 0
Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: x = y
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 2 and y = 2. In this case, the equation xy - x - y = 0 becomes (2)(2) - 2 - 2 = 0, which works!
So, the answer to the REPHRASED target question is
YES, it IS the case that xy - x - y = 0
Case b: x = 1 and y = 1. In this case, the equation xy - x - y = 0 becomes (1)(1) - 1 - 1 = 0, which does NOT work.
So, the answer to the REPHRASED target question is
NO, it is NOT the case that xy - x - y = 0
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
