AbeNeedsAnswers wrote:If a and b are integers, and b > 0, does (a−1)/(b+1) = a/b ?
(1) a = b − 4
(2) a = -b
B
Source: Official Guide 2020
Given: a and b are integers, and b > 0
Target question: Does (a - 1)/(b + 1) = a/b?
This is a good candidate for
rephrasing the target question.
Take the equation:
(a - 1)/(b + 1) = a/b
Cross multiply to get:
(b)(a - 1) = (a)(b + 1)
Expand both sides to get:
ab - b = ab + a
Subtract ab from both sides to get:
-b = a
Add b to both sides to get:
0 = a + b
REPHRASED target question: Does a + b = 0?
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: a = b − 4
Let's TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = -2 and b = 2. In this case, a + b = (-2) + 2 = 0. So, the answer to the target question is
YES, a+b = 0
Case b: a = -1 and b = 3. In this case, a + b = (-1) + 3 = 2. So, the answer to the target question is
NO, a+b does NOT equal 0
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: a = -b
Add b to both sides to get:
a + b = 0
The answer to the target question is
YES, a+b = 0
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
