ktrout2020 wrote:If a and b are positive numbers, is a < b?
(1) a < b/2 + 2
(2) a < b/2 - 2
Source: Kaplan
Target question: Is a < b?
Given: a and b are positive numbers
Statement 1: a < b/2 + 2
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a and b that satisfy statement 1. Here are two:
Case a: a = 0 and b = 2, in which case
a < b
Case b: a = 2.5 and b = 2, in which case
a > b
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: a < b/2 - 2
Since b is POSITIVE, we know that
b/2 < b
We can also say that
b/2 - 2 < b/2
We can COMBINE these inequalities to get:
a < b/2 - 2 < b/2 < b
If we ignore the middle parts, we see that
a < b
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
