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bkpolymers1617
If a and b are positive numbers, is a < b?

(1) a < b/2 + 2
(2) a < b/2 - 2

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:
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