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

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Thu Nov 07, 2019 11:54 pm
ktrout2020 wrote:If a and b are positive numbers, is a < b?

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

Source: Kaplan
Let's take each statement one by one.

(1) a < b/2 + 2

Say a = 1, then b > -2
(a) Say b = 2, we have a < b. The answer is yes.
(b) Say b = 1/2, we have a > b. The answer is no. No unique answer. Insufficient.

(2) a < b/2 - 2

=> 2a + 2 < b

We see that 2 greater than twice a positive no. (a) is less than a no. (b); thus, a must be less than b. Sufficient.

The correct answer: B

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Fri Nov 08, 2019 6:17 am
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
Brent Hanneson - Creator of GMATPrepNow.com
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