## Is $$a > |b|?$$

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### Is $$a > |b|?$$

by BTGmoderatorDC » Wed May 22, 2019 3:22 am

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## Global Stats

Is $$a > |b|?$$

(1) $$2^{a-b} > 16$$
(2) $$|a - b| < b$$

OA C

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by ceilidh.erickson » Sat May 25, 2019 12:05 pm

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## Global Stats

Is $$a > |b|?$$
Since this question contains an absolute value, we must be sure to think about NEGATIVE as well as positive possibilities.
(1) $$2^{a-b} > 16$$
First, get like bases:
$$2^{a-b}>2^4$$

We can infer:
$$a-b>4$$
$$a>b+4$$

Since a is greater than b+4, it must also be greater than b itself. But be careful! That doesn't mean a>|b|.

Think of examples where a and b are both negative:
a = -1
b = -6
This satisfies $$a>b+4$$ but not $$a > |b|$$
(2) $$|a - b| < b$$
This tells us that b must be positive, because it's greater than some absolute value. But this could be true whether a is greater than or less than b:
a = 3
b = 2
|3 - 2| < 2
$$a > |b|?$$ --> yes

a = 2
b = 3
|2 - 3| < 3
$$a > |b|?$$ --> no

This is insufficient.

(1) and (2) together

If $$a>b+4$$ and $$b>0$$, then a must be a positive number greater than b. Thus, the answer to $$a > |b|?$$ is yes.

Ceilidh Erickson
EdM in Mind, Brain, and Education

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by ceilidh.erickson » Sat May 25, 2019 12:10 pm

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## Global Stats

Ceilidh Erickson
EdM in Mind, Brain, and Education