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If a – b < 0 and ab < 0,

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If a – b < 0 and ab < 0,

by Max@Math Revolution » Fri Mar 06, 2020 2:01 am

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[GMAT math practice question]

If a – b < 0 and ab < 0, what is \(\sqrt{a^2-2ab+b^2}+\sqrt{a^2}\) - |b|?

A. -2a
B. -a
C. ab
D. b
E. 3b
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Re: If a – b < 0 and ab < 0,

by Max@Math Revolution » Sun Mar 08, 2020 6:21 pm
=>

Since a – b < 0 and ab < 0, we have b > 0 and a < 0.

\(\sqrt{a^2-2ab+b^2}+\sqrt{a^2}\) - |b|
= \(\sqrt{\left(a-b\right)^2}\) +|a|-|b|
= |a - b| + |a| - |b|
= -(a - b) + (-a) – b since a – b < 0, a < 0, b > 0
= -a + b – a – b
= -2a

Therefore, A is the answer.
Answer: A
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