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which of the following is true?

Expert replies
by Max@Math Revolution » Mon Apr 02, 2018 11:07 pm
[GMAT math practice question]

$$If\ a\ =\sqrt{\sqrt{\frac{1}{5}}+\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{2}}},\ b=\ \sqrt{\sqrt{\frac{1}{5}}-\sqrt{\frac{1}{3}}+\sqrt{\frac{1}{2}}},\ c=\sqrt{-\sqrt{\frac{1}{5}}+\sqrt{\frac{1}{3}}+\sqrt{\frac{1}{2}}},\ which\ of\ the\ following\ is\ true?$$

A. a < c < b
B. a < b < c
C. c < b < a
D. c < a < b
E. b < a < c
Last edited by Max@Math Revolution on Mon Apr 09, 2018 11:44 pm, edited 1 time in total.
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Source: — Problem Solving |

by Jake@ThePrincetonReview » Wed Apr 04, 2018 1:50 pm
Hmm. Those answer choices are illegible. Let me try to fix that:

A. a < c < b
B. a < b < c
C. c < b < a
D. c < a < b
E. b < a < c

Jake Schiff
GMAT Instructor and Master Trainer

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by Max@Math Revolution » Thu Apr 05, 2018 3:22 am
Since $$\sqrt{\frac{1}{5}}<\sqrt{\frac{1}{3}}<\sqrt{\frac{1}{2}}$$

We have $$\sqrt{\frac{1}{5}}+\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{2}}<\sqrt{\frac{1}{5}}-\sqrt{\frac{1}{3}}+\sqrt{\frac{1}{2}}<\ -\sqrt{\frac{1}{5}}+\sqrt{\frac{1}{3}}+\sqrt{\frac{1}{2}}$$

So $$\sqrt{\sqrt{\frac{1}{5}}+\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{2}}}<\sqrt{\sqrt{\frac{1}{5}}-\sqrt{\frac{1}{3}}+\sqrt{\frac{1}{2}}}<\sqrt{-\sqrt{\frac{1}{5}}+\sqrt{\frac{1}{3}}+\sqrt{\frac{1}{2}}}$$

Thus c < b < a.

Therefore, C is the answer.

Answer: C
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