Bunuel wrote:

\(\frac{5}{(\frac{\sqrt{7}+1}{\sqrt{7}-1})}\)

A. \(40-15\sqrt{7}\)

B. \(40-\frac{\sqrt{7}}{3}\)

C. \(40-\frac{\sqrt{7}}{3}\)

D. \(\frac{125-5\sqrt{7}}{3}\)

E. \(\frac{20-5\sqrt{7}}{3}\)

Hi...

\(\frac{5}{(\frac{\sqrt{7}+1}{\sqrt{7}-1})}..........\frac{5*(√7-1)}{√7+1}\)

√7-1 is lesser than √7+1, so our answer has to be LESS than 5..

Except E all are clearly much more than 5, so E is the answer.

Otherwise

\(\frac{5(√7-1)(√7-1)}{(√7+1)(√7-1)}=\frac{5*(7+1-2√7)}{7-1}=\frac{40-10√7}{6}=\frac{20-5√7}{3}\)

E

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372

2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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