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# 5/(7^(1/2)+1)/(7^(1/2)-1)

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Math Expert
Joined: 02 Sep 2009
Posts: 47161

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17 Sep 2017, 03:41
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Question Stats:

79% (04:20) correct 21% (03:34) wrong based on 38 sessions

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

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. $$\frac{20-5\sqrt{7}}{3}$$

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Math Expert
Joined: 02 Aug 2009
Posts: 6263

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17 Sep 2017, 06:29
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
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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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Re: 5/(7^(1/2)+1)/(7^(1/2)-1) &nbs [#permalink] 17 Sep 2017, 06:29
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