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

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5/(7^(1/2)+1)/(7^(1/2)-1)  [#permalink]

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New post 17 Sep 2017, 03:41
00:00
A
B
C
D
E

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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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Re: 5/(7^(1/2)+1)/(7^(1/2)-1)  [#permalink]

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

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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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