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If k > 1, which of the following must be equal to
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16 Jun 2015, 03:11
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If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\)? A. 2 B. \(2\sqrt{2k}\) C. \(2\sqrt{k+1}+\sqrt{k1}\) D. \(\frac{\sqrt{k+1}}{\sqrt{k1}}\) E. \(\sqrt{k+1}\sqrt{k1}\) Kudos for a correct solution.
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Re: If k > 1, which of the following must be equal to
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16 Jun 2015, 05:32
If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k−1}}\)?
\(\frac{2}{\sqrt{k+1}+\sqrt{k−1}}\) Rationalizing the denominator
We get \(\sqrt{k+1}\sqrt{k−1}\)
Ans : E



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Re: If k > 1, which of the following must be equal to
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16 Jun 2015, 09:13
Bunuel wrote: If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\)?
A. 2
B. \(2\sqrt{2k}\)
C. \(2\sqrt{k+1}+\sqrt{k1}\)
D. \(\frac{\sqrt{k+1}}{\sqrt{k1}}\)
E. \(\sqrt{k+1}\sqrt{k1}\)
Kudos for a correct solution. Rationalization is one of the methods, Second is hereSince k>1 , \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\) Let's Substitute k = 2 in the expression, the expression now becomes \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\) = \(\frac{2}{\sqrt{2+1}+\sqrt{21}}\) i.e. \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\) = \(\frac{2}{\sqrt{3}+1}\) = 2/(1.732+1) i.e. \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\) = 2/(2.732) = approx 0.74Check option with k=2 A. 2 > 0.74 INCORRECTB. \(2\sqrt{2k}\) = \(2\sqrt{4}\) = 4 > 0.74 INCORRECTC. \(2\sqrt{k+1}+\sqrt{k1}\) = \(2\sqrt{3}+\sqrt{21}\)>0.74 INCORRECTD. \(\frac{\sqrt{k+1}}{\sqrt{k1}}\) = \(\frac{\sqrt{2+1}}{\sqrt{21}}\)= 1.7 > 0.74 INCORRECTE. \(\sqrt{k+1}\sqrt{k1}\) = \(\sqrt{2+1}\sqrt{21}\)= 1.731 = 0.73 CORRECTAnswer: option
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Re: If k > 1, which of the following must be equal to
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16 Jun 2015, 10:21
If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\)? Solution  Divide the numerator and denominator with \(\sqrt{k+1}\sqrt{k1}\) in the above equation and solve the equation. Results, \(\sqrt{k+1}\sqrt{k1}\). ANS E. Thanks, Kudos please.
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Re: If k > 1, which of the following must be equal to
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16 Jun 2015, 10:57
Bunuel wrote: If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\)?
A. 2
B. \(2\sqrt{2k}\)
C. \(2\sqrt{k+1}+\sqrt{k1}\)
D. \(\frac{\sqrt{k+1}}{\sqrt{k1}}\)
E. \(\sqrt{k+1}\sqrt{k1}\)
Kudos for a correct solution. This one can be easily solved by rationalizing the expression \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\). So multiplying and dividing the expression by \(\sqrt{k+1}\sqrt{k1}\). We get, \(\frac{2}{[k+1][k1]}\) * \(\sqrt{k+1}\sqrt{k1}\). =\(\frac{2}{2}\) * \(\sqrt{k+1}\sqrt{k1}\) that is \(\sqrt{k+1}\sqrt{k1}\). Hence E.



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If k > 1, which of the following must be equal to
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18 Jun 2015, 04:13
Bunuel wrote: If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\)?
A. 2
B. \(2\sqrt{2k}\)
C. \(2\sqrt{k+1}+\sqrt{k1}\)
D. \(\frac{\sqrt{k+1}}{\sqrt{k1}}\)
E. \(\sqrt{k+1}\sqrt{k1}\)
Kudos for a correct solution. Solution : Rationalizing denominator by multiplying Numerator and denominator by \({\sqrt{k+1}\sqrt{k1}}\) So we get \(\sqrt{k+1}\sqrt{k1}\) in numerator Option E



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Re: If k > 1, which of the following must be equal to
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18 Jun 2015, 17:36
Hi All, This question has an interesting 'quirk' to it.... Even though the question tells us that K > 1, if K = 1 then you'll still end up with the correct answer.... TESTing K = 1 in the prompt gives us... 2/(√2 + √0) = 2/(√2) = Now we have to multiply both the numerator and denominator by (√2), which simplifies to... 2(√2)/2 = √2 So we're looking for an answer that equals √2 when K = 1.... Answer A: 2 NOT a match Answer B: 2√2 NOT a match Answer C: 2√2 + 0 NOT a match Answer D: √2/0 = undefined NOT a match Answer E: √2  0 This IS a MATCH Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: If k > 1, which of the following must be equal to
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20 Jun 2015, 10:49
Bunuel wrote: If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\)?
A. 2
B. \(2\sqrt{2k}\)
C. \(2\sqrt{k+1}+\sqrt{k1}\)
D. \(\frac{\sqrt{k+1}}{\sqrt{k1}}\)
E. \(\sqrt{k+1}\sqrt{k1}\)
Kudos for a correct solution. Let us try this by taking values Let k=3 Equation becomes=2/2+\sqrt{2} =\sqrt{2}/\sqrt{2}+1 =2\sqrt{2} Now put k=3 in the given options. Only Option E gives the value as 2\sqrt{2} Answer E



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Re: If k > 1, which of the following must be equal to
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22 Jun 2015, 07:25
Bunuel wrote: If k > 1, which of the following must be equal to \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}\)?
A. 2
B. \(2\sqrt{2k}\)
C. \(2\sqrt{k+1}+\sqrt{k1}\)
D. \(\frac{\sqrt{k+1}}{\sqrt{k1}}\)
E. \(\sqrt{k+1}\sqrt{k1}\)
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:Since there are variables in the answer choices (VIC), we should pick a number and test the choices. If k = 2, then \(\frac{2}{\sqrt{k+1}+\sqrt{k1}}=\frac{2}{\sqrt{2+1}+\sqrt{21}}=\frac{2}{\sqrt{3}+\sqrt{1}}\approx{\frac{1}{1.7+1}}=\frac{2}{2.7}\) which is less than 1. Now test the answer choices and try to match the target: The correct answer is E. Attachment:
20150622_1824.png [ 60.23 KiB  Viewed 3002 times ]
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Re: If k > 1, which of the following must be equal to
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04 Oct 2015, 08:51
multiply both numerator and denominator by sqrt(K+1)  sqrt(k1) ; and u will get the answer
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Re: If k > 1, which of the following must be equal to
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06 Oct 2018, 00:44
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Re: If k > 1, which of the following must be equal to
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