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Of the following sums, which is the greatest?

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Of the following sums, which is the greatest? [#permalink] New post 28 Sep 2013, 15:32
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A
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D
E

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Of the following sums, which is the greatest?

(A) \(\frac{1}{\sqrt{2}}\) + \(\frac{1}{\sqrt{3}}\) + \(\frac{1}{\sqrt{4}}\) + \(\frac{1}{\sqrt{5}}\)
(B) \(\frac{1}{2^2}\) + \(\frac{1}{3^2}\) + \(\frac{1}{4^2}\) + \(\frac{1}{5^2}\)
(C) \(\frac{1}{2^2}\) + \(\frac{1}{2^3}\) + \(\frac{1}{2^2}\) + \(\frac{1}{2^5}\)
(D) 1- \(\frac{1}{2}\) + \(\frac{1}{3}\) - \(\frac{1}{4}\)
(E) \(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) + \(\frac{1}{5}\)
[Reveal] Spoiler: OA
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Re: Of the following sums, which is the greatest? [#permalink] New post 29 Sep 2013, 09:09
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jlgdr wrote:
Of the following sums, which is the greatest?

(A) \(\frac{1}{\sqrt{2}}\) + \(\frac{1}{\sqrt{3}}\) + \(\frac{1}{\sqrt{4}}\) + \(\frac{1}{\sqrt{5}}\)
(B) \(\frac{1}{2^2}\) + \(\frac{1}{3^2}\) + \(\frac{1}{4^2}\) + \(\frac{1}{5^2}\)
(C) \(\frac{1}{2^2}\) + \(\frac{1}{2^3}\) + \(\frac{1}{2^2}\) + \(\frac{1}{2^5}\)
(D) 1- \(\frac{1}{2}\) + \(\frac{1}{3}\) - \(\frac{1}{4}\)
(E) \(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) + \(\frac{1}{5}\)


\(\sqrt{2}<2<2^2\), thus \(\frac{1}{\sqrt{2}}>\frac{1}{2}>\frac{1}{2^2}\).

Answer: A.
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Re: Of the following sums, which is the greatest? [#permalink] New post 12 May 2014, 17:12
Any other approach for this problem over here? I did not quite get your explanation Bunuel, how can we quickly eliminate the other answer choices?

Thanks!
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Re: Of the following sums, which is the greatest? [#permalink] New post 12 May 2014, 19:24
Lets compare A & E first,

sqrt(2)= 1.4 which is <2

As we know,
1/smaller > 1/larger

=>1/sqrt(2) > 1/2

so will be the case for 3,4,5

So clearly A is greater than E,

D<E, clearly because there are negative terms
B & C increase the denominators by increasing the powers, so again B & C are even lesser than E

Hence, A is the greatest

Hope this helps. Hit kudos it it does.
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Re: Of the following sums, which is the greatest? [#permalink] New post 12 May 2014, 19:47
Thanks missionphd.
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Re: Of the following sums, which is the greatest? [#permalink] New post 01 Aug 2014, 01:09
jlgdr wrote:
Any other approach for this problem over here? I did not quite get your explanation Bunuel, how can we quickly eliminate the other answer choices?

Thanks!
Cheers
J :)


One good thing of this question is numerator of all the expressions is 1

Now focus on denominators

More the value of denominator, less would be the sum

Least the denominator, more would be the sum value

\(\sqrt{2} = 2^{\frac{1}{2}}\)

\(2^{\frac{1}{2}} < 2^2\)

Reciprocal both sides

\(\frac{1}{2^{\frac{1}{2}}} > \frac{1}{2^2}\)

(Greater/smaller sign changes for reciprocals/negation)

Same for all other fractions

So highest addition would be of option A

Answer = A
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Re: Of the following sums, which is the greatest?   [#permalink] 01 Aug 2014, 01:09
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Of the following sums, which is the greatest?

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