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Of the following sums, which is the greatest?

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jlgdr
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Of the following sums, which is the greatest? [#permalink] New post   28 Sep 2013, 16:32
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A
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D
E

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25% (medium)

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70% (01:14) correct 30% (01:26) wrong based on 441 sessions
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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) \(\frac{1}{2}\) + \(\frac{1}{3}\) + \(\frac{1}{4}\) + \(\frac{1}{5}\)
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Re: Of the following sums, which is the greatest? [#permalink] New post   29 Sep 2013, 10:09
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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, 20:24
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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   07 Feb 2021, 08:24
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There is one approach that I took i.e.

Square all the choices. Then Convert every option into percentage. Option A then becomes 50% + 33.33% + 25% + 20% which is clearly greater than every other choice.

This way square root will become positive numbers. And clearly the choice is A.
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Re: Of the following sums, which is the greatest? [#permalink] New post   12 May 2014, 18:12
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!
Cheers
J :)
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PareshGmat
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Re: Of the following sums, which is the greatest? [#permalink] New post   01 Aug 2014, 02:09
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] New post   07 Jun 2023, 19:07
Hello from the GMAT Club BumpBot!

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Re: Of the following sums, which is the greatest? [#permalink]
07 Jun 2023, 19:07
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