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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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SVP
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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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