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# Which of the following has the greatest value?

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Which of the following has the greatest value? [#permalink]  24 Jan 2010, 23:20
00:00

Difficulty:

5% (low)

Question Stats:

57% (02:25) correct 43% (00:51) wrong based on 7 sessions
Which of the following has the greatest value?

A) \frac{\sqrt{2}}{\sqrt{3}} + \frac{\sqrt{3}}{\sqrt{4}} + \frac{\sqrt{4}}{\sqrt{5}} + \frac{\sqrt{5}}{\sqrt{6}}

B) \frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6}

C) \frac{2^2}{3^2} + \frac{3^2}{4^2} + \frac{4^2}{5^2} + \frac{5^2}{6^2}

D) 1 - \frac{1}{3} + \frac{4}{5} - \frac{3}{4}

E) 1 - \frac{3}{4} + \frac{4}{5} + \frac{1}{3}
[Reveal] Spoiler: OA
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Re: Which of the following has the greatest value? [#permalink]  25 Jan 2010, 05:19
x^m is greater when

M is more if X >1
M is less if X <1

in this case out of a b c , a will hav max value.

option E > D clearly

in E . 3/4 is greater than 1/3

that means E is at most 1+4/5 = 9/5

now in option 1... \sqrt{2}/\sqrt{3} is smallest .

Thus sum of option 1 is atleast 4*\sqrt{2}/\sqrt{3} which comes more than 2

and 9/5 is less than 2.

lol this method seems to be weird but i calculated it in dat way only
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Re: Which of the following has the greatest value? [#permalink]  14 Feb 2010, 00:53
rahulms wrote:
which of the following has the greatest value?

A) \frac{\sqrt{2}}{\sqrt{3}} + \frac{\sqrt{3}}{\sqrt{4}} + \frac{\sqrt{4}}{\sqrt{5}} + \frac{\sqrt{5}}{\sqrt{6}}

B) \frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6}

C) \frac{2^2}{3^2} + \frac{3^2}{4^2} + \frac{4^2}{5^2} + \frac{5^2}{6^2}

D) 1 - \frac{1}{3} + \frac{4}{5} - \frac{3}{4}

E) 1 - \frac{3}{4} + \frac{4}{5} + \frac{1}{3}

[Reveal] Spoiler:
A

One of this type question is also in the GMATclub tests as well i didn't remember which one it was. However in order to solve the greatest value for the options available we have to find out the lowest denominator of the options available and use POE method.

A) \frac{\sqrt{2}}{\sqrt{3}} + \frac{\sqrt{3}}{\sqrt{4}} + \frac{\sqrt{4}}{\sqrt{5}} + \frac{\sqrt{5}}{\sqrt{6}}
B) \frac{2}{3} + \frac{3}{4} + \frac{4}{5} + \frac{5}{6}
C) \frac{2^2}{3^2} + \frac{3^2}{4^2} + \frac{4^2}{5^2} + \frac{5^2}{6^2}

For all these options it is quite evident that option A has the lowest denominator so it will result in greater value because of the root.

D) 1 - \frac{1}{3} + \frac{4}{5} - \frac{3}{4}
E) 1 - \frac{3}{4} + \frac{4}{5} + \frac{1}{3}
if you quickly solve D and E will reveal that denominator is greater than the option A

So it must be A
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Re: Which of the following has the greatest value? [#permalink]  21 Sep 2010, 04:17
It seems to be easy but time consuming. What is the source of this problem.
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Re: Which of the following has the greatest value? [#permalink]  21 Sep 2010, 04:19
This seems to be simple but time consuming problem what is the source?
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Re: Which of the following has the greatest value? [#permalink]  21 Sep 2010, 05:01
prashantbacchewar wrote:
This seems to be simple but time consuming problem what is the source?

If its taking more time then try this:

Try to find out the option which has the lowest denominator so it will result in greater value.
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Re: Which of the following has the greatest value? [#permalink]  21 Sep 2010, 05:08
1
KUDOS
prashantbacchewar wrote:
This seems to be simple but time consuming problem what is the source?

I really think this is one of those problems which can throw you off because it seems complicated, but I do believe its one of those questions you can easily do in less than 30 secs ... and its this kind of stuff that will make you save time in the real GMAT

Between A,B,C --> A is clearly the biggest

D is clearly less than B, it has the same terms some positive and some negative

E is also less than B : 4/5 - 3/4 + 2/3 + 2/3 which is less than 2/3-3/4+4/5+5/6, which has to be less than B

No calculations, just a quick manipulation mentally is sufficient
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Re: Which of the following has the greatest value? [#permalink]  21 Sep 2010, 05:44
shrouded1

Thanks for sharing approach +1 to you
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Re: Which of the following has the greatest value? [#permalink]  21 Sep 2010, 13:21
+1 A

I think that here is not necessary to make many calculations.
You can eliminate some options with just watching.
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Re: Which of the following has the greatest value?   [#permalink] 21 Sep 2010, 13:21
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