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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]

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25 Jan 2010, 00:20
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Difficulty:

65% (hard)

Question Stats:

53% (02:35) correct 47% (01:22) wrong based on 187 sessions

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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]

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25 Jan 2010, 06:19
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]

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14 Feb 2010, 01:53
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]

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21 Sep 2010, 05:17
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]

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21 Sep 2010, 05:19
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]

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21 Sep 2010, 06:01
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]

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21 Sep 2010, 06:08
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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]

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21 Sep 2010, 06:44
shrouded1

Thanks for sharing approach +1 to you
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Re: Which of the following has the greatest value? [#permalink]

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21 Sep 2010, 14:21
+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]

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04 Mar 2015, 10:45
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Re: Which of the following has the greatest value? [#permalink]

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07 Mar 2015, 17:37
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Hi All,

Certain questions on the GMAT can be solved rather quickly if you spot the Number Properties involved and you have the ability to pattern-match.

The 'key' to answering this question quickly is the knowledge that 'squaring a positive fraction makes the fraction SMALLER, while square-rooting a positive fraction makes the fraction BIGGER.'

Here is the proof:

(1/2)^2 = (1/2)(1/2) = 1/4

Squaring the positive fraction made the fraction SMALLER.

Root(1/4) = Root(1)/Root(4) = 1/2

Square-rooting the positive fraction made the fraction BIGGER.

With that knowledge, take a look at the first 3 answer choices to this question. The prompt asks which of the 5 answers is biggest (and we'll get to all of the answers in a moment). Which of the first 3 answer choices is biggest? Notice how all 3 have the same fractions - one answer square-roots them all, one leaves them as is, and one squares them all. You should be able to say definitively that Answer A is the largest of those 3.

Next, a bit of estimation will come in handy. Notice how Answer A ADDS 4 fractions that are all fairly close to 1.... so that total has to be a little less than 4.....

What do Answers D and E do....? Without doing the calculation, you should notice how BOTH answers subtract at least one fraction; by extension, there's no way that those 2 totals are close to 4.

[Reveal] Spoiler:
A

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Re: Which of the following has the greatest value? [#permalink]

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09 May 2016, 08:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Which of the following has the greatest value?   [#permalink] 09 May 2016, 08:19
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