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Which of the following represents the greatest value?

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Which of the following represents the greatest value?  [#permalink]

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New post Updated on: 08 Jan 2013, 02:30
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

61% (01:52) correct 39% (02:13) wrong based on 286 sessions

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Which of the following represents the greatest value?

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

B) \(2/3 + 3/4 + 4/5 + 5/6\)

C) \(2^2/3^2 + 3^2/4^2 + 4^2/5^2 + 5^2/6^2\)

D) \(1-1/3 + 4/5 - 3/4\)

E) \(1-3/4 + 4/5 + 1/3\)

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Originally posted by jamifahad on 05 Jul 2011, 11:15.
Last edited by Bunuel on 08 Jan 2013, 02:30, edited 1 time in total.
RENAMED THE TOPIC.
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Re: 2-mins challenge  [#permalink]

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New post 05 Jul 2011, 22:02
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jamifahad wrote:
Solve this under 2 mins.

Which of the following represents the greatest value?

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

B) \(2/3 + 3/4 + 4/5 + 5/6\)

C) \(2^2/3^2 + 3^2/4^2 + 4^2/5^2 + 5^2/6^2\)

D) \(1-1/3 + 4/5 - 3/4\)

E) \(1-3/4 + 4/5 + 1/3\)


I think for most people the only confusing options will be A and B.

You can compare fractions very easily by making either their denominator or numerator same.

Say I want to compare \(\sqrt{2} / \sqrt{3}\) with 2/3.
I just multiply and divide \(\sqrt{2} / \sqrt{3}\) by \(\sqrt{2}\) to get 2/\(\sqrt{6}\).
Since \(\sqrt{6}\) is less than 3, 2/\(\sqrt{6}\) (i.e. \(\sqrt{2} / \sqrt{3}\)) is greater than 2/3.
Similarly, all terms of option A will be greater than all corresponding terms of option B.

Perfect example of how complicated looking questions are also based on very fundamental concepts.
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Re: 2-mins challenge  [#permalink]

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New post 05 Jul 2011, 11:37
1
jamifahad wrote:
Solve this under 2 mins.

Which of the following represents the greatest value?

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

B) \(2/3 + 3/4 + 4/5 + 5/6\)

C) \(2^2/3^2 + 3^2/4^2 + 4^2/5^2 + 5^2/6^2\)

D) \(1-1/3 + 4/5 - 3/4\)

E) \(1-3/4 + 4/5 + 1/3\)


I could make direct comparison between A, B and C and locked on A because the difference between numerator & denominator of individual term in A are smaller than that of B and C.

D: 1-0.3+0.8-0.75<1
E: 1-0.75+0.8+0.3= 1.5 approx

A: Every term is definitely more than 0.5 because the denominator was less than twice. Thus
A> 0.5+0.5+0.5+0.5=2

Ans: "A"
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Re: 2-mins challenge  [#permalink]

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New post 06 Jul 2011, 09:14
2/3 < 1, so sq rt(2/3) > 1.
D and E are less by some calculations.
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Re: 2-mins challenge  [#permalink]

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New post 06 Jul 2011, 14:34
1
15 sec.
A
eliminated D and E as there are negatives
2^2/3^2 < 2/3 < [2][/2]
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Re: 2-mins challenge  [#permalink]

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New post 07 Jan 2013, 11:49
out of a/b/c a is surely greatest because diff between numerator and denominator of each term is least in A.
d and e can be calculated to see that d is less than 1 and e is less than 2
A is greater than 2 since each term in A is greater than 0.5.
Hence answer - A
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Re: Which of the following represents the greatest value?  [#permalink]

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New post 01 Nov 2017, 08:33
1
jamifahad wrote:
Which of the following represents the greatest value?

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

B) \(2/3 + 3/4 + 4/5 + 5/6\)

C) \(2^2/3^2 + 3^2/4^2 + 4^2/5^2 + 5^2/6^2\)

D) \(1-1/3 + 4/5 - 3/4\)

E) \(1-3/4 + 4/5 + 1/3\)


We compared A B C and apply the following rule:

If 0 < k < 1, then 0 < k^2 < k < SQRT k <1

But before that, we need to compare B & D & E.
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Re: Which of the following represents the greatest value? &nbs [#permalink] 01 Nov 2017, 08:33
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