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# Which of the following represents the greatest value?

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Senior Manager
Joined: 03 Mar 2010
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Which of the following represents the greatest value? [#permalink]

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05 Jul 2011, 12:15
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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) $$1-3/4 + 4/5 + 1/3$$
[Reveal] Spoiler: OA

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Last edited by Bunuel on 08 Jan 2013, 03:30, edited 1 time in total.
RENAMED THE TOPIC.

Kudos [?]: 368 [3], given: 22

Math Forum Moderator
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Kudos [?]: 2095 [1], given: 376

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05 Jul 2011, 12:37
1
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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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05 Jul 2011, 23:02
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Expert's post
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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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Kudos [?]: 17822 [7], given: 235

Manager
Joined: 11 Apr 2011
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06 Jul 2011, 10:14
2/3 < 1, so sq rt(2/3) > 1.
D and E are less by some calculations.

Kudos [?]: 32 [0], given: 16

Intern
Joined: 06 Jun 2011
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Kudos [?]: 13 [1], given: 2

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06 Jul 2011, 15:34
1
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15 sec.
A
eliminated D and E as there are negatives
2^2/3^2 < 2/3 < [2][/2]

Kudos [?]: 13 [1], given: 2

Manager
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07 Jan 2013, 12:49
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.

Kudos [?]: -9 [0], given: 0

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

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01 Nov 2017, 09:33
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.

Kudos [?]: [0], given: 3

Re: Which of the following represents the greatest value?   [#permalink] 01 Nov 2017, 09:33
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