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# Of the following, which one is third greatest ?

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Joined: 01 Sep 2010
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Of the following, which one is third greatest ? [#permalink]

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28 May 2017, 12:16
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Of the following, which one is third greatest?

A) $$2 \sqrt{2} - 1$$

B) $$\sqrt{2} + 1$$

C) $$1 - \sqrt{2}$$

D) $$\sqrt{2} - 1$$

E) $$\sqrt{2}$$
[Reveal] Spoiler: OA

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Of the following, which one is third greatest ? [#permalink]

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28 May 2017, 15:12
The lowest of the values is Option C because $$1- \sqrt{2}$$ is negative.
The next lowest value is $$\sqrt{2} - 1$$ which is definitely lower than $$\sqrt{2}$$.
The third greatest/smallest value is $$\sqrt{2}$$ (Option E)
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Re: Of the following, which one is third greatest ? [#permalink]

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28 May 2017, 15:46
Square root of 2 is 1.414. If we plug in this 1.414 in for root 2, we will get E as the third greatest!
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Re: Of the following, which one is third greatest ? [#permalink]

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28 May 2017, 22:11
Approx value of √2 = 1.41. Substitute that to get

A) 2*1.41 - 1 = 1.82

B) 1.41 + 1= 2.41

C) 1 - 1.41 = -0.41

D) 1.41 - 1 = 0.41

E) 1.41

Clearly, the values in Ascending order (smallest to largest) are: C < D < E < A < B

So third greatest is E
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Re: Of the following, which one is third greatest ? [#permalink]

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29 Nov 2017, 21:32
Hi All,

We're asked which of the 5 choices is '3rd greatest.' As 'scary' as this question might look, as long as you recognize that √2 is GREATER than 1, you can simply 'compare' answer choices (and avoid doing almost every calculation).

To start, we can look for patterns and similarities in the answer choices to make some easy deductions:

Answer A can be rewritten as √2 + √2 -1. Since √2 is greater than 1, we know that (√2 - 1) would give us a positive result. Thus, Answer A > Answer E.

We now know that two of the Answers are GREATER than E (Answers A and B) and two of the answers are LESS than E (Answers C and D). Thus, the 3rd largest answer is....

[Reveal] Spoiler:
E

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Re: Of the following, which one is third greatest ? [#permalink]

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29 Nov 2017, 22:54
carcass wrote:
Of the following, which one is third greatest?

A) $$2 \sqrt{2} - 1$$

B) $$\sqrt{2} + 1$$

C) $$1 - \sqrt{2}$$

D) $$\sqrt{2} - 1$$

E) $$\sqrt{2}$$

There are total 5 entities. Third greatest is equivalent to thirst smallest.
So, the smallest one here is $$1 - \sqrt{2}$$ which is -ve.
2nd smallest one is $$\sqrt{2} - 1$$ which lies between (0,1)
3rd smallest is $$\sqrt{2}$$ which lies between (1,2)
4th smallest is $$2 \sqrt{2} - 1$$ which also lies between (1,2) but is greater than $$\sqrt{2}$$
5th smallest is $$\sqrt{2} + 1$$
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Re: Of the following, which one is third greatest ? [#permalink]

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04 Dec 2017, 11:48
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Expert's post
carcass wrote:
Of the following, which one is third greatest?

A) $$2 \sqrt{2} - 1$$

B) $$\sqrt{2} + 1$$

C) $$1 - \sqrt{2}$$

D) $$\sqrt{2} - 1$$

E) $$\sqrt{2}$$

Since √2 ≈ 1.4, we can analyze each answer choice:

A) 2 x 1.4 - 1 = 1.8

B) 1.4 + 1 = 2.4

C) 1 - 1.4 = -0.4

D) 1.4 - 1 = 0.4

E) 1.4

So the 3rd greatest is choice E, 1.4.

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Joined: 11 Jan 2018
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Re: Of the following, which one is third greatest ? [#permalink]

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27 Jan 2018, 09:07
1
KUDOS
You can replace √2 by whatever you want.
For instance by 5.
Re: Of the following, which one is third greatest ?   [#permalink] 27 Jan 2018, 09:07
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