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Of the following, which one is third greatest ?

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

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New post 28 May 2017, 11:16
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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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New post 28 May 2017, 14:12
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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New post 28 May 2017, 14:46
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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New post 28 May 2017, 21:11
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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New post 29 Nov 2017, 20:32
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).

Answer A: 2√2 - 1
Answer B: √2 + 1
Answer C: 1 - √2
Answer D: √2 - 1
Answer E: √2

To start, we can look for patterns and similarities in the answer choices to make some easy deductions:
Answer C is the only NEGATIVE answer, so it's "5th"
Answer B > Answer E > Answer D (because of the "+1" and "-1"

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....

Final Answer:
[Reveal] Spoiler:
E


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

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New post 29 Nov 2017, 21:54
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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New post 04 Dec 2017, 10:48
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.

Answer: E
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Re: Of the following, which one is third greatest ?   [#permalink] 04 Dec 2017, 10:48
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