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

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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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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 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....

Concentration: General Management, Entrepreneurship

GPA: 3.8

WE: Engineering (Energy and Utilities)

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

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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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