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Moderator  Joined: 18 Apr 2015
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List L consists of the numbers [#permalink]
Expert's post 00:00

Question Stats: 77% (00:48) correct 22% (01:03) wrong based on 63 sessions

List L consists of the numbers $$1$$, $$\sqrt{2}$$, $$X$$ and $$X^2$$, where X > 0, and the range of the numbers in list L is 4.

 Quantity A Quantity B X 2

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________ GRE Prep Club Legend  Joined: 07 Jun 2014
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Re: List L consists of the numbers [#permalink]
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Expert's post
Explanation

The range of a set of number is the difference between the highest and lowest number. Therefore, given that √2 = 1.4142, there are two possible ranges:

Possibility 1: 1 (low) to 5 (high) [5 − 1 = 4]
Possibility 2: −2.5858 (low) to 1.4142 (high) [1.4142 − 4 = −2.5858]

Since x > 0, possibility 2 is not an option.

Thus, x = 5 or $$x^2 = 5$$.
If x = 5, then $$x^2 = 25$$ and the range is now 24 (25 − 1 = 24) so x cannot equal 5.

If $$x^2 = 5$$, then $$x = \sqrt{5} = 2.236$$.

Compare the quantities:

Quantity A: 2.236
Quantity B: 2

Hence option A is greater.
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Sandy
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Re: List L consists of the numbers [#permalink]
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Hi @Sandy,

I am NOT sure with the possibility 2, [Can you please review my reasoning, as your solution is not making sense to me for the possibility 2 though that is NOT possible in the above question as X>0 given in the question, but still I wanted to clear my doubt]

Possibility 2: −2.5858 (low) to 1.4142 (high) [1.4142 − 4 = −2.5858]

Here, you have assumed X = -2.5858, that is, X is NEGATIVE. But then X^2 will be positive and 6.6863 will be the value of X^2, therefore,
Range = 6.6863 - (-2.5858) = 9.272 which is GREATER THAN 4.

Thus, X=-2.5858 is never possible. Can you please review? Manager  Joined: 26 Jun 2017
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Re: List L consists of the numbers [#permalink]
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what if the number, X is not an integer, I wonder if in every cases, the output is the same?
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Re: List L consists of the numbers [#permalink]
I support to Answer: A Manager Joined: 22 Feb 2018
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Re: List L consists of the numbers [#permalink]
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correct : A
The range of a list is the difference between the highest and the lowest value in the list.
1, \sqrt{2},X and X^2 is the numbers.
in these numbers, as x is not negative, \sqrt{2} can't be minimum as there is '1' in the list, so we ignore \sqrt{2}
for having the range 4 either x^2-1 = 4 or x-1 = 3. if x-1=3 then x = 5 and then x^2 which exists in list equals 25 and therefore the range will be 25-1=24. So x^2 - 1 = 4. and so x= \sqrt{2} which is more than 2.

_________________ Re: List L consists of the numbers   [#permalink] 06 Mar 2018, 18:42
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