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List L consists of the numbers

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List L consists of the numbers [#permalink] New post 23 Jan 2017, 08:55
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Question Stats:

80% (00:47) correct 19% (00:32) wrong based on 51 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

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Re: List L consists of the numbers [#permalink] New post 26 Jan 2017, 18:21
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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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Re: List L consists of the numbers [#permalink] New post 18 Dec 2017, 23:51
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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?
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Re: List L consists of the numbers [#permalink] New post 04 Feb 2018, 05:53
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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] New post 07 Feb 2018, 02:37
I support to Answer: A
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Re: List L consists of the numbers [#permalink] New post 06 Mar 2018, 18:42
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.

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