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# List L consists of the numbers

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

70% (00:44) correct 29% (01:07) wrong based on 177 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]  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]  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]  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]  07 Feb 2018, 02:37
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Re: List L consists of the numbers [#permalink]  06 Mar 2018, 18:42
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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.

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Re: List L consists of the numbers [#permalink]  02 Apr 2019, 14:54
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boxing506 wrote:
what if the number, X is not an integer, I wonder if in every cases, the output is the same?

In the above question, x is not an integer (x = √5 ≈ 2.2)

Cheers,
Brent
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Re: List L consists of the numbers [#permalink]  22 Jan 2020, 06:39
can be solved in the mind
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Re: List L consists of the numbers [#permalink]  28 Mar 2020, 20:58
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aceGRE21 wrote:
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?

I agree, possibility 2 does not make any sense whatsoever. Knowing that the range is 4 and getting the largest known number (in this case: square root of 2) subtract by 4 to find x does make sense, but then we do have X^2 in the list which will be larger than the square root of 2, making the actual range larger than 4.

For this question, the condition that x>0 should be relied upon to solve. If you missed it, then your answer would be wrong. That's it
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Re: List L consists of the numbers [#permalink]  06 Apr 2020, 13:11
not the easiest problem but got it rigth
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Re: List L consists of the numbers [#permalink]  22 May 2020, 19:25
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let's say X=2,
then, increment arrangement goes 1,√2,2,4.
so, range =4-1=3 but the question tells us that the range is 4.
to get the range 4 ,X should be more than 2. hence X is greater.
Re: List L consists of the numbers   [#permalink] 22 May 2020, 19:25
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