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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.
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Re: List L consists of the numbers [#permalink]
26 Jan 2017, 18:21
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ExplanationThe 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
I support to Answer: A



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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^21 = 4 or x1 = 3. if x1=3 then x = 5 and then x^2 which exists in list equals 25 and therefore the range will be 251=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) So, that answers your question 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 =41=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
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22 May 2020, 19:25





