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List L consists of the numbers

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Carcass
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List L consists of the numbers [#permalink] New post   23 Jan 2017, 08:55
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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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A
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sandy
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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
1
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] New post   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 :-D

Cheers,
Brent
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Re: List L consists of the numbers [#permalink] New post   22 Jan 2020, 06:39
can be solved in the mind
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Re: List L consists of the numbers [#permalink] New post   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] New post   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] New post   22 May 2020, 19:25
4
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.
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Re: List L consists of the numbers [#permalink] New post   22 Jun 2021, 09:54
GreenlightTestPrep wrote:
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 :-D

Cheers,
Brent



how do we know 1 is the least number in the list. since x > 0 , it could be 0.2 ,0.5 .....
then the answer changes right ?
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Re: List L consists of the numbers [#permalink] New post   22 Jun 2021, 10:12
Hey aliceeee,

You are right. \(X\) can be any value \(> 0\)
BUT
we are given the range of \(4\). So we can't take \(x = 0.2 or 0.5\)

Hope this answers your question. Please ask if the doubt remains.
aliceeee wrote:
GreenlightTestPrep wrote:
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 :-D

Cheers,
Brent



how do we know 1 is the least number in the list. since x > 0 , it could be 0.2 ,0.5 .....
then the answer changes right ?
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Re: List L consists of the numbers [#permalink] New post   07 Jul 2022, 09:32
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Carcass wrote:

This question is a part of PowerPrep Question Collection



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.


Solution:


We are given that list L contains the numbers 1, √2, X, and X^2.

Since we have a range of 4 and since 1 is the smallest number, we need the largest number in the list to be 5. We see that either X or X^2 could be 5. However, if X = 5, then X^2 = 25, and the range will not be 4. Therefore, X^2 must be 5, and X will then be √5.

Finally, since X = √5 > √4 = 2, Quantity A is greater than Quantity B.

Answer: A
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Re: List L consists of the numbers [#permalink] New post   03 Jan 2024, 11:43
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