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List L consists of the numbers
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23 Jan 2017, 08:55
23 Jan 2017, 08:55
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00:00
Question Stats:
79% (01:09) correct
20% (01:17) wrong based on 314 sessions
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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.
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.
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.
Re: List L consists of the numbers
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26 Jan 2017, 18:21
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.
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.
General Discussion
Re: List L consists of the numbers
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18 Dec 2017, 23:51
18 Dec 2017, 23:51
2
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 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?
