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15 Jun 2023, 01:49
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
51% (01:04) correct
49%
(01:35)
wrong
based on 111
sessions
History
Date
Time
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Not Attempted Yet
If x and y are real numbers. What is the value of x?
(1) \(x = \sqrt{y} + \sqrt{-y}\)
(2) \(y = \sqrt{x} + \sqrt{-x} \)
(1) \(x = \sqrt{y} + \sqrt{-y}\)
(2) \(y = \sqrt{x} + \sqrt{-x} \)
I saw it a in a mock test. Not sure about the second part of the question?
Can anyone help me particularly related to square of negative?
Can anyone help me particularly related to square of negative?
15 Jun 2023, 02:04
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If x and y are real numbers. What is the value of x?
On the GMAT, all numbers are assumed to be real numbers by default, which means that even roots from negative numbers are not defined.
(1) \(x = \sqrt{y} + \sqrt{-y}\).
Given that x is a real number, both \(\sqrt{y}\) and \(\sqrt{-y}\) must also be defined. This implies that both y and -y must be greater than or equal to 0. This is only possible if y = 0. Therefore, \(x = \sqrt{y} + \sqrt{-y} = 0\). Sufficient.
(2) \(y = \sqrt{x} + \sqrt{-x} \)
Given that y is a real number, both \(\sqrt{x}\) and \(\sqrt{-x}\) must also be defined. This implies that both x and -x must be greater than or equal to 0. This is only possible if x = 0. Sufficient.
Answer: D.
On the GMAT, all numbers are assumed to be real numbers by default, which means that even roots from negative numbers are not defined.
(1) \(x = \sqrt{y} + \sqrt{-y}\).
Given that x is a real number, both \(\sqrt{y}\) and \(\sqrt{-y}\) must also be defined. This implies that both y and -y must be greater than or equal to 0. This is only possible if y = 0. Therefore, \(x = \sqrt{y} + \sqrt{-y} = 0\). Sufficient.
(2) \(y = \sqrt{x} + \sqrt{-x} \)
Given that y is a real number, both \(\sqrt{x}\) and \(\sqrt{-x}\) must also be defined. This implies that both x and -x must be greater than or equal to 0. This is only possible if x = 0. Sufficient.
Answer: D.
09 Oct 2024, 10:15
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