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27 Feb 2023, 07:45
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
56% (01:16) correct
44%
(01:16)
wrong
based on 184
sessions
History
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Not Attempted Yet
Is x is an integer ?
(1) x^2/2 is an integer.
(2) \(\sqrt{x}\) is an integer.
(1) x^2/2 is an integer.
(2) \(\sqrt{x}\) is an integer.
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
03 Mar 2023, 22:10
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Bunuel
Question Is x is an integer ?
Statement 1
(1) x^2/2 is an integer.
Case 1: x = \(\sqrt{2}\)
x^2/2 is an integer, however x is not an integer
Case 2: x = \(2\)
x^2/2 is an integer, and x is an integer.
As we have two answers possible, eliminate A and D.
Statement 2
(2) \(\sqrt{x}\) is an integer
\(\sqrt{x}\) = integer
Squaring both sides
x = \(\text {integer}^2\)
x = integer
The statement is sufficient.
Option B
06 Mar 2023, 22:19
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Bunuel
Solution:
Pre Analysis:
- We are asked if x is an integer or not
- This is a YES-NO question
- So, we do not need an exact value of x
Statement 1: x^2/2 is an integer
- According to this statement, \(\frac{x^2}{2}=k\) where k is an integer
\(⇒x^2=2k\)
\(⇒x=\sqrt{2k}\) - Whether \(\sqrt{2k}\) is integer ir not will depend on the value of k which we don't know
- Thus, statement 1 alone is not sufficient and we can eliminate options A and D
Statement 2: \(\sqrt{x}\) is an integer
- According to this statement, \(\sqrt{x}=q\) where q is an integer
\(⇒x=q^2=integer^2=integer\) - Thus, statement 2 alone is sufficient
Hence the right answer is Option B
