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31 Aug 2023, 01:30
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
81% (01:33) correct
19%
(01:38)
wrong
based on 32
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(\sqrt{x + y}\) an integer?
(1) \(x^3 = 64\)
(2) \(x^2 = y – 3\)
(1) \(x^3 = 64\)
(2) \(x^2 = y – 3\)
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
31 Aug 2023, 22:32
Kudos
Bookmarks
Bunuel
Statement 1
(1) \(x^3 = 64\)
We can infer that \(x =4\). However, we don't have any information on the value of \(y\).
Hence, Statement 1 alone is not sufficient. We can eliminate A and D.
Statement 2
(2) \(x^2 = y – 3\)
\(y - x^2 = 3\)
Inference : \(y\) lies to the right of \(x^2\) on a number line. The distance between \(x^2\) and \(y\) equals 3 units.
Let's assume that \(x\) and \(y\) are positive integers. On a number line, the position of \(x\), \(x^2\), \(y\), and \(x+y\) is shown below -
Attachment:
1.jpg [ 10.35 KiB | Viewed 1010 times ]
- Case 1: \(x = 2, x^2 = 4, y = 7\) and \(x+y=9\) → Is \(\sqrt{x + y}\) an integer? -- Yes
- Case 2: \(x = 3, x^2 = 9, y = 12\) and \(x+y=9\) → Is \(\sqrt{x + y}\) an integer? -- No
Attachment:
2.jpg [ 24.76 KiB | Viewed 996 times ]
Eliminate B
Combined
\(x = 4, x^2 = 16, y = 19\) and \(x+y=23\) → Is \(\sqrt{x + y}\) an integer? -- No
Option C
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