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Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
06 Dec 2018, 05:50
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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:
35%
(medium)
Question Stats:
65% (01:09) correct
35%
(01:09)
wrong
based on 291
sessions
History
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Time
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If x is a positive integer, what is the value of x?
(1) 2x = x!
(2) x^2 - 3x = 0
M36-38
(1) 2x = x!
(2) x^2 - 3x = 0
M36-38
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18 Oct 2021, 11:09
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Bunuel
Official Solution:
If \(x\) is a positive integer, what is the value of \(x\)?
(1) \(2x = x!\)
Test numbers:
If \(x=1\), then \(2x \neq x!\)
If \(x=2\), then \(2x \neq x!\)
If \(x=3\), then \(2x = x!=6\). BINGO!
If \(x=4\), then \(2x \neq x!\)
From this point, as we increase \(x\), \(x!\) increases much faster than \(2x\), so \(2x = x!\) won't have any solution for larger values of \(x\).
Sufficient.
(2) \(x^2 - 3x = 0\)
\(x(x - 3) = 0\)
\(x= 0\) (discard since we are given that \(x\) is positive) or \(x=3\). Sufficient.
Answer: D
General Discussion
06 Dec 2018, 05:55
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The answer is D.
1) this is not true for x=1 (2=1) or x=2 (4=2), for which the left side is greater. it is true for x=3 (6=6). for x=4 (8=24) the right side is greater, and we can easily see that as we progress, the right side will increase even more in relation to the left side. In other words, there is no way there will be another value that works - only x=3. sufficient!
2) x(x-3)=0 ==> x=0, x=3 - but since we know x is a positive integer, only x=3 works. Sufficient!
1) this is not true for x=1 (2=1) or x=2 (4=2), for which the left side is greater. it is true for x=3 (6=6). for x=4 (8=24) the right side is greater, and we can easily see that as we progress, the right side will increase even more in relation to the left side. In other words, there is no way there will be another value that works - only x=3. sufficient!
2) x(x-3)=0 ==> x=0, x=3 - but since we know x is a positive integer, only x=3 works. Sufficient!
