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08 Oct 2021, 10:16
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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:
25%
(medium)
Question Stats:
74% (01:18) correct
26%
(01:26)
wrong
based on 68
sessions
History
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Time
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Not Attempted Yet
If \(x\) is a positive integer, is \((x+2)\) prime?
(1) The greatest common divisor of \(x\) and \((x+1)\) is 1.
(2) \(x\) and \((x+1)\) are consecutive primes.
(1) The greatest common divisor of \(x\) and \((x+1)\) is 1.
(2) \(x\) and \((x+1)\) are consecutive primes.
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
08 Oct 2021, 10:19
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GMATWhizTeam
Statement 1:
This is true for any x. Neighboring numbers will always have a GCF of 1. Insufficient.
Statement 2:
The only consecutive primes that are exactly 1 apart, are 2 and 3. Then x = 2 and x + 2 = 4 would not be prime. Sufficient.
Ans: B
11 Oct 2021, 06:44
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GMATWhizTeam
Solution:
We are given that \(x\) is a positive integer. And we are asked if \((x+2)\) is prime or not. It is a YES-NO question.
Statement 1: The greatest common divisor of \(x\) and \((x+1)\) is 1.
Well, this is not something special. Every \(2\) consecutive positive integers are co-primes i.e., their GCD is \(1\).
This doesn't give us anything on \(x\) or \(x+2\). Thus statement 1 alone is not sufficient and we can eliminate options A and D.
Statement 2: \(x\) and \((x+1)\) are consecutive primes.
This on the other hand is something special. When you say \(x\) and \((x+1)\) are consecutive primes, this can only mean that \(x=2\) and \(x+1=3\) because 2 and 3 are only consecutive primes that differ by 1.
From this statement, we are getting \(x=2\) so \(x+2=2+2=4\). We can say that 4 is NOT a prime number.
Statement 2 alone is sufficient.
Hence the right answer is Option E.
