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14 May 2018, 01:58
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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:
62% (01:46) correct
38%
(01:45)
wrong
based on 406
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GMAT CLUB'S FRESH QUESTION
Is a positive integer x odd?
(1) The greatest common factor of the smallest positive factor of x and the largest positive factor of x is odd
(2) The least common multiple of the smallest positive factor of x and the largest positive factor of x is even
M36-26
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11 Oct 2021, 08:07
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Bunuel
Official Solution:
Is a positive integer \(x\) odd?
(1) The greatest common factor of the smallest positive factor of \(x\) and the largest positive factor of \(x\) is odd
The smallest positive factor of any positive integer is 1 and the largest positive factor of any positive integer is the integer itself. So, we are given that the greatest common factor of 1 and \(x\) is odd. This is true for any positive integer \(x\) because the greatest common factor of 1 and \(x\) is always 1, which is odd. So, \(x\) could be any positive even or any positive odd number. Not sufficient.
(2) The least common multiple of the smallest positive factor of \(x\) and the largest positive factor of \(x\) is even
The smallest positive factor of any positive integer is 1 and the largest positive factor of any positive integer is the integer itself. So, we are given that the least common multiple 1 and \(x\) is even. Since the least common multiple 1 and \(x\) is \(x\) itself, then we are basically told that \(x\) is even. Sufficient.
Answer: B
General Discussion
14 May 2018, 02:56
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Solution
Given:
• x is a positive integer
To find:
• Is the value of x odd?
Approach and Working:
As x is a positive integer,
• The smallest positive factor of x = 1
• The largest positive factor of x = x
Analysing Statement 1
• As per the information provided in Statement 1, the GCF of the smallest positive factor of x and the largest positive factor of x is odd
- o Or, GCF (1, x) = odd
- o Hence, we cannot say anything about the nature of the number x
Analysing Statement 2
• As per the information provided in Statement 2, the LCM of the smallest positive factor of x and the largest positive factor of x is even
- o Or, LCM (1, x) = even
- o Hence, we can say that the number x is an even number
Hence, the correct answer is option B.
Answer: B
