If n and t are positive integers, what is the greatest prime factor of nt?
(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105
OA B
Source: GMAT Prep
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If n and t are positive integers, what is the greatest prime factor of nt?
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BTGmoderatorDC
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From statement 1, we haveBTGmoderatorDC wrote: ↑Tue May 18, 2021 5:52 pmIf n and t are positive integers, what is the greatest prime factor of nt?
(1) The greatest common factor of n and t is 5
(2) The least common multiple of n and t is 105
OA B
Source: GMAT Prep
- It's possible that \(n = t = 5.\) Then the greatest prime factor of \(nt\) is \(5.\)
- It's possible that \(n = 5\) and \(t = 35.\) Then the greatest prime factor of \(nt\) is \(7.\)
Not Sufficient \(\Large{\color{red}\chi}\)
From statement 2
The least common multiple contains every factor of \(t\) or \(n\) at least once (it has to; if, say, \(t\) had a factor that wasn't contained in it, then it would fail to be a multiple of \(t.\)) so, the biggest prime factor of this \(\#\) will also be the biggest prime factor of the product \(nt.\)
Sufficient \(\Large{\color{green}\checkmark}\)
Therefore, B
