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14 Jun 2022, 23:20
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Difficulty:
65%
(hard)
Question Stats:
51% (02:02) correct
49%
(02:33)
wrong
based on 72
sessions
History
Date
Time
Result
Not Attempted Yet
If \(s\) is a prime number less than \(19\), and \(x\) is equal to the smallest number that is divisible by \(49\) and \(7s\), how many distinct factors does \(x\) have?
1) \(s>5\)
2) \(s>11\)
1) \(s>5\)
2) \(s>11\)
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
14 Jun 2022, 23:26
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EthanTheTutor
The number of factors a number has depends on the exponents of its prime factors and not the value of the prime factors. In other words, \(2^5\) and \(13^5\) both have the same number of factors: \(5+1=6\). In that case, in order to find the number of factors of \(x\), we need to find the exponents of its prime factors.
If we look for the LCM of \(49\) and \(7𝑠\), we have 2 different situations: either \(𝑠=7\), or it doesn’t.
If \(𝑠=7\), then \(𝑥 = LCM(49, 7𝑠) =LCM(49, 7^2)= 7^2\).
So if \(𝑠=7\), then \(x\) has \(2+1=3\) factors.
If \(𝑠≠7\), then \(𝑥=LCM(49, 7𝑠)=7^2\cdot s\).
So if \(𝑠≠7\), then \(x\) has \((2+1)(1+1)=6\) factors.
And thus, the question can be rephrased as: does \(𝑠=7\)?
Statement 1: \(𝑠=7\) is possible, but so is \(s=13\). Not Sufficient
Statement 2: \(𝑠=7\) is not possible. Sufficient
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