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03 Jun 2022, 10:48
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
26% (01:17) correct
74%
(01:13)
wrong
based on 187
sessions
History
Date
Time
Result
Not Attempted Yet
If 15 is a factor of 25N2, which of the following must be a factor of N?
I. 3
II. 5
III. 75
(A) None
(B) I only
(C) II only
(D) I and II only
(E) I and III only
I. 3
II. 5
III. 75
(A) None
(B) I only
(C) II only
(D) I and II only
(E) I and III only
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03 Jun 2022, 19:52
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BrentGMATPrepNow
\(25N^2\) could equal 15, 30, 45, 60, ...
Let's check a couple of these to see if they tell us anything:
\(25N^2 = 15\)
\(N^2 = 0.6\)
\(N=\sqrt{0.6}\)
N is not an integer at all. None of the integer options available is a factor of N.
How about that?!? We didn't even need to check any other options!
Answer choice A.
04 Jun 2022, 11:39
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The first obvious thing to note is that we do not know the nature of N – it may or may not be an integer. Therefore, we are not to assume that it is an integer.
In fact, in 'Must Be' questions, it always pays to be a contrarian and look the other way. This means, you will be able to disprove the statements very easily if you assume that N is NOT an integer.
Prime factorising 15 and 25 tells us that 15 = 5 * 3 and 25 = \(5^2\).
It is given that 15 is a factor of 25\(N^2\); therefore, \(\frac{25N^2 }{ 15}\) = integer.
Or, 5 * 5 * \(N^2\) = 5 * 3 * integer.
Dividing the equation by 5, we are left with 5 * \(N^2\) = 3 * integer or \(N^2\) = \(\frac{3 * integer }{ 5}\)
If the integer = 1, \(N^2\) = \(\frac{3}{5}\); therefore, N = \(\sqrt{(\frac{3}{5})}\). In this case, none of the numbers given in the statements are factors of N.
Therefore, we cannot claim any of the numbers MUST be a factor of N.
The correct answer option is A.
In fact, in 'Must Be' questions, it always pays to be a contrarian and look the other way. This means, you will be able to disprove the statements very easily if you assume that N is NOT an integer.
Prime factorising 15 and 25 tells us that 15 = 5 * 3 and 25 = \(5^2\).
It is given that 15 is a factor of 25\(N^2\); therefore, \(\frac{25N^2 }{ 15}\) = integer.
Or, 5 * 5 * \(N^2\) = 5 * 3 * integer.
Dividing the equation by 5, we are left with 5 * \(N^2\) = 3 * integer or \(N^2\) = \(\frac{3 * integer }{ 5}\)
If the integer = 1, \(N^2\) = \(\frac{3}{5}\); therefore, N = \(\sqrt{(\frac{3}{5})}\). In this case, none of the numbers given in the statements are factors of N.
Therefore, we cannot claim any of the numbers MUST be a factor of N.
The correct answer option is A.
