If 15 is a factor of 25N², which of the following must be a factor of

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.