Problem Solving - Factorization Question??

JohnQ2011 wrote:Check this out when you have a minute and let me know if you know how to solve it properly...

If both 5^2 (25) and 3^3 (27) are factors of n x 25 x 62 x 73, what is the smallest possible positive value of n?

a) 25
b) 27
c) 45
d) 75
e) 125

Thanks!

Hi! This is an old question (and actually quite poorly constructed), but it illustrates a common feature in some GMAT questions, so it's worth reviewing.

First, let's break down the question:

both 5^2 (25) and 3^3 (27) are factors of n x 25 x 62 x 73

Whenever you see this type of question, always rewrite it as:

n x 25 x 62 x 73/(5^2 * 3^3) = integer

Now, in order for the left side to be an integer, all of the numbers in the denominator must be accounted for in the numerator.

We can start by simplifying the 25 on top and 5^2 on the bottom to get:

n x 62 x 73/3^3 = integer

Next, a quick check of 62 and 73 reveals that neither is a multiple of 3. Accordingly, n must account for all 3 instances of 3 in the denominator and the smallest possible value of n is 3^3=27... choose (B).

Why is this a poorly constructed question? Because the 5^2 on the bottom exactly cancels out with 25 on top, leaving us with 3^3=27 on the bottom. Since only one answer is less than or equal to 27 and contains a multiple of 3, we don't even need to do any factoring to identify (b) as the only possibly correct choice.

JohnQ2011 wrote:Check this out when you have a minute and let me know if you know how to solve it properly...

If both 5^2 (25) and 3^3 (27) are factors of n x 25 x 62 x 73, what is the smallest possible positive value of n?

Thanks!

I don't think its a necessarily poorly construction question, albeit, it certainly is, a poorly transcribed one. Based on the previous responses and the provided OE, this is what the question must have actually read:

If both 5^2 and 3^3 are factors of n x 2^5 x 6^2 x 7^3, what is the smallest possible positive value of n?

In this case, we'll have min. value of n as 3x25 = 75, which would make D correct.

The reasoning/approach to solve this question is similar to quite a few PS questions seen on the GMAT prep. Knowing the approach of using the divisibility will surely help in other questions.

The answer is B for this question and it seems a pretty straight forward question to be asked on the actual test. As mentioned by Eagle Eye, it could have be better with one factor missing.

(B) 27