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.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!
First, let's break down the question:
Whenever you see this type of question, always rewrite it as:both 5^2 (25) and 3^3 (27) are factors of n x 25 x 62 x 73
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.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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