n is a positive integer. What is the value of n?

[Max@Math Revolution]

[GMAT math practice question]

n is a positive integer. What is the value of n?

1) n is less than 200
2) the number of positive factors of n is 15

[Max@Math Revolution]

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each condition on its own first.
Condition 1) is obviously not sufficient.

Condition 2)
If n has 15 factors, then n = p^4*q^2 or n=p^14, where p and q are prime numbers.
Condition 2) is not sufficient, since there are a lot of possibilities.

Conditions 1) & 2)
If p = 2 and q = 3 and n = p^4*q^2, then n = (2^4)(3^2) = 144. Note that 2^14 = 16384 > 200 and 3^4 2^2 = 324 > 200, so this is the only possible value of n satisfying conditions 1) and 2). For example, if p = 2 and q = 5, then n = 400.

Therefore, C is the answer.
Answer: C

If the original condition includes "1 variable", or "2 variables and 1 equation", or "3 variables and 2 equations" etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

[deloitte247]

Statement 1=> n + 200 is a perfect square.
possible values of n = 25, 56, 89, 124, 161, 200 etc
So, the information given is not enough to arrive at a specific answer
Hence, statement 1 is NOT SUFFICIENT.

Statement 2 => n + 292 is a perfect square
possible value of n =32, 69, 108, 149, 192 etc
Here, the information given is not enough to arrive at a specific answer
Hence, statement 2 is NOT SUFFICIENT.

Combining both statements together
n number that will be added to 200 to produce a perfect square if the same number is added to 292 it will not yield a perfect square. Hence, the value of n remains unknown.
Therefore, both statements combined together are NOT SUFFICIENT
Answer = option E