n is an integer strictly between 10 and 20. What is the value of n?

1) The tens digit of n^2 is 2.
2) The hundreds digit of n^2 is 3.

statement 1) The range of values for $$n^2$$ based on the given info is 100 < n $$n^2$$ < 400. So $$n^2$$ can be any perfect square between 100 & 400

Let's start finding the perfect squares of possible values for n and see how many give a tens digit 2
n = 11 ---> 121 ------> works
n = 12 -----> 144 ----> doesn't work
n = 13 ----> 169 -----> doesn't work
n = 14 -----> 196 ----> doesn't work
n = 15 -----> 225 --------> works

Since n can be 11 or 15 this is INSUFFICIENT

statement 2)
From our work in statement 1 we know we can start from where we left off since 11-15 won't give a hundreds digit of 3

n = 16 -----> 256 ----> doesn't work
n = 17 -----> 289 ----> doesn't work
n = 18 ------> 324 -----> works
n = 19 -------> 361 -----> works

Since n can be 18 or 19 this is INSUFFICIENT

statement 1 & 2)
Between 324 and 361 only 324 satisfies statements 1 & 2. Therefore n = 18 --------> SUFFICIENT

Answer: C

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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.

The squares of the integers that are strictly between 10 and 20 are
11^2 = 121, 12^2 = 144, 13^2 = 169, 14^2 = 196, 15^2 = 225, 16^2 = 256, 17^2 = 289, 18^2 = 324, 19^2 = 361.

Condition 1):
The values for which the tens digit of n^2 is 2 are n = 11, n = 15 and n = 18.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
The values for which the hundreds digit of n^2 is 3 are n = 18 and n = 19.
Since we don't have a unique solution, condition 2) is not sufficient.

Conditions 1) & 2)
n = 18 is the unique solution that satisfies both conditions 1) and 2).
Conditions 1) and 2) are sufficient, when considered together.

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.