Data Sufficiency

[GMAT math practice question]

We define 'a mod n' to be the remainder when a is divided by n. What is the value of 'a mod 12'?

1) a mod 3=1
2) a mod 4=a mod 2

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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)
The numbers satisfying condition 1) are 1, 4, 7, 10, 13, 16, 19, 22, ... .
Their remainders, when they are divided by 12, are 1, 4, 7 and 10.
Condition 1) is not sufficient since it doesn't yield a unique answer.

Condition 2)
The numbers satisfying condition 2) are 0, 1, 4, 5, 8, 9, 12, 13, 16, 17, ... .
Their remainders, when they are divided by 12, are 0, 1, 4, 5, 8 and 9.
Condition 2) is not sufficient, since it doesn't yield a unique answer.

Conditions 1) & 2)
The numbers satisfying conditions 1) & 2) are 1, 4, 13, 16, ... .
Their remainders, when they are divided by 12, are 0 and 1.
Both conditions together are not sufficient, since they don't yield a unique answer.

Therefore, E is the answer.
Answer: E

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.