Data Sufficiency

[GMAT math practice question]

What is the value of the positive integer k?

1) When k is divided by 3, the remainder is 2.
2) When k is divided by 5, the remainder is 1

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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 (k) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1):
Two possible values of k which satisfy condition 1) are 5 and 8.
Since it does not give us a unique value of k, condition 1) is not sufficient.

Condition 2):
Two possible values of k which satisfy condition 2) are 1 and 6.
Since it does not give us a unique value of k, condition 2) is not sufficient.

Conditions 1) & 2):
Two possible values of k which satisfy both conditions 1) & 2) are 11 and 26.
Since they do not give us a unique value of k, conditions 1) & 2) together are not sufficient.

Therefore, E is the answer.

Answer: E