k is a positive integer. When 2^{-k/2} ≤ 1/1,024, k=?

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[GMAT math practice question]

k is a positive integer. When 2^{-k/2} ≤ 1/1,024, k=?

1) k is an integer less than 21
2) k is an integer greater than 12

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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 first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

2^{-k/2} ≤ 1/1,024
=> 2^{k/2} ≥ 1,024
=> 2^{k/2} ≥ 1,024 = 2^{10}
=> k/2 ≥ 10
=> k ≥ 20
We have the simplified original condition k ≥ 20.

Condition 1)
"k < 21" yields the unique solution k = 20, since k is an integer and k ≥ 20. Condition 1) is sufficient.

Condition 2)
We have k > 12 from condition 2) and k ≥ 20 from the original condition.
The integer k has many possible values.
Since it does not yield a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A