Data Sufficiency

[GMAT math practice question]

When 32 is divided by k, the remainder is k-3. What is the value of k?

1) k > 20
2) k < 40

Max@Math Revolution wrote:[GMAT math practice question]

When 32 is divided by k, the remainder is k-3. What is the value of k?

1) k > 20
2) k < 40

Dividing 32 by k leaves a remainder of k-3.
In other words, 32 is equal to k-3 more than a multiple of k:
32 = ak + (k-3), where a is a nonnegative integer and k is an integer such that k≥3.

Simplifying 32 = ak + (k-3), we get:
35 = ak + k
35 = k(a+1)

The resulting equation implies that k and a+1 must be FACTORS OF 35, yielding 3 options such that k≥3:
k=35 and a+1=1
k=7 and a+1=5
k=5 and a+1=7

Statement 1:
Of the three options for k, only k=35 is such that k>20.
SUFFICIENT.

Statement 2:
Here, it's possible that k=35, k=7 or k=5.
Since k can be different values, INSUFFICIENT.

The correct answer is A.

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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.

The original condition says that 32 = k*q + ( k - 3 ) or 35 = k*q + k = k(q+1).
That is, k is a factor of 35.
So, k = 1, 5, 7 or 35.

Since condition 1) "k>20" yields the unique solution "k=35", condition 1) is sufficient.

Condition 2) yields k = 1, 5, 7 or 35. Since it does not yield a unique solution, condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A