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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