deadmank2s wrote:How many integers from 0 to 50, inclusive, have a remainder of 1 when divided by 3 ?
A. 15
B. 16
C. 17
D. 18
E. 19
An integer that has a remainder of 1 when divided by 3 can be represented as follows:
3k + 1, where k is an integer greater than or equal to 0.
Since the integer must be less than 50:
3k + 1 < 50
3k < 49
k < 16.33.
Thus, 0≤k<16.33, implying that k could any of the 17 integers between 0 and 16, inclusive.
Since there are 17 values for k, there are 17 integers less than 50 that will have a remainder of 1 when divided by 3.
(The smallest is 3(0)+1 = 1; the greatest is 3(16)+1 = 49.)
The correct answer is
C.
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