A number, when divided by \(3,\) gives a remainder of \(1.\) How many distinct values can the remainder take when the same number is divided by \(9?\)
A) 1
B) 2
C) 3
D) 4
E) 5
Answer: C
Source: Veritas Prep
A number, when divided by \(3,\) gives a remainder of \(1.\) How many distinct values can the remainder take when the
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Solution:
We see that the possible values of the number are 1, 4, 7, 10, 13, 16, …. The remainder when these values are divided by 9 are 1, 4, 7, 1, 4, 7, …. We see that there are 3 distinct remainders.
Answer: C
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