A number, when divided by \(3,\) gives a remainder of \(1.\) How many distinct values can the remainder take when the

[Vincen]

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

[Scott@TargetTestPrep]

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

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