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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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Wed Oct 28, 2020 8:48 am

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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

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Source: Beat The GMAT — Problem Solving | Wed Oct 28, 2020 8:48 am

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Re: A number, when divided by $3,$ gives a remainder of $1.$ How many distinct values can the remainder take when th

by Scott@TargetTestPrep » Thu Nov 05, 2020 4:13 pm

Vincen wrote: ↑
Wed Oct 28, 2020 8:48 am
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

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