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Number Theory Level 2

If a number is divided by 15, it leaves a remainder of 7. If thrice the number is divided by 5, then what is the remainder?

0 3 1 Indeterminate 2

1 solution

Chew-Seong Cheong
Dec 25, 2017

Let the number be $n$ . Then $n \equiv 15k + 7$ , where $k$ is an integer. Implies that $3n \equiv 45k + 21 \equiv \boxed{1} \text{ (mod 5)}$ .