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Mathematical Puzzles Expert 2 min

A positive integer leaves remainder 2 when divided by 5 and remainder 3 when divided by 7. What is the smallest such integer?

Hint
List numbers that leave remainder 2 when divided by 5.

Answer

17.

Explanation

Numbers congruent to 2 modulo 5 are 2, 7, 12, 17, ... Among these, 17 leaves remainder 3 when divided by 7.

Step-by-Step Solution

2 mod 5 = 2
7 mod 5 = 2
12 mod 5 = 2
17 mod 5 = 2
17 mod 7 = 3
Therefore the answer is 17.
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