A number leaves a remainder of 2 when divided by 5 and a remainder of 3 when divided by 7. What is the smallest positive integer that satisfies both conditions?
17
Numbers that leave remainder 2 when divided by 5: 2, 7, 12, 17, 22, 27, ...
Check each for remainder 3 when divided by 7: \(17 \div 7 = 2\) remainder \(3\), which satisfies the condition.
Verification: \(17 \div 5 = 3\) remainder \(2\), and \(17 \div 7 = 2\) remainder \(3\).
Hence, the smallest positive integer satisfying both conditions is 17.
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