Discussion
A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. What is the least such number?
Answer: A
Correct answer: 17
Successive division means the quotient from the first division is what gets divided next. Write \(N = 4x + 1\), where \(x\) is the first quotient, and then \(x = 5y + 4\).
The least value of \(N\) comes from the smallest admissible \(y\), which is \(y = 0\). That gives \(x = 4\) and
\[N = 4\times 4 + 1 = 17\]
Checking against the conditions: \(17 \div 4\) gives quotient 4 and remainder 1, and dividing that quotient, \(4 \div 5\) gives quotient 0 and remainder 4. Both requirements hold, so 17 is the least such number.
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