Question:
How many integers from \(1\) to \(100\) exist such that each is divisible by \(5\) and also has \(5\) as a digit?
How many integers from \(1\) to \(100\) exist such that each is divisible by \(5\) and also has \(5\) as a digit?
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For divisibility by \(5\), first list numbers ending in \(0\) or \(5\), then apply the digit condition.
Updated On: Jul 3, 2026
- \(10\)
- \(11\)
- \(12\)
- \(20\)
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The Correct Option is B
Solution and Explanation
Concept:
A number divisible by \(5\) must end in \[ 0\quad \text{or}\quad 5 \] The number must also contain digit \(5\).
Step 1: List multiples of \(5\) from \(1\) to \(100\) which contain digit \(5\). The numbers ending in \(5\) are: \[ 5,\ 15,\ 25,\ 35,\ 45,\ 55,\ 65,\ 75,\ 85,\ 95 \] These are \(10\) numbers.
Step 2: Check numbers ending in \(0\) but containing digit \(5\). Among multiples of \(10\), the number containing digit \(5\) is: \[ 50 \] So this adds \(1\) more number.
Step 3: Total count. \[ 10+1=11 \]
Step 4: Final answer. \[ \boxed{11} \]
A number divisible by \(5\) must end in \[ 0\quad \text{or}\quad 5 \] The number must also contain digit \(5\).
Step 1: List multiples of \(5\) from \(1\) to \(100\) which contain digit \(5\). The numbers ending in \(5\) are: \[ 5,\ 15,\ 25,\ 35,\ 45,\ 55,\ 65,\ 75,\ 85,\ 95 \] These are \(10\) numbers.
Step 2: Check numbers ending in \(0\) but containing digit \(5\). Among multiples of \(10\), the number containing digit \(5\) is: \[ 50 \] So this adds \(1\) more number.
Step 3: Total count. \[ 10+1=11 \]
Step 4: Final answer. \[ \boxed{11} \]
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