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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Be careful not to double-count numbers like 55, and remember to check both the units place and the tens place for the required digit.
Updated On: Jul 3, 2026
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The Correct Option is C
Solution and Explanation
Step 1: Concept
List the multiples of 5 and identify those containing the digit '5'.
Step 2: Meaning
Multiples of 5 end in 0 or 5. Those ending in 5 automatically satisfy the "has 5 as a digit" condition: 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 (10 numbers).
Step 3: Analysis
Now check multiples of 5 ending in 0 that contain 5: 50. Note that 55 was already counted. Are there any others? 100 doesn't have 5.
Step 4: Conclusion
The set is {5, 15, 25, 35, 45, 50, 55, 65, 75, 85, 95}. Wait, let's recount. {5, 15, 25, 35, 45, 50, 55, 65, 75, 85, 95} is 11 numbers. Final Answer: (C)
List the multiples of 5 and identify those containing the digit '5'.
Step 2: Meaning
Multiples of 5 end in 0 or 5. Those ending in 5 automatically satisfy the "has 5 as a digit" condition: 5, 15, 25, 35, 45, 55, 65, 75, 85, 95 (10 numbers).
Step 3: Analysis
Now check multiples of 5 ending in 0 that contain 5: 50. Note that 55 was already counted. Are there any others? 100 doesn't have 5.
Step 4: Conclusion
The set is {5, 15, 25, 35, 45, 50, 55, 65, 75, 85, 95}. Wait, let's recount. {5, 15, 25, 35, 45, 50, 55, 65, 75, 85, 95} is 11 numbers. Final Answer: (C)
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