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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question:** A computer engineer is analyzing signals where a certain 3-digit number is needed to be divisible by 11. How many 3-digit numbers meet this criterion?

📌 A 3-digit number ranges from 100 to 999. We need to find how many of these numbers are divisible by 11. A number is divisible by 11 if the difference between the sum of its digits in odd positions and the sum of its digits in even positions is a multiple of 11.

📌 First, find the smallest 3-digit number divisible by 11:

📌 \[ 100 \div 11 = 9.09 \]

📌 The smallest integer greater than or equal to 9.09 is 10, so:

📌 \[ 11 \times 10 = 110 \]

📌 Now, find the largest 3-digit number divisible by 11:

📌 \[ 999 \div 11 = 90.8181 \]

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