How many two digit numbers are divisible by 5 such that remainder is 1.

To find how many two-digit numbers are divisible by 5 with a remainder of 1, we first need to identify the two-digit numbers that meet these criteria.

Understanding the Criteria

A number that is divisible by 5 can end in either 0 or 5. However, since we want a remainder of 1, we can express our two-digit number as:

• Numbers ending in 1 (e.g., 11, 21, 31, etc.)

Identifying the Range

The smallest two-digit number is 10 and the largest is 99. We will look for numbers in this range that fit our criteria.

Finding the Numbers

We can write the two-digit numbers that are 1 more than multiples of 5:

• 11 (5 * 2 + 1)
• 16 (5 * 3 + 1)
• 21 (5 * 4 + 1)
• 26 (5 * 5 + 1)
• 31 (5 * 6 + 1)
• 36 (5 * 7 + 1)
• 41 (5 * 8 + 1)
• 46 (5 * 9 + 1)
• 51 (5 * 10 + 1)
• 56 (5 * 11 + 1)
• 61 (5 * 12 + 1)
• 66 (5 * 13 + 1)
• 71 (5 * 14 + 1)
• 76 (5 * 15 + 1)
• 81 (5 * 16 + 1)
• 86 (5 * 17 + 1)
• 91 (5 * 18 + 1)
• 96 (5 * 19 + 1)

Counting the Valid Numbers

Now, let’s count these numbers:

11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96.

There are a total of 18 two-digit numbers that are divisible by 5 and leave a remainder of 1.

Final Answer

Thus, the answer is 18.