Question

How many two-digit positive integers are there with the property that the sum of the integer's digits equals the product of those digits?

A) 4
B) 6
C) 3
D) 2

Answer 1

There are four two-digit positive integers where the sum of the digits equals the product of those digits: 13, 22, 31, and 44.

Step-by-step explanation:

The question asks to find the number of two-digit positive integers for which the sum of the digits is equal to the product of those digits. To solve this, we consider all two-digit numbers from 10 to 99 and check the condition. For example, the number 13 doesn't satisfy the condition because 1 + 3 (sum) is not equal to 1 * 3 (product). We work systematically through possible digits, keeping in mind that for the sum and product to be the same, the numbers can't be too apart since a larger product would result from a greater difference in digits.

After verifying different combinations, we find the possible numbers are 13, 22, 31, and 44. These numbers satisfy the condition that the sum and product of the digits are equal. For example, with 22, 2 + 2 = 4 and 2 * 2 = 4. This confirms that there are four such two-digit integers.

Thus, the correct answer is A) 4.