Question

Find the number of positive integers that satisfy both the following conditions: each digit is a $1$ or a $3$, the sum of the digits is $12$.

A) 1
B) 2
C) 3
D) 4

Answer 1

There are 4 positive integers where each digit is either a 1 or a 3 and the sum of the digits is 12. The numbers are 1113, 1131, 1311, and 3111. The correct answer is D) 4.

Step-by-step explanation:

The student is asking to find the number of positive integers where each digit is either a 1 or a 3 and the sum of the digits is 12.

Let's approach this step by step:

1. Since the smallest number we can make with 1's and 3's that sums to 12 is with four 3's (3+3+3+3=12).
2. The largest number we can make would involve ten 1's and one 2, but since we can only use 1's and 3's, the closest we can get is nine 1's and one 3, which doesn't give us a sum of 12.
3. Now we try to form numbers with 1's and 3's that sum to 12, and we find: 1113, 1131, 1311, and 3111.

So there are 4 positive integers that satisfy both conditions.

The correct answer is D) 4.