Max@Math Revolution wrote:If 2-digit positive integer n is 12 times the tens digit of n, what is the value of n?

1) The tens digit of n is 3.
2) The sum of the tens digit and the units digit of n is 9.

Target question: What is the value of n?

Given: 2-digit positive integer n is 12 times the tens digit of n
Let's see what 2-digit integers meet this condition.
Case a: If the tens digit of n is 1, then n could be 12
Case b: If the tens digit of n is 2, then n could be 24
Case c: If the tens digit of n is 3, then n could be 36
Case d: If the tens digit of n is 4, then n could be 48
That's it! There are no other possible values of n.
So, n must be one of these four values.
No onto the statements...

Statement 1: The tens digit of n is 3
When we check our 4 possible cases, we see that case c (n = 36) is the only one that meets the information provided in statement 1.
So, n MUST equal 36
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The sum of the tens digit and the units digit of n is 9.
When we check our 4 possible cases, we see that case c (n = 36) is the only one that meets the information provided in statement 1.
So, n MUST equal 36
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent