M23-13

Official Solution:


If \(z\) is a three-digit positive integer, what is the tens digit of \(z\) ?

(1) The tens digit of \(z - 91\) is 3.

If \(z-91=130\), then \(z=130+91=221\) and the tens digit of \(z\) is 2.;

If \(z-91=139\), then \(z=139+91=230\) and the tens digit of \(z\) is 3..

Two different answers, hence this statement is not sufficient.

(2) The units digit of \(z + 9\) is 5.

From this information, we can determine that the units digit of \(z\) is 6. However, the tens digit of \(z\) could be any digit between 0 and 9. If \(z+9=115\), then \(z=115-9=106\) and the tens digit of \(z\) is 0.;

If \(z+9=125\), then \(z=125-9=116\) and the tens digit of \(z\) is 1. .

Two different answers, hence this statement is not sufficient.

(1)+(2) From (1) we know that \(z\) is the sum of a number with a tens digit of 3 and 91 and from (2) we know that the units digit of \(z\) is 6.

In order for the sum to have a units digit of 6, the units digit of the first number must be 5. Hence:
Therefore, the tens digit of \(z\) is 2. Sufficient.

Answer: C