An integer is defined to be upright if the sum of its first two digits equals its third digit. For example, 145 is an upright integer since $1+4=5$. How many positive 3-digit integers are upright?
(A) 28
(B) 39
(C) 36
(D) 45
(E) 50
From the definition, the first and second digits of an upright integer automatically determine the third digit, since it is the sum of the first two digits.

Consider first those upright integers beginning with 1.

These are $101,112,123,134,145,156,167,178$, and 189 , since $1+0=1,1+1=2$, and so on. (The second digit cannot be 9 , otherwise the last "digit" would be $1+9=10$, which is impossible.) There are 9 such numbers.

Beginning with 2 , the upright integers are 202, 213, 224, 235, 246, 257, 268, and 279. There are 8 of them.

We can continue the pattern and determine the numbers of the upright integers beginning with $3,4,5,6,7,8$, and 9 to be $7,6,5,4,3,2$, and 1 .

Therefore, there are $9+8+7+6+5+4+3+2+1=45$ positive 3 -digit upright integers.

ANSWER: (D)