The sum of ten consecutive integers is $S$. Ten times the smallest of these integers is $T$. What is the value of $S-T$ ?
(A) 45
(B) 55
(C) 10
(D) 9
(E) 66
Solution 1

Let the ten integers be $n, n+1, n+2, n+3, n+4, n+5, n+6, n+7, n+8$, and $n+9$.

Therefore, $S=n+(n+1)+(n+2)+(n+3)+(n+4)+(n+5)+(n+6)+(n+7)+(n+8)+(n+9)$ or $S=10 n+45$ and $T=10 n$.

Thus, $S-T=(10 n+45)-10 n=45$.

## Solution 2

Since the question implies that the value of $S-T$ must be the same no matter what 10 integers we try, then we calculate $S-T$ for the integers 1 through 10 .

In this case, $S=1+2+3+4+5+6+7+8+9+10=55$ and $T=10(1)=10$ or $S-T=45$.

ANSWER: (A)