$U V W$ and $X Y Z$ are each 3-digit integers. $U, V, W, X, Y$, and $Z$ are different digits chosen from the integers 1 to 9 . What is the largest possible value for $U V W-X Y Z$ ?
(A) 678
(B) 864
(C) 885
(D) 888
(E) 975

Part B: Each correct answer is worth 6.
To make the difference $U V W-X Y Z$ as large as possible, we make $U V W$ as large as possible and $X Y Z$ as small as possible.

The hundreds digit of a number contributes more to its value than its tens digit, and its tens digit contributes more to its value than its units digit.

Thus, we construct the largest possible number $U V W$ by choosing 9 (the largest digit) to be its hundreds digit, $U$, and by choosing 8 (the second largest digit) to be its tens digit, $V$, and by choosing 7 (the third largest digit) to be the units digit, $W$.

Similarly, we construct the smallest possible number $X Y Z$ by choosing 1 (the smallest allowable digit) to be its hundreds digit, $X$, and 2 (the second smallest allowable digit) to be its tens digit, $Y$, and by choosing 3 (the third smallest allowable digit) to be its units digit, $Z$.

The largest possible difference is $U V W-X Y Z$ or $987-123$ or 864 .

ANswer: (B)