Mnahattan Challenge Problem of the week! - 21/03/07

For a three-digit number xyz, where x, y, and z are the digits of the number, the function f(xyz) = 5^x2^y3^z. If f(abc) = 3 * f(def), what is the value of abc - def?

(A) 1
(B) 2
(C) 3
(D) 9
(E) 27


Answer : A
It is given in the question that .

It is obvious that the digits b, c, e, f are integers from 0 to 9 whereas that the digits a and d are integers from 1 to 9 (can't be equal to 0 because they are in the hundreds place).
For the above statement to be true, must be equal to , and .
Hence .

As the only difference between abc and def is in the units digits, the difference between these three-digit numbers is equal to , or 1.

Thus the right answer is A.