VJesus12 wrote: ↑

Fri Feb 19, 2021 6:56 am

Jorge's bank statement showed a balance that was \(\$0.54\) greater than what his records showed. He discovered that he had written a check for \(\$x.yz\) and had recorded it as \(\$x.zy,\) where each of \(x, y,\) and \(z\) represents a digit from \(0\) through \(9.\) Which of the following could be the value of \(z?\)

A. 2
B. 3
C. 4
D. 5
E. 6

Answer: E

Source: Official Guide

Solution:

Since the bank statement has a balance that is greater than his records, the check he wrote must be less than what he had recorded. That is, x.yz < x.zy, and their difference is 0.54. Therefore, in cents, we can create the equation:

(100x + 10z + y) - (100x + 10y + z) = 54

9z - 9y = 54

z - y = 6

z = 6 + y

Since y is nonnegative, z must be at least 6. Therefore, E is the correct answer.

Answer: E