Vincen wrote: ↑

Thu Sep 03, 2020 6:22 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 x, the whole dollar amount, on the check is the same as on the record book, we can ignore it. Therefore, only yz, the cent amount on the check and zy, the cent amount on the record book can differ by 54 cents. Furthermore, since the balance of the bank statement is 54 cents higher than his record book, it must be the case zy is greater than yz. Since 60 - 06 = 54, 71 - 17 = 54, 82 - 28 = 54, and 93 - 39 = 54, we see that zy can be 60, 71, 82, or 93, i.e., z can be 6, 7, 8 or 9. Since only 6 is given in the answer choices, 6 is the correct answer.

Answer: E