Problem Solving

BTGModeratorVI wrote: ↑

Wed Jan 06, 2021 8:02 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 though 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