GMAT Practice Question: Jorge's bank statement showed a balance that was 0.54 dollars greater than what his records...
Question
Jorge's bank statement showed a balance that was 0.54 dollars greater than what his records showed. He discovered that he had written a check for x.yz dollars and had recorded it as x.zy dollars, where each of x, y, and z represents a digit from 0 though 9. Which of the following could be the value of z ?
- 2
- 3
- 4
- 5
- 6
Topics: decimals, digits as unknowns, simultaneous equations
Solution
Step 1
We translate the phrases to set up the difference between the recorded and actual check amounts.
\textbf{\text{"recorded it as x.zy dollars\textbf{\text{"}} - \textbf{\text{"}}written a check for x.yz dollars"}} = 0.54
Step 2
We write each amount in terms of x, y, and z based on place value.
x + \frac{z}{10} + \frac{y}{100} - (x + \frac{y}{10} + \frac{z}{100}) = 0.54
Step 3
We combine like terms to simplify the expression.
\frac{9(z - y)}{100} = 0.54
Step 4
We clear the denominator and solve for the difference.
9(z - y) = 0.54 \times 100 9(z - y) = 54 z - y = 6
Step 5
Since z and y are digits from 0 to 9 and their difference is 6, z could be 6, 7, 8, or 9, and among the answer choices only 6 appears.
z - y = 6 \text{Possible values for }z\text{ are }6, 7, 8, \text{ or }9 \text{Only }6\text{ appears in the answer choices}
Answer
6
