The apartments in Greg's building are named using the letters A, B, C, and D and the digits 1 through 9. How many apartments are there in Greg's building if each apartment is named by a single letter followed by a single digit?

Rationale

There are 36 apartments in Greg's building.

Each apartment name consists of one letter from the set {A, B, C, D} and one digit from the set {1, 2, 3, 4, 5, 6, 7, 8, 9}. Since there are 4 letters and 9 digits, the total number of unique apartment names can be calculated by multiplying the number of letters by the number of digits: 4 × 9 = 36.

A (36) CORRECT

This choice correctly represents the total number of unique combinations of letters and digits. With 4 letters and 9 digits, the multiplication yields 36 distinct apartment names, confirming the calculation.

B (16) YOUR ANSWER

This choice incorrectly suggests that there are only 16 apartments. It appears to be derived from a misunderstanding, possibly by assuming there are 4 combinations from letters and 4 from digits (e.g., 4 × 4), which is not applicable here since the digits range from 1 to 9.

C (40) YOUR ANSWER

This choice implies there are 40 apartments, which is incorrect. The miscalculation might arise from mistakenly adding the number of letters and digits (4 + 9 = 13) and then inaccurately multiplying or assuming a different range of digits.

D (13) YOUR ANSWER

This selection suggests a total of 13 apartments, likely based on a misinterpretation of how to combine the letters and digits. It does not account for the full range of digits available (1 through 9), which results in a significant undercount of potential combinations.

Conclusion

In total, Greg's building comprises 36 uniquely named apartments achieved through the combination of 4 letters and 9 digits. Understanding the multiplication of available options highlights the correct count, while the other choices stem from various miscalculations or misunderstandings regarding the naming convention.

The apartments in Greg's building are named using the letters A, B, C, and D and the digits 1 through 9. How many apartments are there in Greg's building if each apartment is named by a single letter followed by a single digit?

There are 36 apartments in Greg's building.

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test