If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions...
GMAT Advanced Topics : (AT) Questions
Source: Mock
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Post a Query
If all of the telephone extensions in a certain company must be even numbers, and if each of the extensions uses all four of the digits 1, 2, 3, and 6, what is the greatest number of four-digit extensions that the company can have?
Solution
- Translate the problem requirements: We need to find how many different four-digit telephone extensions can be formed using digits 1, 2, 3, and 6 exactly once, subject to the extension being even.
- Identify the constraint: Only 2 or 6 can occupy the last digit to yield an even number.
- Fix the constrained position: Place 2 or 6 last, then permute the remaining three digits (\(3! = 6\) ways each).
- Apply the multiplication principle: Sum the cases to get 12 total extensions.
Execution
Case 1: Ends in 2 → \(3! = 6\) ways. Case 2: Ends in 6 → \(3! = 6\) ways. Total = 12.
Final Answer
12
Answer Choices Explained
A
4
B
6
C
12
D
16
E
24
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