Question

Let \( x \) be the 2-digit numbers which can be created from 5 distinct numbers. Which of the following options is less than \( x \)? Indicate all possible options.

• A. 10
• B. 15
• C. 20
• D. 40
• E. 60

Hint:

When working with problems involving digits, always test the extreme smallest and largest values to narrow down possibilities.

Answer 1

The Correct Option is A

Step 1: Understanding the problem.
We are asked about the possible 2-digit numbers that can be formed using 5 distinct digits.
Step 2: Smallest possible two-digit number.
The smallest 2-digit number that can be formed using 5 distinct digits must be at least 12 (since the tens digit cannot be 0).
Step 3: Compare with options.
- Option (1) 10: Less than 12, so valid.
- Option (2) 15: Also less than many possible 2-digit values, valid.
- Option (3) 20: Less than many possible 2-digit numbers, valid.
- Option (4) 40: Less than 2-digit numbers formed later, valid.
- Option (5) 60: Not necessarily less than all, so not correct. Thus, correct answers are 10, 15, 20, and 40.