Show Hint
- The quantity on the left is greater
- The quantity on the right is greater
- Both are equal
- The relationship cannot be determined without further information
The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
This problem involves forming three-digit numbers from a given set of digits with a condition on their value (greater or less than 500). Since the problem does not state that repetition is not allowed, we assume repetition is allowed. The key is to analyze the choices for the hundreds digit.
Step 2: Key Formula or Approach:
We will use the fundamental principle of counting. The total number of possibilities is the product of the number of choices for each of the three places (hundreds, tens, units).
Step 3: Detailed Explanation:
The set of available digits is 2, 3, 4, 5, 6. There are 5 available digits.
For Column A: Numbers greater than 500
- For a three-digit number to be greater than 500, its hundreds digit must be 5 or 6.
- Hundreds place: 2 choices (5 or 6).
- Tens place: 5 choices (any of the 5 digits, as repetition is allowed).
- Units place: 5 choices (any of the 5 digits).
Total numbers>500 = (Choices for hundreds) \( \times \) (Choices for tens) \( \times \) (Choices for units)
\[ \text{Total numbers} = 2 \times 5 \times 5 = 50 \] So, Quantity A is 50.
For Column B: Numbers less than 500
- For a three-digit number to be less than 500, its hundreds digit must be 2, 3, or 4. - Hundreds place: 3 choices (2, 3, or 4). - Tens place: 5 choices (any of the 5 digits). - Units place: 5 choices (any of the 5 digits). Total numbers<500 = (Choices for hundreds) \( \times \) (Choices for tens) \( \times \) (Choices for units)
\[ \text{Total numbers} = 3 \times 5 \times 5 = 75 \] So, Quantity B is 75.
Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 50
Quantity B = 75
Quantity B is greater than Quantity A.
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