Question:
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In quantitative comparison questions, always carefully analyze the wording. Here, "without using the digits..." is an indirect way of specifying the allowed digits. The two columns were designed to look different but result in the same calculation.
Updated On: Oct 3, 2025
- 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
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Both columns ask for the number of three-digit numbers that can be formed from a given set of digits. Since it's not specified that repetition is not allowed, we assume repetition of digits is allowed. The key is to correctly identify the set of usable digits for each column.
Step 2: Key Formula or Approach:
We will use the fundamental principle of counting. For a three-digit number, we have three places to fill: hundreds, tens, and units. The total number of possibilities is the product of the number of choices for each place.
Step 3: Detailed Explanation:
For Column A:
The available digits are {1, 2, 4, 9}. There are 4 available digits.
We need to form a three-digit number. Repetition is allowed.
Number of choices for the hundreds place = 4.
Number of choices for the tens place = 4.
Number of choices for the units place = 4.
Total number of three-digit numbers = 4 × 4 × 4 = 4³ = 64.
For Column B:
The digits we cannot use are {0, 3, 5, 6, 7, 8}.
The set of all digits is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
The digits we can use are those remaining: {1, 2, 4, 9}.
This is the exact same set of digits as in Column A.
We need to form a three-digit number using {1, 2, 4, 9}. Repetition is allowed.
Number of choices for the hundreds place = 4.
Number of choices for the tens place = 4.
Number of choices for the units place = 4.
Total number of three-digit numbers = 4 × 4 × 4 = 4³ = 64.
Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 64
Quantity B = 64
The two quantities are equal.
Both columns ask for the number of three-digit numbers that can be formed from a given set of digits. Since it's not specified that repetition is not allowed, we assume repetition of digits is allowed. The key is to correctly identify the set of usable digits for each column.
Step 2: Key Formula or Approach:
We will use the fundamental principle of counting. For a three-digit number, we have three places to fill: hundreds, tens, and units. The total number of possibilities is the product of the number of choices for each place.
Step 3: Detailed Explanation:
For Column A:
The available digits are {1, 2, 4, 9}. There are 4 available digits.
We need to form a three-digit number. Repetition is allowed.
Number of choices for the hundreds place = 4.
Number of choices for the tens place = 4.
Number of choices for the units place = 4.
Total number of three-digit numbers = 4 × 4 × 4 = 4³ = 64.
For Column B:
The digits we cannot use are {0, 3, 5, 6, 7, 8}.
The set of all digits is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.
The digits we can use are those remaining: {1, 2, 4, 9}.
This is the exact same set of digits as in Column A.
We need to form a three-digit number using {1, 2, 4, 9}. Repetition is allowed.
Number of choices for the hundreds place = 4.
Number of choices for the tens place = 4.
Number of choices for the units place = 4.
Total number of three-digit numbers = 4 × 4 × 4 = 4³ = 64.
Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 64
Quantity B = 64
The two quantities are equal.
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