Question:
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In quantitative comparison questions, be vigilant about missing information. If any variable or number needed for a calculation is not provided for one of the columns, the answer is almost always (D).
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 D
Solution and Explanation
Step 1: Understanding the Concept:
This problem requires using the combination formula and the fundamental principle of counting to determine the total number of ways to make a purchase. We need to evaluate whether we have sufficient information to calculate the values for both columns.
Step 2: Key Formula or Approach:
The number of ways to choose \(r\) items from a set of \(n\) is \(C(n, r)\). The total number of choices for a sequence of independent events is the product of the choices for each event.
Step 3: Detailed Explanation:
For Column A:
The person needs to make three separate choices: 1. Choose 1 fountain pen from 10 available varieties: \( C(10, 1) = 10 \) ways. 2. Choose 1 ball pen from 12 available varieties: \( C(12, 1) = 12 \) ways. 3. Choose 2 pencils from 5 available varieties: \( C(5, 2) = \frac{5 \times 4}{2} = 10 \) ways. The total number of choices is the product of these individual choices: \[ \text{Total Choices} = 10 \times 12 \times 10 = 1200 \] So, Quantity A is 1200.
For Column B:
The person wants to buy 1 book, 1 notebook, and 2 pencils. However, the problem does not provide the following crucial information:
The number of available book varieties to choose from.
The number of available notebook varieties to choose from.
The number of available pencil varieties to choose from.
Without knowing the size of the selection pools for books, notebooks, and pencils, we cannot calculate the total number of choices.
Step 4: Final Answer:
Quantity A = 1200. Quantity B cannot be calculated due to missing information. Therefore, the relationship between the two quantities cannot be determined.
This problem requires using the combination formula and the fundamental principle of counting to determine the total number of ways to make a purchase. We need to evaluate whether we have sufficient information to calculate the values for both columns.
Step 2: Key Formula or Approach:
The number of ways to choose \(r\) items from a set of \(n\) is \(C(n, r)\). The total number of choices for a sequence of independent events is the product of the choices for each event.
Step 3: Detailed Explanation:
For Column A:
The person needs to make three separate choices: 1. Choose 1 fountain pen from 10 available varieties: \( C(10, 1) = 10 \) ways. 2. Choose 1 ball pen from 12 available varieties: \( C(12, 1) = 12 \) ways. 3. Choose 2 pencils from 5 available varieties: \( C(5, 2) = \frac{5 \times 4}{2} = 10 \) ways. The total number of choices is the product of these individual choices: \[ \text{Total Choices} = 10 \times 12 \times 10 = 1200 \] So, Quantity A is 1200.
For Column B:
The person wants to buy 1 book, 1 notebook, and 2 pencils. However, the problem does not provide the following crucial information:
The number of available book varieties to choose from.
The number of available notebook varieties to choose from.
The number of available pencil varieties to choose from.
Without knowing the size of the selection pools for books, notebooks, and pencils, we cannot calculate the total number of choices.
Step 4: Final Answer:
Quantity A = 1200. Quantity B cannot be calculated due to missing information. Therefore, the relationship between the two quantities cannot be determined.
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