Question

• A. The quantity on the left is greater
• B. The quantity on the right is greater
• C. Both are equal
• D. The relationship cannot be determined without further information

Hint:

Problems involving routes, paths, or sequences of choices are often solved with the multiplication principle. Note that the order of multiplication does not affect the final product (commutative property), so even though the journeys are in reverse order, the result is the same.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem is a direct application of the fundamental principle of counting (or the multiplication principle). When a journey consists of several sequential, independent stages, the total number of routes is the product of the number of options available for each stage.
Step 2: Key Formula or Approach:
If there are \(n_1\) ways to perform the first task, \(n_2\) ways for the second, and \(n_k\) for the \(k\)-th task, then the total number of ways to perform the sequence of tasks is \(n_1 \times n_2 \times \dots \times n_k\).
Step 3: Detailed Explanation:
For Column A:
Sunita's journey is a sequence of three stages: A \(\rightarrow\) B \(\rightarrow\) C \(\rightarrow\) D. - Number of routes from A to B = 3. - Number of routes from B to C = 5. - Number of routes from C to D = 2. Total number of routes for Sunita = (Routes A\(\rightarrow\)B) \( \times \) (Routes B\(\rightarrow\)C) \( \times \) (Routes C\(\rightarrow\)D) \[ \text{Total Routes} = 3 \times 5 \times 2 = 30 \] So, Quantity A is 30.
For Column B:
Shelly's journey is also a sequence of three stages: D \(\rightarrow\) C \(\rightarrow\) B \(\rightarrow\) A. The number of flights between two cities is the same regardless of the direction of travel. - Number of routes from D to C = 2. - Number of routes from C to B = 5. - Number of routes from B to A = 3. Total number of routes for Shelly = (Routes D\(\rightarrow\)C) \( \times \) (Routes C\(\rightarrow\)B) \( \times \) (Routes B\(\rightarrow\)A) \[ \text{Total Routes} = 2 \times 5 \times 3 = 30 \] So, Quantity B is 30.
Step 4: Final Answer:
Comparing the two quantities:
Quantity A = 30
Quantity B = 30
The two quantities are equal.