In this number analogy, “357 is to 714 as 468 is to ______”. Identify the number that completes the analogy using the same multiplication pattern applied in the first pair.

Introduction / Context:
This is a simple numeric analogy where one number is an exact multiple of the other. For the pair 357 : 714, the second number is clearly related to the first by a simple multiplication. We need to discover that rule and then apply it to 468 to find the missing term in the second pair.

Given Data / Assumptions:

• First pair: 357 corresponds to 714. • Second pair: 468 corresponds to ? • Options: 579, 417, 936, 864. • We suspect direct multiplication by a small integer such as 2.

Concept / Approach:
Checking for a factor of 2 is an obvious first step because 714 is exactly twice 357. That is, 357 * 2 = 714. If the pattern is simply “multiply by 2”, then we apply the same rule to 468 and check which option matches the result. This style of analogy helps to verify basic multiplication and scaling skills with three digit numbers.

Step-by-Step Solution:
Step 1: Verify the relationship between 357 and 714. Compute 357 * 2. 300 * 2 = 600, 50 * 2 = 100, and 7 * 2 = 14. Adding gives 600 + 100 + 14 = 714. So 714 = 2 × 357. Step 2: Apply the same rule to 468. Compute 468 * 2. 400 * 2 = 800, 60 * 2 = 120, and 8 * 2 = 16. Adding gives 800 + 120 + 16 = 936. Step 3: Compare 936 with the options. It appears as option C.

Verification / Alternative check:
We can express the pattern as y = 2x. For x = 357, y = 714. For x = 468, y = 936. None of the other options is equal to 2 × 468. For example, 579 is far smaller, and 864 equals 3 × 288, not directly related to 468 by a factor of exactly 2. This confirms that 936 alone preserves the simple doubling pattern.

Why Other Options Are Wrong:
• 579: This is not an integer multiple of 468 that mirrors the original 2× pattern. • 417: Less than the original number 468, so it cannot be a “times 2” result. • 864: While 864 is 2 × 432, it is not 2 × 468; thus it does not follow the same rule as 357 : 714.

Common Pitfalls:
Some candidates may over search for patterns in the digits (for example, trying to add or rearrange digits), but the cleanest explanation uses direct multiplication. Whenever one number is exactly twice another, doubling is almost always the intended pattern. Recognising this quickly saves time and reduces the chance of overcomplicating the problem.

Final Answer:
The number that completes the analogy is 936.