25 : 625 :: 35 : ? — Identify the numerical pattern connecting the pairs and compute the missing term.

Introduction / Context:
Number analogies require spotting the transformation from the first to the second number in a pair, then applying the same rule to the next pair. Here, 25 maps to 625. We must infer the simplest consistent rule and use it to determine the image of 35.

Given Data / Assumptions:

• 25 → 625.
• We must find 35 → ? according to the same rule.
• The correct answer should be present among the options.

Concept / Approach:
Two natural hypotheses are: square (n^2) or multiply by a fixed factor. 25^2 = 625 is true, but if the rule were squaring, 35^2 = 1225, which is not in the options. The next simplest rule is multiplying by 25: 25 * 25 = 625; then 35 * 25 = 875, which appears in the options.

Step-by-Step Solution:
1) Test n^2: 25^2 = 625, 35^2 = 1225 (not listed).2) Test multiplication by 25: 25*25 = 625; apply to 35: 35*25 = 875.3) Match to available options: 875 fits.

Verification / Alternative check:
Check other options against simple patterns (e.g., +600, +?); none fits both pairs as naturally as *25.

Why Other Options Are Wrong:

• 1575, 1205, 635: Do not result from a single consistent transformation matching 25 → 625 as *25.

Common Pitfalls:
Locking onto squaring without verifying the second pair against choices. Always cross-check the hypothesized rule with all available options.

Final Answer:
875