In this number analogy, “7 is to 34” follows a certain rule. Using the same rule, “5 is to” which number?

Introduction / Context:
This is a simple number analogy question of the form “7 is to 34 as 5 is to what?”. You must identify the arithmetic rule that transforms 7 into 34 and then apply the same rule to 5 to find the corresponding number. Such problems are common in reasoning sections and usually involve basic algebraic expressions.

Given Data / Assumptions:

• The given relation is 7 → 34.
• We must find the number N such that 5 → N under the same rule.
• We assume a simple linear relation, such as N = a * x + b, where x is the starting number.
• Exactly one option should satisfy the pattern in a reasonable way.

Concept / Approach:
We try to express 34 in terms of 7 using basic operations. One neat possibility is to consider a linear transformation of the form f(x) = 5x - 1. If x = 7, then f(7) = 5 * 7 - 1 = 35 - 1 = 34, which matches the given relation. Once we have identified such a pattern, we apply it to x = 5 and compare the result with the answer choices.

Step-by-Step Solution:
Step 1: Begin with the relation 7 → 34.Step 2: Try a simple function f(x) = 5x - 1.Step 3: Evaluate f(7) = 5 * 7 - 1 = 35 - 1 = 34, which matches the given number.Step 4: Assume the same rule holds for 5, so compute f(5) = 5 * 5 - 1.Step 5: f(5) = 25 - 1 = 24.Step 6: Therefore, 5 should correspond to 24.

Verification / Alternative check:
We can briefly test if any simpler pattern might exist, such as squaring or adding a fixed number, but none matches as neatly as 5x - 1. For example, 7 squared is 49, not 34. Adding a fixed number “n” directly to 7 to get 34 would require n = 27, but then 5 + 27 = 32, which is not in the options. The linear transformation 5x - 1 is therefore the simplest and most consistent pattern that explains the given pair.

Why Other Options Are Wrong:
Option A (33): This would require a different function or inconsistent pattern when applied to 7.
Option C (54): There is no straightforward relationship from 5 that matches the rule producing 34 from 7.
Option D (41): Again, this does not come from 5 using the rule that maps 7 to 34.

Common Pitfalls:
Some candidates try to force a complex rule involving squares, cubes, or multiple steps without checking for a simpler linear relation. Others may guess by proportion or random arithmetic, leading to incorrect answers. A good strategy is to test small linear forms like ax + b first, because exam setters usually prefer simple patterns for such single-pair analogies.

Final Answer:
Applying the rule f(x) = 5x - 1, we get 5 → 24, so the correct answer is 24.