Complete the following number analogy by finding the missing term: 12 : 30 :: 14 : ?

Introduction / Context:
This is a simple number analogy question. The pair 12 : 30 is given, and we are asked to complete the analogous pair 14 : ?. To solve such questions, we have to identify the numerical relationship that links the first number in the pair with the second and then apply the same relationship to the new first number to find the missing second number.

Given Data / Assumptions:

• First pair: 12 and 30.
• Second pair: 14 and an unknown number.
• We assume a simple arithmetic or proportional relationship between the numbers in each pair.

Concept / Approach:
A very common pattern in such analogies is a simple ratio or proportion between the two numbers in each pair. We examine whether 12 and 30 form a ratio that can be preserved when we move to 14 and the unknown number. Specifically, we test if the pair follows a constant ratio like 12:30 = 2:5, and then map this ratio to the second pair 14:x.

Step-by-Step Solution:
Compute the ratio of the first pair: 12:30 can be simplified by dividing both numbers by 6, giving 2:5.Assuming the same ratio holds for 14 and the unknown number x, we set up 14:x = 2:5.From the property of proportions, x = (14 × 5) / 2.Calculate x: 14 × 5 = 70, and 70 ÷ 2 = 35. So the missing number must be 35.

Verification / Alternative check:
Check that the simplified ratio 14:35 again reduces to 2:5. Divide both numbers by 7 to obtain 2:5, which matches the ratio from the first pair.This confirms that the same proportional relationship holds for both pairs, so the analogy is consistent.

Why Other Options Are Wrong:
Option 36 would give the ratio 14:36, which simplifies to 7:18 and does not match 2:5.Option 28 gives 14:28 = 1:2, which again is different from 2:5.Option 42 gives 14:42 = 1:3, which clearly does not match the original ratio either.

Common Pitfalls:
A frequent mistake is to look for an additive pattern, for example noticing that 12 + 18 = 30 and then wrongly adding the same increment to 14, which would give 32 instead of any offered option.Ignoring the possibility of a proportional relationship can easily lead to incorrect guesses in analogy questions.

Final Answer:
Maintaining the ratio 2:5 between the two numbers in each pair, the correct completion of the analogy is 35.