Find the set that is like the given set (13 : 20 : 27). The three numbers must form an arithmetic progression with a common difference of 7.

Introduction / Context:
Similarity questions often rely on reproducing the same structural relation in a new set. The reference set (13 : 20 : 27) is an arithmetic progression with common difference 7. We must choose the option that also forms an AP with d = 7.

Given Data / Assumptions:

• Reference: 13, 20, 27 → differences: +7 and +7.
• Options: (3, 11, 18), (18, 25, 32), (18, 27, 72), (7, 14, 28).

Concept / Approach:
For each option, compute consecutive differences. A matching set must have both gaps equal to 7.

Step-by-Step Solution:

Verification / Alternative check:
AP condition: middle − first = last − middle. Only (18, 25, 32) satisfies 25 − 18 = 32 − 25 = 7.

Why Other Options Are Wrong:
They either do not have equal gaps or have gaps different from 7.

Common Pitfalls:
Assuming that one difference being 7 is enough. For an AP, both differences must be equal (here, both must be 7).

Final Answer:
(18 : 25 : 32) is like the given set.