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.
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A(3 : 11 : 18)
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B(18 : 25 : 32)
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C(18 : 27 : 72)
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D(7 : 14 : 28)
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ENone of these
Answer
Correct Answer: (18 : 25 : 32)
Explanation
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:
(3, 11, 18): differences +8 and +7 → not consistent (d ≠ 7 for first gap).(18, 25, 32): differences +7 and +7 → perfect match.(18, 27, 72): differences +9 and +45 → not an AP with d = 7.(7, 14, 28): differences +7 and +14 → not equal gaps.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.