Select the triad in which the numbers are related in the same way as are the numbers of the given triads. (54, 65, 76), (48, 59, 70) (NOTE : Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g. 13 – Operations on 13 such as adding /deleting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed)
- (a)(42, 57, 68)
- (b)(27, 38, 50)
- (c)(38, 49, 60)
- (d)(31, 41, 53)
Answer
Why
Correct — C. Take the two gaps inside each given triad.
Rule: +11, then +11 again.
(54, 65, 76): 54 + 11 = 65, 65 + 11 = 76
(48, 59, 70): 48 + 11 = 59, 59 + 11 = 70
Option (c): 38 + 11 = 49, 49 + 11 = 60. Both gaps are 11, so option (c) is the triad built the same way.
Why the others are wrong
- (a)(42, 57, 68) — 42 → 57 is a jump of 15. The second gap, 57 → 68, is 11, so this triad is right on its second step and wrong on its first.
- (b)(27, 38, 50) — 27 → 38 is 11 but 38 → 50 is 12. A triad in this family adds the same 11 twice, so one correct gap is not enough.
- (d)(31, 41, 53) — 31 → 41 is 10 and 41 → 53 is 12. The middle number should be 42; 41 is printed, and the two wrong gaps cancel in the total.
Concept
A triad analogy is a three-term arithmetic progression in disguise. Compute both gaps for each given triad and check that they agree.
The danger is testing the span instead. A triad with a common difference of 11 runs 22 from first to last, and an option can span 22 while neither of its own gaps is 11.
So test gap by gap. The span is a consequence of the rule, not the rule itself.
Option (d) spans 53 − 31 = 22, exactly like the keyed triad's 60 − 38 = 22. A candidate who checks only first-to-last cannot separate them.
Key facts
- Both given triads step +11 twice: 54, 65, 76 and 48, 59, 70.
- A triad with a common difference of 11 spans 22 from first term to last.
- Option (d) also spans 22, so the span alone does not decide the question.
Study next
Common traps
- Checking only the first-to-last span, which lets (31, 41, 53) through.
- Checking only the first gap, which lets (27, 38, 50) through.
- Looking for a multiplication because the wording resembles a set analogy, when both steps here are plain addition.
SSC sets the triad stem at Reasoning Q.14 on 19 Sep 2024, 16:00 and Q.10 on 23 Sep 2024, 09:00.
The wording is nearly identical to the three-number set stem, and both bracket their groups the same way, so the layout tells you nothing. Derive the rule from the numbers themselves.
Related PYQs
No directly related past PYQ was found.