Select the triad in which the numbers are related in the same way as are the numbers of the given triads. (16, 33, 67), (19, 39, 79) (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)(22, 45, 91)
- (b)(14, 27, 53)
- (c)(18, 36, 80)
- (d)(21, 45, 90)
Answer
Why
Correct — A. Each number is double the one before it, plus 1 — and the same correction has to work on both steps of the chain.
Rule: next = previous × 2 + 1.
16 × 2 + 1 = 33, then 33 × 2 + 1 = 67 ✓
19 × 2 + 1 = 39, then 39 × 2 + 1 = 79 ✓
Option (a): 22 × 2 + 1 = 45, then 45 × 2 + 1 = 91 ✓ Both steps hold, so (22, 45, 91) belongs to the family.
Why the others are wrong
- (b)(14, 27, 53) — 14 × 2 + 1 = 29, not 27. This triad is tidy inside itself — 14 × 2 − 1 = 27 and 27 × 2 − 1 = 53 — but its correction is −1, not the +1 the two model triads use.
- (c)(18, 36, 80) — 18 × 2 + 1 = 37, not 36, and 36 × 2 + 1 = 73, not 80. Neither step matches; the numbers only roughly double.
- (d)(21, 45, 90) — 21 × 2 + 1 = 43, not 45, so it fails at the very first step. Its second step is a plain doubling (45 × 2 = 90), so its two steps do not even share one rule.
Concept
A triad applies the same operation twice in a chain, so any candidate rule must survive both steps, not just the first.
When the numbers roughly double, test doubling with a small correction: ×2 + 1, ×2 − 1, ×2 + 3. Fix the correction on the first step, then insist the identical correction works on the second.
Two model triads are given for exactly this reason. One model alone cannot separate ×2 + 1 from ×2 − 1, because both would look like "about double".
Option (b) is the near-miss to watch. It is perfectly consistent inside itself on ×2 − 1, so it reads as a rule-following triad.
Consistency inside an option is not the test. Agreeing with the two triads in the stem is.
Key facts
- 16 × 2 + 1 = 33 and 33 × 2 + 1 = 67.
- 19 × 2 + 1 = 39 and 39 × 2 + 1 = 79.
- 22 × 2 + 1 = 45 and 45 × 2 + 1 = 91.
- Option (b), (14, 27, 53), is consistent on ×2 − 1 — the wrong correction, not a wrong arithmetic.
Study next
Common traps
- Settling for "roughly double" and picking whichever option is nearest — all three wrong triads double approximately.
- Judging an option by whether it is self-consistent. Option (b) is, on ×2 − 1, and is still wrong.
- Working backwards with (x − 1) ÷ 2 in a hurry and dropping the correction on one of the two steps.
SSC supplies two model triads precisely so that one model cannot fix the correction. The same shift uses the other common shape at Reasoning Q.4 (9 Sep 2024, 12:30), where the constant is added once — first × second + 11 — rather than at every step.
Related PYQs
No directly related past PYQ was found.