The same operation(s) are followed in all the given number pairs except one.…
2024
The same operation(s) are followed in all the given number pairs except one. Find that odd number pair.
(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.)
Answer: C. 11 : 35 — Concept: In an odd-pair question, every pair is built by one and the same arithmetic rule that turns the first number into the second. The method is therefore…
- A.
12 : 39
- B.
15 : 48
- C.
11 : 35
- D.
13 : 42
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Correct answer: C
Concept: In an odd-pair question, every pair is built by one and the same arithmetic rule that turns the first number into the second. The method is therefore two-step: first fit a single rule to the majority of the pairs, then test every pair against that one rule. The pair the rule fails to reproduce is the odd pair. Because the note bars digit-splitting, the rule must act on the whole number, so only operations such as multiplying, adding or subtracting a constant are admissible.
Application: Fit the linear form second = 3 × first + 3, and test each pair against it.
For 12 : 39 — 3 × 12 = 36, and 36 + 3 = 39, which is the second number of the pair.
For 15 : 48 — 3 × 15 = 45, and 45 + 3 = 48, which is the second number of the pair.
For 13 : 42 — 3 × 13 = 39, and 39 + 3 = 42, which is the second number of the pair.
For 11 : 35 — 3 × 11 = 33, and 33 + 3 = 36, but the second number of the pair is 35, one less than the rule requires.
Cross-check: Compute the surplus (second − 3 × first) for every pair. Three pairs give the same constant surplus of 3 and one gives 2, so the rule 3n + 3 is the shared operation and exactly one pair stands outside it.
Pair | 3 × first | Second number | Surplus |
|---|---|---|---|
12 : 39 | 36 | 39 | 3 |
15 : 48 | 45 | 48 | 3 |
13 : 42 | 39 | 42 | 3 |
11 : 35 | 33 | 35 | 2 |
Contrast: No competing rule rescues the outlier. The gaps between the two numbers of each pair are 27, 33, 24 and 29, which follow no pattern, and the ratios 3.25, 3.2, 3.18 and 3.23 are not constant either. The multiply-by-3-then-add-3 rule is the only one that fits three pairs exactly.
Result: The odd number pair is 11 : 35.