In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. Select the set in which the numbers are related in the same way as are the numbers of the following sets. (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.) (280, 140) (186, 93)
- (a)(92, 51)
- (b)(86, 48)
- (c)(166, 84)
- (d)(118, 59)
Answer
Why
Correct — D. Rule: second number = first number ÷ 2.
280 ÷ 2 = 140
186 ÷ 2 = 93
Option (d) is the only set that repeats it: 118 ÷ 2 = 59, exactly the pair printed.
The rest fail the halving: 92 ÷ 2 = 46, not 51; 86 ÷ 2 = 43, not 48; 166 ÷ 2 = 83, not 84.
Why the others are wrong
- (a)(92, 51) — 92 halves to 46, and the pair prints 51 — five above half. Near-misses like this are what the item is built on, so the division has to be done rather than eyeballed.
- (b)(86, 48) — 86 halves to 43, five below the printed 48. No halving relation links 86 to 48, which is the relation both given sets share.
- (c)(166, 84) — 166 halves to 83, one below the printed 84. A single unit off is exactly the gap an estimated halving misses, and it is enough to break the rule.
Concept
A number-pair analogy hands you two worked examples and asks you to name the operation they share.
Test the cheapest relations first: halve, double, add or subtract a constant, square, cube. Here 280 to 140 and 186 to 93 are both an exact halving, so the rule is settled on the second example.
The bracketed NOTE is doing real work. It bars reading 280 as the digits 2, 8 and 0, so only whole-number arithmetic is legal.
Each wrong option sits within five of half its own first number — 51 against 46, 48 against 43, 84 against 83. That spacing is what the item is built on: it rewards exact division and punishes an estimate.
Key facts
- 280 ÷ 2 = 140 and 186 ÷ 2 = 93, so both given sets share a halving rule.
- Among the options only 118 and 59 satisfy the halving, since 118 ÷ 2 = 59.
- The bracketed NOTE bars splitting a number into digits, so 280 may not be read as 2, 8 and 0.
Study next
Common traps
- Halving only the first given set and assuming the rule without checking 186 and 93
- Accepting an option that is within a unit or two of half, such as 166 and 84
- Breaking a number into its digits despite the NOTE that forbids it
The identical stem, NOTE and all, runs at 9 Sep 2024, 16:00, Reasoning Q.18 with the sets (12, 145) and (9, 82), and at 24 Sep 2024, 16:00, Reasoning Q.11 with (26, 114) and (47, 198).
The odd-one-out form of the same question type is at Reasoning Q.13 of this paper, where the shared rule is first = second × 8 − 1 rather than a halving.
Related PYQs
No directly related past PYQ was found.