The second number in the given number pairs is obtained by performing certain mathematical operation(s) on the first number. The same operation(s) are followed in all the 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.)

Correct — A. No two pairs share a difference, so the rule is not arithmetic on the gap. Test squares instead.

Rule: the second number is the next perfect square above the first.

13 → 16 = 4² (16 is the first square above 13)
23 → 25 = 5²
35 → 36 = 6²
34 → the first square above 34 is 36, but the pair prints 44

34 : 44 is the pair that does not follow the rule → option (a).

Why the others are wrong

• (b)
  23 : 25 — 25 is 5², and it is the first perfect square above 23, so this pair obeys the rule.
• (c)
  35 : 36 — 36 is 6², the first square above 35. The gap of only +1 looks wrong, but the rule is about squares, not about a fixed difference.
• (d)
  13 : 16 — 16 is 4², the first square above 13. Its gap of +3 differs from the others, which is exactly why the rule cannot be a difference.

Number-pair odd-one-out gives you four relations and asks which one is not the shared rule. The gaps here are +10, +2, +1 and +3, all different, so a fixed difference cannot be the rule.

That is the signal to look at structure rather than arithmetic. When the second numbers include 16, 25 and 36 — that is 4², 5² and 6² — perfect squares are the first thing to test.

The question's note matters: 34 may not be split into 3 and 4. Every operation has to act on the whole number.

Key facts

• 16, 25 and 36 are 4², 5² and 6².
• The first perfect square above 34 is 36, not 44.
• The question forbids breaking a number into its digits, so 34 must be handled as thirty-four.

Common traps

• Hunting for a constant difference, which no pair in this set shares
• Splitting 34 into 3 and 4 to force a rule, which the question's note forbids
• Rejecting 35 : 36 because a gap of +1 looks too small, when 36 is the square the rule requires

No directly related past PYQ was found.