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.)

Correct — A. Start from the smallest pair, 19 : 3, because small numbers narrow the candidate operations fastest. 6 × 3 = 18, one short of 19.

Rule: first = 6 × second + 1.

49 : 8 → 6 × 8 + 1 = 49
19 : 3 → 6 × 3 + 1 = 19
55 : 9 → 6 × 9 + 1 = 55
24 : 4 → 6 × 4 + 1 = 25, not 24

Three pairs obey the rule and one falls a unit short, so the odd pair is option (a).

Why the others are wrong

• (b)
  49 : 8 — 6 × 8 + 1 = 49 exactly. This pair obeys the shared rule, so it belongs with the group rather than standing apart from it.
• (c)
  19 : 3 — 6 × 3 + 1 = 19. These are the smallest numbers in the set, which is where the pattern is easiest to spot in the first place.
• (d)
  55 : 9 — 6 × 9 + 1 = 55. Its size invites you to test it first and reject it, but it fits as cleanly as the other two.

Odd-pair items give four pairs and expect one operation shared by three of them. Work from the smallest pair outward, then test the candidate rule on the rest before committing.

Here 19 : 3 suggests dividing by about 6. Checking 6 × 3 = 18 and 6 × 8 = 48 shows a leftover of 1 in each case, and 6n + 1 then reproduces 49, 19 and 55 while leaving 24 one short.

The near-miss is deliberate. A rule of the form multiple-plus-a-small-constant is chosen precisely because one pair can be made to fail by a single unit.

Key facts

• 49, 19 and 55 are each one more than a multiple of 6.
• 24 is itself a multiple of 6, so it fails the plus-one part rather than the times-six part.
• The whole-number note bars digit-wise work, so 55 must be handled as fifty-five.

Common traps

• Testing division alone and missing the constant that goes with it
• Accepting 24 : 4 because dividing exactly by 6 looks tidier than the real rule

No directly related past PYQ was found.