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 — C. Rule: first number = second number × 8 − 1.

17 × 8 = 136, and 136 − 1 = 135
19 × 8 = 152, and 152 − 1 = 151
13 × 8 = 104, and 104 − 1 = 103

16 × 8 = 128 exactly — there is no subtraction. The rule would have printed 127 : 16.

So the pair that breaks the group is 128 : 16, option (c).

Why the others are wrong

• (a)
  135 : 17 — 135 : 17 obeys the rule — 17 × 8 = 136, one above 135 — so it belongs to the group and cannot be the odd pair.
• (b)
  151 : 19 — 151 : 19 obeys it too: 19 × 8 = 152, and 152 − 1 = 151. It sits with the group.
• (d)
  103 : 13 — 103 : 13 obeys it: 13 × 8 = 104, and 104 − 1 = 103. Three pairs sharing one rule is what leaves the fourth as the answer.

Odd-one-out number pairs usually hide a rule of the shape a × b ± c. Divide the larger number by the smaller and look at what is left over.

135 ÷ 17, 151 ÷ 19 and 103 ÷ 13 all come to a shade under 8, while 128 ÷ 16 is exactly 8. That single difference is the whole question.

Multiplying is faster than dividing here. 8 × 17, 8 × 19, 8 × 13 and 8 × 16 take seconds, and three land one above the printed number while the fourth lands on it.

Key facts

• 17 × 8 = 136, 19 × 8 = 152 and 13 × 8 = 104, each exactly one above the printed first number.
• 16 × 8 = 128, which equals the printed first number and so breaks the shared rule.
• The rule the group follows is first = second × 8 − 1.

Common traps

• Accepting 128 : 16 as the group's cleanest pair when clean is what makes it odd
• Testing two pairs, finding a rule that fits both, and stopping there
• Missing the −1 and concluding that no rule fits any of the pairs

No directly related past PYQ was found.