97 is related to 49 following a certain logic. Following the same logic, 115 is related to 58. To which of the following is 133 related to, following the same logic? (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 — D. Rule: add 1, then halve — the second number is (n + 1) ÷ 2.

97 → (97 + 1) ÷ 2 = 98 ÷ 2 = 49 ✓
115 → (115 + 1) ÷ 2 = 116 ÷ 2 = 58 ✓
133 → (133 + 1) ÷ 2 = 134 ÷ 2 = 67

67 is option (d).

Why the others are wrong

• (a)
  89 — 89 would need an input of 177, because 2 × 89 − 1 = 177, and the number given is 133.
• (b)
  82 — 82 would need 163 as its input, since 2 × 82 − 1 = 163.
• (c)
  64 — 64 is the result of halving 128, not 134, so it belongs to an input of 127.

Both worked numbers are odd, which is the giveaway: 97 and 115 cannot be halved cleanly on their own, so something must happen before the halving.

Test any rule against both pairs. Plain halving fails immediately, because 97 ÷ 2 is not 49, while (n + 1) ÷ 2 clears both.

Carry the inverse as well: if the answer is x, the input must be 2x − 1. That turns each option into a single-line check.

Key facts

• (n + 1) ÷ 2 is the same as rounding n ÷ 2 upwards when n is odd.
• The inverse of (n + 1) ÷ 2 is 2x − 1, which tests any option in one step.
• 133 is odd, so no rule that halves it directly can return a whole number.

Common traps

• Halving 133 directly and rounding, instead of adding 1 first.
• Fitting a rule to the first pair alone when the second pair is given to confirm it.
• Breaking 133 into its digits, which the stem's note forbids.

No directly related past PYQ was found.