12 is related to 235 by certain logic. Following the same logic, 14 is related to 287. To which of the following is 18 related, 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 — B. Rule: square the number, then add 91.

12 → 12² = 144, and 144 + 91 = 235 ✓
14 → 14² = 196, and 196 + 91 = 287 ✓

Both samples fix the same constant, so
18 → 18² = 324, and 324 + 91 = 415 → option (b).

Why the others are wrong

• (a)
  512 — 512 needs +188 after squaring, not the +91 both given pairs agree on. It is 8³, a cube rule neither sample uses.
• (c)
  438 — 438 needs +114 after squaring — 23 more than the constant the two samples fix.
• (d)
  320 — 320 falls below 18² itself, so no addition can reach it. It sits 4 short of 324.

These is-related-to items hand you two worked pairs and one unknown. Two pairs are exactly enough to fix a two-step rule and to kill a rule that fits only the first.

Work on the whole number, as the note insists: square it, cube it or multiply it, then measure the gap to the target. Here 235 − 144 = 91 and 287 − 196 = 91, and a gap that repeats is the rule.

Key facts

• 235 − 12² = 91 and 287 − 14² = 91, so the operation is square-then-add-91.
• 18² = 324, so the target is 415.
• Two given pairs are the minimum needed to fix a constant, and a rule must satisfy both before you apply it.

Common traps

• Fitting a rule to the first pair and never checking it against the second
• Splitting 18 into 1 and 8 despite the note forbidding it
• Reading 512 as a cube and assuming the series is cubic

No directly related past PYQ was found.