Three of the following numbers are alike in a certain way and one is different. Pick the odd one out. (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.) weerbb

Correct — B. Rule: the second number is 3 × (the first number)².

11 → 3 × 11² = 3 × 121 = 363 ✓
13 → 3 × 13² = 3 × 169 = 507 ✓
9 → 3 × 9² = 3 × 81 = 243 ✓
15 → 3 × 15² = 3 × 225 = 675, but the paper prints 450

Three pairs obey the rule and 15 – 450 does not, so option (b) is the odd one out.

450 is 2 × 15², so the pair is built on the same skeleton with a multiplier of 2 where the others use 3.

Why the others are wrong

• (a)
  11 – 363 — 11 – 363 fits the rule: 11² = 121 and 121 × 3 = 363. It belongs to the group, so it is not the exception the question is after.
• (c)
  13 – 507 — 13 – 507 fits: 13² = 169 and 169 × 3 = 507. Its larger second number makes it look unlike the others, but the arithmetic is the same.
• (d)
  9 – 243 — 9 – 243 fits: 9² = 81 and 81 × 3 = 243. The small first number is the only thing setting it apart, and size is not the rule.

The NOTE printed with this item is the instruction that matters: operate on the whole number, never on its digits. Without it, a pair like 11 – 363 invites digit games that never generalise to the other three.

The whole-number rules in this family are usually a short formula in the first number — square it, cube it, multiply it, add a constant. Test the shortest formulas first, and test them on the pair with the smallest numbers.

Here 9 – 243 is the cheapest test. 243 ÷ 9 = 27, which is 3 × 9, so the second number is three times the square. Confirm on 11 and 13, then check 15 and the exception falls out.

Key facts

• Three pairs satisfy second = 3 × first², giving 363, 507 and 243.
• 15 under the same rule would give 675, not the 450 the paper prints.
• 450 equals 2 × 15², so its multiplier is 2 rather than 3.

Common traps

• Operating on the digits of 363 or 450 despite the NOTE that forbids it.
• Stopping once two pairs agree and assuming the third one checked is the exception.
• Treating divisibility by the first number as the rule, since 450 and 675 are both multiples of 15.

No directly related past PYQ was found.