Select the option that is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number. 14 : 30 :: 9 : 20 :: 4 : ? (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. Fit an operation to the first pair, then make it survive the second before you use it.

Rule: second number = 2 × first + 2.

14 → 2 × 14 + 2 = 28 + 2 = 30
9 → 2 × 9 + 2 = 18 + 2 = 20
4 → 2 × 4 + 2 = 8 + 2 = 10 → option (b)

The bracketed note bars digit-splitting, so the rule has to act on 14, 9 and 4 as whole numbers — and 2n + 2 does.

Why the others are wrong

• (a)
  11 — 11 needs 2n + 3, which is tuned to the 4 alone. On the first pair it gives 2 × 14 + 3 = 31, not the 30 the question supplies.
• (c)
  13 — 13 needs 2n + 5. Test it where you can be checked: 2 × 9 + 5 = 23, not 20.
• (d)
  12 — 12 is 3 × 4, a tripling. Tripling the middle pair gives 3 × 9 = 27, not 20, so it never described the pattern in the first place.

A three-slot analogy hands you two worked pairs and one to complete. Both worked pairs exist to be used: a rule that fits only one of them is not the rule.

Work in this order — guess from the first pair, verify on the second, apply to the third. Here 14 → 30 could be 2n + 2 or n + 16, and the second pair settles it: 9 + 16 = 25, not 20, so n + 16 dies and 2n + 2 stands.

Key facts

• 2n + 2 factorises to 2(n + 1), so 4 gives 2 × 5 = 10.
• The whole-number note bars digit-wise work, so 14 must be handled as fourteen.
• A candidate rule must reproduce every pair the question gives, not just the nearest one.

Common traps

• Fitting a rule to the pair you read first and never testing it on the second
• Splitting 14 into 1 and 4 despite the note that forbids it

No directly related past PYQ was found.