Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets? (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) 14 – 196 – 186 – 172; 15 – 225 – 215 – 200

Correct — B.

Rule: square the first number, subtract 10, then subtract the first number again.

14 → 14² = 196 → 196 − 10 = 186 → 186 − 14 = 172.
15 → 15² = 225 → 225 − 10 = 215 → 215 − 15 = 200.

Both given chains obey it, so apply the same three steps to each option.

9 → 9² = 81 → 81 − 10 = 71 → 71 − 9 = 62.

That is 9 – 81 – 71 – 62 → option (b).

Why the others are wrong

• (a)
  3 – 9 – 19 – 14 — 3² = 9 is right, but the second step here adds 10 to give 19. In both given chains the second step subtracts 10, and 196 to 186 makes that unmistakable.
• (c)
  6 – 36 – 26 – 22 — 6² = 36 and 36 − 10 = 26 both hold, then the chain subtracts 4 instead of the first number. The rule takes away 6, which would end at 20, not 22.
• (d)
  8 – 64 – 54 – 40 — 8² = 64 and 64 − 10 = 54 are correct, but the last step drops 14, not 8. The rule subtracts the chain's own first number, which would end at 46; 14 is the first number of the other chain.

Chain items give you two worked examples, and both must be satisfied before you touch the options. A rule fitted to one chain alone will usually survive the first step of the other and then fail.

The step that catches candidates is the third. It does not subtract a fixed number: it subtracts the first term of the chain, which is 14 in one set and 15 in the other.

Note that 186 − 14 = 172 and 215 − 15 = 200 are the only steps where the two chains differ in what they take away, and that difference is the whole rule.

Key facts

• Both given chains run: square, subtract 10, then subtract the first number.
• 14, 196, 186, 172 and 15, 225, 215, 200 both follow that sequence.
• Applied to 9 the chain runs 81, then 71, then 62.

Common traps

• Deriving the rule from the first chain alone and never testing it on 15 – 225 – 215 – 200.
• Reading the third step as a fixed subtraction rather than one that uses the chain's own first number.
• Checking only that the second term is a perfect square and choosing on that.

No directly related past PYQ was found.