17 is related to 21 following a certain logic. Following the same logic, 22 is related to 36. To which of the following is 29 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 — A. Two worked pairs are given, so treat them as two points and read the rate of change instead of guessing an operation.

The input moves 17 → 22, a rise of 5. The output moves 21 → 36, a rise of 15. So the output moves 3 for every 1 of the input.

Rule: second = 3 × first − 30, that is 3(n − 10).

17 → 3 × 17 − 30 = 51 − 30 = 21
22 → 3 × 22 − 30 = 66 − 30 = 36
29 → 3 × 29 − 30 = 87 − 30 = 57 → option (a)

Why the others are wrong

• (b)
  46 — 46 comes from 3n − 41, a constant tuned to 29 alone. On the first pair it gives 3 × 17 − 41 = 10, nowhere near 21.
• (c)
  49 — 49 is 2n − 9. Test it where the question can check you: 2 × 17 − 9 = 25, not 21.
• (d)
  58 — 58 is simply 2 × 29. Doubling fails both given pairs, since 2 × 17 = 34 and 2 × 22 = 44.

When a relation item gives two worked pairs, you have two points on a line. Divide the change in outputs by the change in inputs to get the multiplier: (36 − 21) divided by (22 − 17) is 15 over 5, which is 3.

Then back-substitute for the constant. 3 × 17 = 51 while the output is 21, so 30 is subtracted every time.

This two-point method settles linear items in seconds and, unlike trial and error, it cannot fit one pair while quietly missing the other.

Key facts

• The rule is 3n − 30, which factorises to 3(n − 10).
• (36 − 21) divided by (22 − 17) equals 3, which fixes the multiplier before any guessing.
• A rule that reproduces only one of the two given pairs is not the rule.

Common traps

• Adding a constant because the first gap is small, when the second gap is three times larger
• Solving from the pair nearest the answer and skipping the check on the other

No directly related past PYQ was found.