7 is related to 40 by certain logic. Following the same logic, 5 is related to 16. To which of the following is 9 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. Square the number, then take 9 away.

Rule: n² − 9
7 → 7² = 49, then 49 − 9 = 40
5 → 5² = 25, then 25 − 9 = 16
9 → 9² = 81, then 81 − 9 = 72

So 9 is related to 72 — option (b).

Why the others are wrong

• (a)
  48 — Squaring is forced by both given pairs, and 9² − 9 = 72. The rule 6n − 6 that would produce 48 turns 7 into 36, not into the 40 the paper gives.
• (c)
  54 — 54 is 9 × 6, and multiplying by 6 turns 7 into 42 and 5 into 30 — neither matches 40 or 16. The relation squares before it subtracts.
• (d)
  70 — 70 is 9² − 11. The constant has to be the same every time, and 49 − 40 and 25 − 16 both give 9, not 11.

A number analogy fixes one operation from the worked pairs and applies it unchanged to the third number.

Look for landmarks first. 40 sits just below 49 and 16 sits just below 25, both perfect squares of the given numbers, and both fall short by exactly 9. One rule, n² − 9, explains both pairs, so it is the rule.

The bracketed NOTE matters: 40 may not be split into 4 and 0. Every operation acts on the whole number.

Key facts

• The relation is n squared minus 9: 7 gives 40, 5 gives 16 and 9 gives 72.
• Both worked pairs must satisfy a candidate rule before it is applied to the third number.
• The NOTE forbids breaking a number into digits, which rules out digit-sum and digit-reversal readings.

Common traps

• Testing only the first pair, so a rule such as 6n − 2 survives until the second pair kills it
• Breaking 40 into 4 and 0 despite the NOTE forbidding it
• Squaring correctly but forgetting the constant, which lands on 81 instead of 72

No directly related past PYQ was found.