If 9 % 2 = 81 and 8 % 2 = 64, what is 7 % 2?

Correct — B.
Rule: a % b = a raised to the power b.

9 % 2 = 9² = 81 ✓
8 % 2 = 8² = 64 ✓
7 % 2 = 7² = 49 → option (b).

Why the others are wrong

• (a)
  56 — 56 is 7 × 8, multiplying by the next number. That rule would make 9 % 2 = 9 × 10 = 90, not 81.
• (c)
  45 — 45 is not a square at all: it falls between 6² = 36 and 7² = 49. The examples square the first number.
• (d)
  63 — 63 is 7 × 9, that is 7 × (7 + 2). The same rule would make 9 % 2 = 9 × 11 = 99, not 81.

An invented operator is defined only through its examples. Guess a rule, then test it on every example before you use it: one mismatch rules it out.

Here 9 % 2 = 81 and 8 % 2 = 64 are the squares of 9 and 8, so the symbol means 'raise the first number to the power of the second'.

Key facts

• Squares to know: 7² = 49, 8² = 64, 9² = 81.
• % here is a made-up operator: as a percentage or a remainder, 9 % 2 could not be 81.
• A rule has to fit every example given, not just the first.

Common traps

• Reading % as percentage or remainder: 9% of 2 is 0.18, and 9 divided by 2 leaves 1
• Multiplying by a neighbouring number (7 × 8 = 56) instead of by itself

No directly related past PYQ was found.