If 6 * 3 = 54 and 8 * 2 = 48, what is 5 * 4?

Correct — D.
Rule: multiply the two numbers, then multiply by 3: a * b = 3 × a × b.

Check 6 * 3: 6 × 3 = 18, then 18 × 3 = 54 ✓
Check 8 * 2: 8 × 2 = 16, then 16 × 3 = 48 ✓
Apply 5 * 4: 5 × 4 = 20, then 20 × 3 = 60 → option (d)

Why the others are wrong

• (a)
  40 — 40 is 5 × 4 × 2, a doubled product. Doubling fails the first example: 6 × 3 × 2 = 36, not 54.
• (b)
  44 — 44 is not a multiple of 3 (4 + 4 = 8), while the rule's results always are, as 54 and 48 show. The rule gives 3 × 5 × 4 = 60.
• (c)
  45 — 45 is a × (a + b) = 5 × 9. That rule fits 6 * 3 (6 × 9 = 54) but breaks on 8 * 2: 8 × 10 = 80, not 48.

A made-up operator gives two worked examples, and the rule must fit both before you apply it.

Test each candidate rule on the first example, then on the second. A rule that fits one example and not the other is a lure: a × (a + b) gives 54 for 6 * 3 but 80 for 8 * 2.

3 × a × b survives both, giving 54 and 48.

Key facts

• The rule here: a * b = 3 × a × b.
• 6 × 3 × 3 = 54 and 8 × 2 × 3 = 48, so 5 × 4 × 3 = 60.
• Every whole-number result of 3 × a × b is a multiple of 3, which removes 40 and 44 at once.

Common traps

• Stopping at the first example: 6 × 9 = 54 suggests a × (a + b), which fails 8 * 2 and leads to 45.
• Doubling the product instead of tripling it, which gives 40.

No directly related past PYQ was found.