What is the product of all the numbers in the dial of a telephone?

Question

What is the product of all the numbers in the dial of a telephone?

1. A. 362880
2. B. 388620
3. C. 366820
4. D. 0 (Correct answer)

Correct Answer

Option D — 0

Detailed Solution & Explanation

The correct answer is 0.

Key Points

• A telephone dial carries the digits 0 to 9, and zero is one of them.
• Any product that includes a factor of 0 is 0, regardless of the other numbers.

Additional Information

• The distractor 362880 is 9! = 9 × 8 × 7 × … × 1, the product of 1 to 9 — the answer you get by forgetting the zero, which is precisely the trap.
• The same principle appears in questions about the product of all digits of a number containing 0, or of the numbers on a clock face — a clock has no 0, so that product is not zero.
• The zero product property is the formal statement: if a product is zero, at least one factor must be zero.