Perform the multiplication on the 13-hour clock.
8 × 10
A)11
B)12
C)2
D)6

Question

Quizplus · Accepted Answer

On a 13-hour clock, multiplying any number by 8 is the same as multiplying it by 2 because 8 is equivalent to 2 modulo 13. Therefore, 8 × 10 is equivalent to 2 × 10, which equals 20 on a regular calculator. However, on a 13-hour clock, 20 is equivalent to 7 (since 20 divided by 13 leaves a remainder of 7). Therefore, the answer is 2 in the 13-hour clock system. To perform multiplication on the 13-hour clock, we need to use modular arithmetic. 
8 hours after 12 noon is equivalent to 8+12=20, and 10 hours after 12 noon is equivalent to 10+12=22.
Now, we take the product modulo 12 because we are working with a 12-hour clock. 
(8 × 10) mod 12 = 80 mod 12 = 8 mod 12 = 8, which is equivalent to 2 on the 13-hour clock. Therefore, the correct choice is C) 2.

Perform the Multiplication on the 13-Hour Clock