Okay. I will list all the relatively prime numbers up to 331. 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101, 103,107,109,113,127,131,137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331. Okay, so look at this list and see which match up. For A. 102 and 312. Neither of these numbers are relatively prime. For B. 10 and 45. Neither of these are relatively prime. For C. 3 and 51. 3 is a relatively prime number, 51 is not. For D. 35 and 72. Neither of these are relatively prime numbers. But the answer would be D. because to get a relatively prime pair of numbers you have to have both of them not be divisible by the same number. 102 and 312 can be divided 2, so that's not the answer. 10 and 45 can be divided by 5, so that is incorrect. 3 and 51 can be divided by 3, so that is also incorrect. 35 and 72 cannot be divided by the same numbers. So, the answer is D. 35 and 72.
3 cakes translates to 30 minutes each, so 1.5 hours. If he worked 12 hours total and 1.5 were used to make cakes then the rest were used for cupcakes. This means 12-1.5 = 10.5 hours were spent on cupcakes.
Each cupcake takes 10 minutes, which means in 10.5 hours, or 630 minutes, 63 cupcakes can be made. So C
