If integer m is 3 more than a multiple of 5 and 2 more than a multiple

If integer m is 3 more than a multiple of 5 and 2 more than a multiple of 6, which of the following could be 7m + 4?

A. 65
B. 104
C. 158
D. 270
E. 291

hloonker Let's look at the two sequences, and see where they overlap:

"3 more than a multiple of 5" = 5a + 3 --> 3,8,13,18... Note that all of these end in either "3" or "8".

"2 more than a multiple of 6" = 2b +2 --> 2,8,14...

We can quickly see that they first overlap with 8.

They will overlap again every 30 numbers (30 is the LCM of 5 and 6): 8, 38, 68, 98...

Therefore, m = 8 + 30I (8 more than a multiple of 30)

The question asks for 7m + 4, so we substitute this equation above for m:

7m + 4 = 7(8 + 30I) + 4 = 56 + 210I + 4 = 60 + 210I

Now, we look at the answer choices, and we can see that if I=1, 60 + 210(1) = 270


Please let me know if this is helpful or if you have further questions.