Question

If a is divisible by 5 and b is divisible by 7, which of the following mys be divisible by 35?
I. ab
II. 7a+5b
III. 5a+7b

Can have up to 3 answers max and 1 answer min.

Answer 1

From the hypotheses, we can say that a=5k and b=7m, where k and m are integers.
Let's look at each choice:
ab=(5k)(7m)=35(km)
7a+5b=7(5k)+5(7m)=35k+35m=35(k+m)
5a+7b=5(5k)+7(7m)=25k+49m
We can then see that ab and 7a+5b are divisible by 35.