Problem Solving

If each term in the sum a1 + a2 +....+ an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

A) 38

B) 39

C) 40

D)41

E)42


C

Thanks guys for your help!

I guess I was lucky enough to get this question on my first shot. This is all I did:
Since either number in the sequence is a 7 or a 77 and all the numbers in the sequence add up to 350, let's assume that one term is 77 and subtract that term from 350 to get 350-77=273, now let's see if 273 is divisible by 7, 273/7=39 BINGO! So n could be 39+1=40.

exhilaration wrote:If each term in the sum a1 + a2 +....+ an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

A) 38

B) 39

C) 40

D)41

E)42


C

Thanks guys for your help!

This can be answered very quickly in the following manner.

If all of them are 7s, then we need 50 terms.

Now every 11 7s can be replaced with one 77.

So, the number of terms will always be in the form

50 - 11x + x = 50-10x.

So for x = 1, we get number of terms as 40