series

kaustubh_b wrote:This one is from GMAT Prep.
If each term of the series 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

The answer in this case is C and I was able to solve using substitution.
However, it would be great to know if there are any simpler and better approaches to this problem.

Thanks in advance.

If each term of the series a1 + a2 + ... + an is either 7 or 77
If each term of the series a1/7 + a2 /7+ ... + an/7 is either 1 or 11

a1/7 + a2 /7+ ... + an/7 =50

Now if one of the terms is 11 and all others 1s ; no of terms = 39 (1's) + 1 = 40
if two of the terms are 11 and all others 1s ; no of terms = 28 (1's) + 2 = 30
if Three of the terms are 11 and all others 1s ; no of terms = 17 (1's) + 3 = 20
if four of the terms are 11 and all others 1s ; no of terms = 6 (1's) + 4 = 10

These are the only possibilities 40 is given in the choices - hence C

kaustubh_b wrote:This one is from GMAT Prep.
If each term of the series 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

The answer in this case is C and I was able to solve using substitution.
However, it would be great to know if there are any simpler and better approaches to this problem.

Thanks in advance.

15 second solution: if each term ends in 7, and the sum of the terms ends in 0, then the number of terms MUST be a multiple of 10... choose (C)!

Stuart Kovinsky wrote:

kaustubh_b wrote:This one is from GMAT Prep.
If each term of the series 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

The answer in this case is C and I was able to solve using substitution.
However, it would be great to know if there are any simpler and better approaches to this problem.

Thanks in advance.

15 second solution: if each term ends in 7, and the sum of the terms ends in 0, then the number of terms MUST be a multiple of 10... choose (C)!

Damn ! missed it!