GMAT Math

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

Let number of 7 - x
Let number of 77 - y
7x+77y = 350 ........... (1)
x + y =n .....................(2)

Perform (1) - 7(2)
70y = 350 - 7n
7n = 350 - 70y
n = (350 - 70y)/7
n = 350/7 - 70y/7
n = 50 - 10y
As y can be integer only, n is less than 50 and multiple of 10
From option answers n = 40 and y=1
Choice C.
Cross check.
y=1, number of 77 = 1
number of 7 = 39
39*7 + 77* 1 = 350

In my opinion answer is C. As Either the term could be 7 or 77. And sumof all the terms could be 350 only.

Case1: If there is one 77 term in the series then 350-77=273. And as 273/7=39.

So there will be 39, 7 terms and one 77 term. in total 40 term in the series.

Case 2: If there are two 77 terms in the series then 350-(2*77)=196. And 296/7=28.

So there will be 28, 7 terms and 2 77 terms. In total 30 terms in the series. But is not in the option.

And the best avaliable option is C with 40 terms.

Hey guys,

Great discussion. And, actually, there's a little trick here if you keep in mind that the GMAT loves to test Number Properties.

Because we need the to sum to 350, therefore ending in 0, and we know that the unit's digit of each term will be 7 (either 7 or 77), we can calculate the unit's digit by taking 7*n. The only possible n (from the answer choices) to get us a unit's digit of 0 is 40.