Either 7 or 77 in series

[shrads.jp]

This is very common sum in GMAT Prep..yet i dont find any easy method to approach it...pls help

If each term in the sum a1 + a2+...an is either 7 or 77 and the sum equals 350, which of the following cold be the value of n?
1) 38
2) 39
3) 40
4) 41
5) 42

OA - 40

[vaibhav.tripathi]

the equation is 7x + 77y = 350

x + 11y = 50 ---------- eq.1
x + y = n ------------- eq.2

both x and y are 0 or positive integer and y has to be less than 5 (since 11*5 = 55)

lets try substituting values in eq.2 corresponding to answer choices
n = 38
x = 37 & y = 1, value smaller then eq.1
x = 36 & y = 2, value greater then eq.1

n = 39
x = 38 & y = 1, value smaller then eq.1
x = 37 & y = 2, value greater then eq.1

n = 40
x = 39 & y = 1, value equal to eq.1. Correct answer

n = 41
x = 40 & y = 1, value greater then eq.1

n = 42
x = 41 & y = 2, value greater then eq.1



Though the approach is bit lengthy, but it works. Moreover, in such questions its always a nice idea to start with option C since you'd know whether you need a smaller value or a greater value. Once that is settled, you wouldnt have to try more then 3 options.
Let me know if you have any doubt.


Thanks,
Vaibhav

[RonPurewal]

see here

sequence-each-term-is-either-7-or-77-t2731.html

or...

if-each-term-in-the-sum-a1-a2-a3-an-is-either-7-or-t1103.html