Algebra Strategy Guide 5th Edition pg 141 problem 4

[jonruss03]

This question is with regard to problem 4 on page 141 of the Algebra Strategy Guide (5th ed).

I do not believe I would have approached this problem as they do in the solution. I understand that there are many ways to solve this problem, however, I was wondering if there is an efficient way to solve it without realizing patterns?

If c+d = 11 and c and d are positive integers, which of the following is a possible value for 5c + 8d
a)55
b)61
c)69
d)83
e)88

I solved this problem by substituting d=11-c into the expression to obtain 88-3*c and set this equal to each of the answer choices. If, by plugging c back into c+d=11, d yielded a positive integer then I am done.

It took me a while to realize this and I don't believe it would have served me well on test day, however I would never have considered either approach in the solutions. Any suggestions?

[tim]

your solution method is just fine, although you need to recognize that hitting a correct value once isn't enough (2 of the answers actually work, and you need to figure out which one is the real answer). you would also want to use c = 11 - d and see which two answers check for that approach as well, then you'll see that there is only one answer that is consistent with both of those substitutions. as for what solution method to use, on the GMAT of course you should use whatever you think of first. :) if you encounter a solution in practice that you wouldn't have though of, you should study that solution and keep it in mind as a viable solution method for future problems of that type..