I don't know if there's a straightforward algebraic solution to this one. One thing I tried was setting up Statement (1) as follows:

2n = 70 + b (following your setup)
n = 35 + b/2

Then, I realized that, implicit in Statement (1) is that 0<b<10, so, when we divide by 2, we also must realize that 0<b/2<5. Since n must be an integer, b must be even, so b/2 must be 3 or 4, making n = 37 or 39, Sufficient.

However, this isn't pure algebra, I know. I guess what I'd like to ask you is: Why do you want to find a way to do this problem with pure algebra? Let me give you an example question:

If p is even and q is odd, is p^2*q odd?

The answer, of course, is no. But we can also do algebra:

p = 2n and q = 2m+1, where n and m are integers
(2n)^2 * (2m+1) = 4n^2 * (2m+1) = 8mn^2 + 4n^2 = 2*(4mn^2 + 2n^2), which is even because the term in parentheses is an integer and 2 times an integer is even.

Seriously? Seriously? Let's not do this anymore. To all who seek algebraic answers to easy questions: Don't do this anymore. The goal of this, remember, is to get a high GMAT score, get into business school, and then succeed with your MBA. That is the only point. Also remember that a good businessperson doesn't look for the most complex-but-interesting solution to a problem: he or she looks for the best, most efficient, most situation-appropriate solution to the problem. The GMAT tests this skill, and well it should.

Not that I mind posting these questions here, after all, it's fun, and I am eager to see if someone DOES have a purely algebraic solution here ... but let's all remember that, in terms of studying for the GMAT, trying to find a longer, more awkward way of doing an otherwise-easy problem is somewhat counterproductive.
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Adam
GMAT Instructor
Knewton, Inc.


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