i chose c, since i had 2 equations and 2 unknowns.
i didnt even stop to think about delving into the statement 2 equation to try and come up with one pair of x and y.

in general how do i know when to stop and try to make an equation work vs. moving on if i have or dont have another equation.

also can you please show algebraically what the quickest way is to actually determine the values of x and y in the statement 2 equation.
thanks.

We can definitely figure out the number of small lemonades with both statements combined; as you said, two independent linear equations will allow us to solve for two variables. Is it possible for us to derive both equations from Statement 2?

In this case, yes. The condition that makes this possible is the fact that our two unknowns are constrained to a limited set of possible values. Since we can't sell fractional cups of lemonade, our two variables (small and large lemonades) must be integers. With this in mind, we can figure out many total lemonades we would need.

What if we sold only small lemonades?
We can see how close we can get to our total value of $4.92.

$.52 * 9 = $4.68; 9 small lemonades isn't enough.
$.52 * 10 = $5.20; 10 small lemonades is too much.

What if we sold only large lemonades?

Again, we can close in on $4.92

$.58 * 8 = $4.64; not enough
$.58 * 9 = $5.22; too much

We can see that 8 large lemonades alone and 10 small lemonades alone won't work, so we have to have a combination of the two. If we start replacing the large lemonades with smalls, that will take away value, putting us further away from our target of $4.92. If we replace small lemonades with larges, that will add value, again taking us farther away from our target. Thus, we can see ghat we have to have a number of lemonades between 8 and 10, which leaves us with 9.

We have successfully derived Statement 1's equation from Statement 2, which means that the answer is B.

Bill

I believe you provided an explanation to 19, not 20.
Please see my original post questions for #20.
Thanks for the help.

Hey tj,

Can you post the text of the question? Bill answered the problem that I have listed as #20 in my book, but I'd be happy to look at your question as well.

: ) ....unless i was seeing things, Im 99.9% sure the original post from yesterday was in fact for 19.

Anyway, Im still not sure when to really identify when to invest the time to determine if there is one solution versus identifying the standard concept of "two variables must have two equations" and if either component is missing, then the equation cant be solved.

Also, trial and error seems time consuming. is there another way?

Hey TJ,

I hear you about this one being time-consuming, but there's some art to that, too - proving that statement 2 alone is sufficient takes a little bit of time, but it's a worthy investment when it seems too easy that the two statements together will work. That should prompt you to recognize that the GMAT won't likely hand you an "obvious" answer C, and encourage you to spend some extra time.

You can read more about that strategy at our blog, here: http://blog.veritasprep.com/2010/03/gma ... -c-me.html