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It is clear that statement (2) by itself is sufficient.
What about statement (1)?
It is possible to know X and Y if you have the values of XY and X-Y. Let's take C=-A.
We have AC=-40 and A+C=18
A and C are solutions of XÂ²-(A+C)X+AC=0, ie, XÂ²+40X+18=0. Thus, we can obtain A and C, A and B and calculate AB(A+2B).
What is the problem with this since the correct solution is B???
It is clear that statement (2) by itself is sufficient. What about statement (1)? It is possible to know X and Y if you have the values of XY and X-Y. Let's take C=-A. We have AC=-40 and A+C=18 A and C are solutions of XÂ²-(A+C)X+AC=0, ie, XÂ²+40X+18=0. Thus, we can obtain A and C, A and B and calculate AB(A+2B). What is the problem with this since the correct solution is B???
PS: Following my point of view, the answer is C
if you've already written that statement 2 by itself is sufficient, then you have to choose B. B always over-rides C.
Alex_NL wrote:
A = 2 or -2 B = 20
Which will give different solutions
Combined statements will say A = 2 and B = 20
Correct me if I am wrong.
A could be 2 or -2, but only 2 will work with 20 to make 80, so it has to be the positive version.
This is a great question because it exemplifies a common trick ont he GMAT. They want us to pick D. The question starts out with an equation with two variables, and if we've got two variables, then another equation should be enough to solve the problem.
But be weary of that. Always double check. When variables multiply by themselves, they square, and that often leads to 2 solutions and not enough information. In the first statement, that's what happens. If you solve for B, you get that it could be either 20 or -2. That means A could be either -20 or 2, and both solutions work in both equations. So not enough information.
2 let's us know that A^2B is 80. Since we already knew that AB is 40, the extra A must be a positive 2, so be must be a positive 20, and that's sufficient.
If you are looking for me to comment on your method for solving 1, I'm not sure I understand it. I think you've made it too difficult. Don't try to look for sophisticated solutions on most problems. The GMAT won't ask you to do the kind of thing you did. If you're already comfortable with substitution to the point where you're changing variables around, then just do the substitution and see logically if it makes sense that there could be two different answers. If yes, then there's not enough information to solve the problem.