Overlapping Sets with Algebraic Representation

[ZacharyS701]

In an overlapping set with algebraic representation, how do I know where to put the "x".

Where do I put the "x" in the following question when I create a double matrix and why?
10% of all aliens are capable of intelligent thought and have more than 3 arms, and 75% of aliens with 3 arms or less are capable of intelligent thought. If 40% of all aliens are capable of intelligent thought, what percent of aliens have more than 3 arms?

[StaceyKoprince]

Please remember to read (and follow!) the forum guidelines before posting. This folder is only for general strategy questions, not content or specific test problems. Check out the content / problem folders and post in the relevant folder depending upon the source of the problem you want to post (and make sure to follow the rules about banned sources).

For instance, since this is an MPrep problem from one of our books, you'd post in the MPrep GMAT Non-CAT math folder.

I will give you a quick answer here but if you want to discuss in more depth, please post in the appropriate folder.

10% of all aliens are capable of intelligent thought and have more than 3 arms,

These are the two groups for the matrix: capable and not capable; more than 3 arms and 3 or fewer arms.
Put 100 in the Total-Total box.
This first piece of info goes in the box "capable + >3 arms": put 10 there.

and 75% of aliens with 3 arms or less are capable of intelligent thought.

This is not talking about 75% of the WHOLE group (the 100). Rather, it's telling you something about 75% of the subgroup "3 or fewer arms." You don't know how many are in that subgroup, so put an x there.
You can then put 0.75x in the box ""capable + 3 or fewer arms.
Note: This is not the ultimate thing you were asked to solve for—but it's the first unknown you encounter / where you need to start.

Keep following the problem from there and you will eventually be able to fill everything in with numbers to get to what you really want: The subgroup ">3 arms" (the total line for this group—including everyone whether capable or not capable).