WP MGMAT strat guide CH-5 overlapping sets

[aashray.thatai]

Q- 10% of 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?

I need help solving this problem in a systematic way.
This is what i did
- Created a table that had intelligent/ not intelligent and <=3 and >=3.
- Assumed total number of aliens =100
-im getting confused between total number and total number of aliens capable of intelligent thought ? how would i name that quantity .
Please help thanks

[RonPurewal]

That sounds like the right kind of table, but it's hard for me to understand what you tried from there. Can you try to show us what you already put into the table?

If it's too hard to format the table on here, you can always draw it, take a picture of it, and then upload the image.

Thanks.

[danr969]

assume 100 aliens total. 10 are capable of both intelligent thought and have more than 3 arms. Since 40 are capable of intelligent thought, 30 must be intelligent and have 3 or fewer arms.
but, it also says that 75% of aliens with 3 arms or less are intelligent. This means that the number 30 is 75% of aliens with 3 arms or less. Thus, there must be 40 aliens with 3 arms or less.
Now, you can complete the table. There must be 10 aliens that are not intelligent and also have 3 arms or less. There must be 60 aliens that are not intelligent, so there are 50 that are not intelligent and have more than 3 arms. The total with more than three arms is 60.

[RonPurewal]

That's a valid approach, but we were hoping to hear back from the original poster.

With these problems, the math itself is almost never an issue, so simply narrating a complete solution"”as in the post above"”is sometimes unhelpful.
Instead, the problem almost always lies in the wording of the problem. (The words are not "deliberately tricky"; the given phrasings are actually the simplest ones possible for such facts.) So, knowing which words were specifically problematic for the original poster would be more helpful.