Question that involves a portion of the total

Question

Hi!

I'd like to know if there is a rule or formula for solving a question such as this one below:

"1/3 of the total participants were students, 3/4 of the total participants were female students. If 45 of the parcicipants were neither female nor students, what was the number of the total participants?"

I feel really overwhelmed whenever I see that kind of problems, because I don't recall studying these types of problems in school (or I may have just forgotton. It's been a while...)

I do feel certain that there must be a general set of rules or formula for solving this question type, because I don't think otherwise 2 minutes will do for manually trying to solve it out!

Any advice will be appreciated. Thanks guys!

esledge · Answer

Yes, there is a great method for these called a Double Set Matrix. You'll use it when your total is described by two qualities (here, student status and gender).

Draw a 3-by-3 grid. To the left, label from top to bottom: Women, Men, Total. Across the top, label left to right: Student, Not Student, Total. The key to setting it up correctly is to make sure the rows are mutually exclusive (Men = not Women, Not Student obviously means you can't be a Student).

Now you have a place to put any values given, and you can typically fill in other boxes with the knowledge that each row should total to the right, and each column should total to the bottom.

Try it and let me know how it works for you.

almostfamous · Answer

Hi!

Thanks for your post! It sounds similar to drawing a logical tablw that shows all the combination of each team. So the concept is familiar to me.

I was wondering, if there is actual mathematical (and "fool-proof") formula which I can apply for evaluating actual value in question that involves subgroups in a set. For example, if I see a question such as "1/3 of a total is female students and 2/3 of the total is female and 1/5 of the total is not a student. How many are neither student nor female?" (not a real question, so might not be a good description), is there any formula that I could apply (eg. sub group ratio x multiplied by subgroup ratio m equals to non-subgroup ratio l)

Thanks again!

Ps. I'm taking MGMAT course & private tutoring. MGMAT rocks

esledge · Answer

Some people use this formula: Total = (total of A) + (total of B) - (both A & B) + (neither A nor B)

It's valid, but in my opinion you will have more flexibility with the Double Set Matrix. The GMAT could give you values for  any  box in the matrix (for example, "there are 10 things that are A but not B," which isn't directly a term in the formula above). Even worse, the GMAT could give you a relationship between two boxes in the matrix, which again might not fit nicely into a predetermined formula. And, of course, the question could ask for any box in the matrix, not just a simple total or subtotal.

Question that involves a portion of the total

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