Know the GMAT Code: Overlapping Sets - Part 2
Welcome to the second installment of our Know the Code series on overlapping sets. Were learning how to recognize (quickly!) that you have an overlapping sets problem in the first place; were also talking about best approaches and how to avoid traps on this question type.
Heres the GMATPrep free test problem I gave at the end of the first installment:
*A certain one-day seminar consisted of a morning session and an afternoon session. If each of the 128 people attending the seminar attended at least one of the two sessions, how many of the people attended the morning session only?(1) [pmath]3/4[/pmath] of the people attended both sessions.
(2) [pmath]7/8[/pmath]of the people attended the afternoon session.
(Havent done Data Sufficiency before? Or are you new enough to DS that youre wondering where the answer choices are? Start here and come back to this article later.)
Lets do this!
1-second Glance. Story. DS. Some fractions.
Read. Morning session. Afternoon session. Can attend just one or both this is starting to smell like a sets question.
Jot.
There are 128 people and they want to know how many attend the morning session onlythats my purple circle. (Wouldnt it be nice if we could have multi-colored pens on the real test, too? :))
Reflect. People can attend just one session or both oh! Everyone attended at least one session. In other words, the Neither category is equal to 0. Thats a key detail to noticeif I miss that, Im probably going to get this one wrong.
Note: if you like Venn diagrams, read this. If you dont, skip this paragraph. My visual brain does like the Venn better, but the matrix lays out all of the categories more clearly, so I default to the matrix. In this case, because the Neither category is 0 and because theyre asking for M~A (a clearly-laid-out category on the Venn) , the Venn may be a fine choice. Im still defaulting to the matrix, though, because over the years, Ive learned that its easier to make mistakes on the Venn (for me, anyway!).
Back to our problem. Neither = 0.
Anything else we can glean from the question stem?
Nope, thats about it. Time for the statements.
(1) [pmath]3/4[/pmath]of the people attended both sessions.
Of the people means of all of the people who attended, or 128. So we can find the MA box.
Note two things:
(1) I didnt put a number, just a check mark. This is DS; I just have to figure out whether I can solve. I dont actually have to solve.
(2) I put the check mark in the upper left corner. This is my own shorthand for this information is from statement (1) and it reminds me that I can use it only when Im evaluating statement (1). Later, when I evaluate statement (2), Ill put the information in the upper right corner. (This matches how I organize my scrap paper on non-matrix problems: statement (1) on the left and statement (2) on the right.)
And if the information is from the question stem, it goes in the middle of the box, because I can use it anywhere. This organization saves me from having to draw the table multiple times. (If you decide to use my method too, draw a big table. Give yourself plenty of space to segregate the information properly!)
Okay, can we find M~A with statement (1)?
Nope, I dont see how. Cant calculate anything else in either the row M or the column A. Not sufficient. Cross off answers (A) and (D).
(2) [pmath]7/8[/pmath]of the people attended the afternoon session.
Where does this one go?
Ooh, now weve got something interesting. First, we can find Tot~A, because the rows add across. And then we can find M~A because the columns also add down!
Even though it seems like theyre giving us the same kind of information that was given in statement (1)the number of people in just one discrete group in the mixthe placement of that box makes all the difference! In statement (1), we didnt know any additional info in the row or column of the number we were given.
But in statement (2), we were given a second number in the same row. In the matrix, all you need is two of anything in the same row or column to calculate the third.
The correct answer is (B).
What can you take away from this problem that will help you on future problems? Think about that for yourself before you read my takeaways below.
Key Takeaways for Knowing the Code:
(1) Overlapping sets problems hinge on being aware that there are up to 9 potential cuts of data, or categories, (represented by the 9 boxes in the double-set matrix). Its crucial to add all info to the relevant boxes, and that means its also crucial to make sure you know which box the problem is talking about at any given time.
(2) In this problem, the main twist was noticing the negative information: if everyone has to attend at least one seminar, then the Neither category must be 0.
* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.