Executive Assessment: Fast Math for Faster Solutions – Part 6

by on October 19th, 2017

math copyWelcome to the sixth installment of Fast Math for the EA! If you’re just joining us now, head back to the first part and work your way back here.

We’re going to try another type of Integrated Reasoning (IR) problem today: a Graph problem. Give yourself about 3 minutes to try out this free problem from the Executive Assessment official website.

“Refer to the pictograph of a survey of students at Central Community College. Each symbol represents 10 students in a sample of 300. Use the drop-down menus to complete each statement according to the information presented in the diagram.

“If one student is selected at random from the 300 surveyed, the chance that the student will be under 30 or a high school graduate or both is __________.

“If one student is selected at random from the 300 surveyed, the chance that the student will be both under 30 and a high school graduate is __________.”

Answer options for blank 1:

“1 out of 6

“1 out of 3

“2 out of 3

“5 out of 6″

Answer options for blank 2:

“1 out of 6

“1 out of 3

“2 out of 3

“5 out of 6″

That’s not a typo—the answer options are the same for both blanks. This isn’t that common but it can happy (obviously!).

Okay, ready to review this one?

On the real test, instead of an actual blank, you will see a little drop down menu with an arrow to the right. You will have to physically click in order to see the options.

And here’s your first important piece of strategy for Graph questions: Do not even start to think about how you might solve until you look at the answer choices. Seriously—promise me right now that you will always look first!

The form of the answers can drastically affect how you choose to solve the problem. When I first started doing these, back when the IR section was added to the GMAT, I spent a bunch of time on a problem calculating an exact numerical answer … only to discover that the answer choices were so far apart that I could have estimated heavily the entire way. :(

Don’t be me! Or don’t be me back then, anyway.

Okay, let’s do this. The graph has all these dots, each of which represents 10 students. And the question stem indicates that there are 300 students total (so there must be 30 dots total).

“If one student is selected at random from the 300 surveyed, the chance that the student will be under 30 or a high school graduate or both is __________.”

The first statement asks for the chance that a particular thing is true, and then the answer choices are in the form of a fraction (1 out of 6, or one-sixth, and so on). That’s very interesting. In fact, it’s going to form the basis of our Fast Math approach on this problem!

If I tell you there are 10 people in a club and then say that 1 has brown hair, you could say that 1 in 10 has brown hair.

If there are 100 people in the club and 10 have brown hair…then 10 out of 100 have brown hair and that still simplifies down to 1 in 10.

In other words, if you’re going to take this down to the simplest fraction (and you are—look at the answers!), you don’t actually need to calculate based on 100 people (or 300, as in the given problem). You can just go based on the 10 (or the 30 dots that are in the given problem). Make your life easier!

So now, pretend there are just 30 students. The question asks for the chance that the student will be under 30 or a high school graduate or both. Look at the pictograph. What are the categories?

The left-hand circle is for people who are 30 or older, so the under 30 folks are the people who are not in that circle. How many are not in that circle?

There are 4 in the part of the other circle that does not overlap with the 30+ years circle. And there are an additional 10 outside of both circles (these are the “neither” folks—they fall into neither of the two circles). So there are 14 total who are under 30.

What about high school graduates?

The right-hand circle represents people with no diploma, so all those people in the partial circle to the left do have diplomas. Count them up—there are 11. And then there are also those 10 people up above … hmm, but we already counted them once. Should we count them again?

Go back to the question stem. It asks for people who are under 30 or a high school graduate or both. Okay, the under-30-only folks are the 4 with no high school diploma. The high-school-graduate-only folks are the 11 who are 30+ years. And then the 10 outside of both circles represent the people who are both (under 30 and a high school graduate). So just add them once.

Add them up: 4 + 11 + 10 = 25. How many students total are there? Oh right, 30. So 25 out of 30 fall into the desired categories. Simplify that fraction down. Both numbers are divisible by 5, so the answer is 5 out of 6.

You could do that same math with the “real” numbers: 300 students, and then 40, 110, and 100 in the three categories…you’d get the same answer. But why make this any harder than you have to?

Let’s try the second statement.

“If one student is selected at random from the 300 surveyed, the chance that the student will be both under 30 and a high school graduate is __________.”

This is the same type of statement, so we can use the same shortcut we did on the first one. There are 30 students. How many are both under 30 and a graduate?

Hey, we already figured that out last time: the 10 who are outside of the circles entirely. So 10 out of 30 fall into the specified categories this time, or 1 out of 3 students. Done!

Key Takeaways for EA Fast Math:

(1) On Graph problems, look at the answers in the drop-down menus before you start thinking about how to solve. Take the form of the answers into account as you formulate your strategy.

(2) Just because they give you big numbers, you don’t necessarily have to use them. If the problem is asking for a fraction or a percentage, you may very well be able to get away with using smaller numbers. After all one-third is still one-third, no matter how many actual students you have.

(3) Turn that knowledge into Know the Code flash cards:

* Executive Assessment questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

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