Executive Assessment: Quant Strategies for Faster Solutions – Part 1

by on October 27th, 2017

mathThe Executive Assessment (EA) shares a lot of roots with the GMAT, GMAC’s flagship graduate business school exam. The Quant section covers almost all of the same material and uses the same question types, and the Integrated Reasoning section is identical.

Luckily, we get to use all of the same test-taking techniques that can make the GMAT easier to take. (Not easy…but easier!) We’ll explore the major techniques in this series.

Give yourself ~2 minutes to try the below problem and then we’ll talk. All problems in this series are from the free problem sets that appear on the official Executive Assessment website.

Note: This is a Data Sufficiency (DS) problem. If you’ve never seen anything like this before—and are wondering, for example, where the answer choices are?—then follow this link first to a GMAT article explaining how DS works. DS is exactly the same on the GMAT and the EA.

“Is the integer n odd?

“(1) n is divisible by 3.

“(2) n is divisible by 5.”

Got an answer? Even if you’re not sure, guess—that’s what you want to do on the real test, too, so practice that now (even if your practice consists of saying “I have no idea, so I’m randomly picking B!”).

Ready? Let’s do this!

 

Glance: This is a DS problem.

Read: They told us that n is an integer and they’re asking whether it’s odd. This is a Yes/No question (as opposed to a Value question). We don’t need to figure out what the value of n is, just whether it is odd.

Pause for a second: What’s the difference between odd and even, mathematically speaking?

If you divide an integer by 2 and get another integer, then that starting number was even. But if you divide the integer by 2 and get a decimal, then that starting number was odd.

Jot:

Time to Reflect. The statements look about equally hard, so just start with the first one. What does divisible by mean again?

If something is divisible by 3, then you get an integer when you divide by 3. Okay. I’m noticing that this question keeps talking about n but never provides a real value for n anywhere. It just keeps giving characteristics of n (or asking about characteristics of n).

That’s a great clue that I should Test Cases on this question. Testing Cases is a super-useful technique that you will use repeatedly on the EA. When the question is abstract, as in this case, you can just try real numbers to see what happens in the problem.

Let’s dive into this to see how it Works! You’re going to be working under Statement (1) on your scratch paper. Set up a little table that lists out the steps that you need to do.

The first rule of Testing Cases is to choose a value that makes the statement—and any other facts in the problem—true. Also, you want to start from a fact, not from the question itself.

The question stem gives one fact (n is an integer) and statement (1) gives another (that n / 3 is an integer). You can start with whichever one you like. Most people will probably want to start with n—it’s easier.

Set up your table. The first two columns are n and n / 3. I’ll explain the V thing in a minute. Finally, put a column for the question asked.

 Okay, let’s pick a value for n. It needs to be an integer, so start with a small positive integer. Try 1. What happens?

If n is 1, then n / 3 is 1/3. In that third column, V stands for Valid. Pause to make sure that everything you’ve done so far fits with all of the facts given in the problem.

n is an integer? Check.

n / 3 is an integer? Uh-oh … it’s not. :(

What does this mean? You have to toss out this case. You’re only allowed to try cases that fit all of the facts in the problem—so this is one of the skills to practice to get better at Testing Cases.

Start again. What kind of number do you need to make both of the first two columns work?

In order to get the second column to work, n has to be a multiple of 3.

 

Great! Now, everything is valid and we can get to the real question: Is n odd? In this case, yes; the number 3 is odd.

Will it always be odd, no matter what value you pick? We don’t know yet—we have to test some more cases.

You’ve already found one Yes answer, so the goal now is to see whether you can find a No answer. This is called Proving Insufficiency. If you can find one Yes answer and one No answer, using Valid numbers, then you have proved that the statement is not sufficient to answer the question.

Look back at how the math worked. Can you think of something to try that might give you a No answer?

In this problem, what does a No answer actually mean? The number n has to be an integer no matter what, so there are two possible classifications: odd or even. If integer n is not odd, then it has to be even. Can you get it to be even, given the restrictions that you were given?

Sure! Try this:

 

You’ve got one Yes and one No answer, so statement (1) is not sufficient to answer the question. Cross off the AD row on your AD/BCE answer grid.

Now, let’s take a look at statement (2). It uses a different number, but the set-up is the same, so test cases again. (But be careful: You are only testing the second statement now. Ignore the first statement completely.)

Follow the process yourself before you look at my work below.

Great! We can prove this one not sufficient, too. Cross off answer (B) in your answer grid.

Now, try the two statements together. You can only pick values that work for both statements. That could be tricky, so take a look back at your prior work.

For statement 1, the values for n were multiples of 3. In statement 2, n was multiples of 5.

If you’re going to use the two statements together, then, the values of n are going to have to be multiples of 3 × 5 = 15.

If you’ve gotten this far, you may also feel comfortable enough with the process to just think it through. For example:

n = 15

Valid? It is an integer. It is divisible by 3. It is  divisible by 5. Valid!

Is it odd? Yes.

n = 30

Valid? It is an integer. It is divisible by 3. It is  divisible by 5. Valid!

Is it odd? No!

Since you once again got Yes and No answers, using the two statements together is still not sufficient to answer the question. Cross off (C); only one answer is left!

The correct answer is (E).

Key Takeaways for EA Testing Cases on Data Sufficiency:

(1) Know whether you have a Value or Yes/No Data Sufficiency question. If the question is theoretical (they never give you real values, just characteristics to test), you can Test Cases.

(2) Try to Prove Insufficiency. Set up a table. Start from a fact. Don’t forget the V step! Make sure your values are all valid for the problem. Try to get two different answers (Yes and No on a Yes/No question or 2 different values on a Value question). If you can do so, the statement is Not Sufficient. If you always get the same answer, that statement is Sufficient.

(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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