Executive Assessment: Quant Strategies for Faster Solutions - Part 1
The Executive Assessment (EA) shares a lot of roots with the GMAT, GMACs 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 easybut easier!) Well explore the major techniques in this series.
Give yourself ~2 minutes to try the below problem and then well 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 youve never seen anything like this beforeand 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 youre not sure, guessthats 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 Im randomly picking B!).
Ready? Lets do this!
Glance: This is a DS problem.
Read: They told us that n is an integer and theyre asking whether its odd. This is a Yes/No question (as opposed to a Value question). We dont need to figure out what the value of n is, just whether it is odd.
Pause for a second: Whats 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. Im 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).
Thats 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.
Lets dive into this to see how it Works! Youre 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 statementand any other facts in the problemtrue. 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 nits easier.
Set up your table. The first two columns are n and n / 3. Ill explain the V thing in a minute. Finally, put a column for the question asked.
Okay, lets 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 youve 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 its not. :(
What does this mean? You have to toss out this case. Youre only allowed to try cases that fit all of the facts in the problemso 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 dont know yetwe have to test some more cases.
Youve 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:
Youve 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, lets 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 youre going to use the two statements together, then, the values of n are going to have to be multiples of 3 5 = 15.
If youve 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. Dont 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.