GMAT Data Sufficiency: Follow Your Process - Part 2
In the first installment of this series, we talked about an overall process that allows you to work methodically and make sure that youre performing the necessary analysis to give yourself the best shot at answering the question correctly (avoiding traps and careless mistakes).
First glance at the problem to see what youve got. Consciously notice whether its Problem Solving (PS) or Data Sufficiency (DS). (Seriously! Your whole mindset changes depending on which type it is, so notice.) Also note where the complexity seems to lie. Anything ugly in the question stem? In the statements? Both?
As you read, jot down any important information. Dont do anything with it yet; you are not solving. The word jot was chosen deliberately: just get the info down on paper.
Next, still dont start solving. :) Give yourself a little time to look at what youve got and think about what they could tell you that would be sufficientand what would not be sufficient. (In other words, reflect!) If applicable, organize or combine information that you already know in order to simplify or rephrase the question. Decide how youre going to tackle the problem.
Finally, you can start solvingassuming you made it through the first two rows successfully. If you dont actually Understand (the goal of row 1) or you havent come up with a good Plan (the goal of row 2), then dont continue to work on the problem. Trying to solve without a good understanding of the problem or a good plan is a waste of precious time.
Everything weve talked about so far can apply to any problem on the GMAT. Today, were going to add a few more process layers that are specific to DS.
You ready to try another problem? Here you go. (This one is from the free GMATPrep exams.)
*Is the average (arithmetic mean) of 5 different positive integers at least 30?(1) Each of the integers is a multiple of 10.
(2) The sum of the 5 integers is 160.
(I again havent listed the answer choices here; if you havent done enough DS to know what the answer choices are, then dont start with this series. Start here.)
Got your answer? Okay, lets get started.
Glance at the problem. Its DS! Draw a T on your scrap paper and jot down the relevant info as you read.
Why do I draw things out that way? Its really important to separate the information given in a DS problem into one of three categories:
- The question stem
- Statement (1)
- Statement (2)
Info in the question stem applies to both statements. Statements (1) and (2), however, are distinct. You have to keep them completely separate at first; later in the problem, you might have to put those two statements together, but youre not allowed to do that at first.
Time for step 2: reflect and organize. Whats the significance of the information given in the question stem?
These 5 numbers are positive. Theyre integers. And theyre different from one another. Make sure your scrap paper reflects every last detail of that info.
Next, the stem mentions average. When a problem mentions something for which you know a formula, jot it down. Plug in what you know.
Check it out. If the average is at least 30, then the sum is at least 150. So if they tell you the average, that would be sufficient to answerbut they could also tell you something about the sum. (This is what we call rephrasing the question, by the way.)
If the average > 30, then the answer is Yes. If the average is < 30, the answer is No. Either way, that information is Sufficient. If, on the other hand, the average is a range that crosses that threshold, the answer is Maybe and the information is Not Sufficient.
Likewise, if the sum is > 150, the answer is Yes (= Sufficient). If the sum is < 150, the answer is No (= Sufficient). If the sum is a range that crosses that threshold, the answer is Maybe (= Not Sufficient).
Great. Lets work this thing. Glance at those statements. Any preference where to start?
Now that weve rephrased the question, definitely start with statement 2. :)
(2) The sum of the 5 integers is 160.
Boom. Sum is greater than 150. Thats sufficient. Cross off ACE. See how useful it was to take the time to rephrase the question?
Moving on to statement (1).
(1) Each of the integers is a multiple of 10.
At first glance, this one doesnt look all that useful. Remind yourself of the constraints given in the question stem. Each number is a different positive integer.
Test a Case. What are the smallest values that will still fit the criteria?
10, 20, 30, 40, 50
In this case, the sum islets see, its a consecutive set, and there are an odd number of terms, so the average is just the middle number, 30.
So for this case alone, the answer is Yes, because the average is > 30.
Whats the next step in the Testing Cases process? Your goal is to try to disprove the statement (if you can!), so try to get the opposite answer. Can you get a No?
Its impossible to get a No answer. Why?
The first Case represented the smallest possible set, so any other set will include at least one larger number. The smallest possible set already averaged to 30, so any other set will average to more than 30.
This statement is Always Yes, which is Sufficient to answer the question.
The correct answer is (D).
Key Takeaways for Data Sufficiency:
(1) Your first goal is to Understand. See what the moving parts are. Jot everything down.
(2) Dont solve yet. First, come up with a Plan. Most of the time, Data Sufficiency questions are hiding something of relevance. Unless the question is very simple / straightforward, theres probably something you could figure out before you go to the statements that will really speed up your processing of the statements. Look for those opportunities to rephrase or simplify the question.
(3) You can Solve now. When solving, its often useful to Test Cases, especially on Yes/No DS questions. When you do this, remember that you have to test more than one case. After you test your first case, your goal is to try to get the opposite answer (Yes No or No Yes) for your second case. If you can find both a Yes and a No, that statement is Not Sufficient. If you have an Always Yes or Always No situation, then that statement is Sufficient.
* GMATPrep questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.