Data Sufficiency
Now we come to a very unique part of the GMAT Quantitative section, the data sufficiency portion. These types of questions are only found on the GMAT, and about a third of the points available on the math section come from these questions. The rest of the points in this section are from problem-solving questions, as we covered in previous sections.
With problem-solving questions, you are looking at the problem and finding the answer choice that best matches it. However, with data sufficiency, you don’t actually have to solve problems; you only have to determine whether the question can be solved with the information provided.
As with the problem solving questions, these questions will only cover basic arithmetic, averages, fractions, decimals, algebra, factoring, and basic principles of geometry (triangles, circles, and areas/volumes of simple shapes). Okay, so it sounds like a lot when you list it out like that! But my point is that you shouldn’t expect any surprises beyond these!
These types of questions will seem difficult at first, but as you move on, you will find that they get easier and easier. In this section, we are going to take a look at the basic structure of Data Sufficiency question stems and answer choices to make sure that you are familiar with the layout before moving into any of the techniques for handling these questions. Next, we’ll discuss the two main Data Sufficiency question types, the core topics tested, and other Data Sufficiency strategies. Finally, we’ll try a bonus question that’s a little more difficult and shows how sneaky the GMAT writers try to be. Don’t worry though, you’ll learn how to outsmart them here! ;)
All data sufficiency questions come in a similar format. You are given a question stem followed by two statements that, together or apart, may or may not answer the question in the passage. You have to choose one of the five options.
You will get a question followed by two statements that contain data. You then choose the correct answer based on the data in the statement, what you know, and common sense. Here is how the answers choices look:
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
You can use this method to try to answer data sufficiency questions when you come to them. It is a step-by-step process that’s quite easy once you get the hang of it.
1. Look at the question thoroughly. This may seem obvious, but the number of people who do not look at the questions when trying to answer them is surprising. You need to be able to decipher the question quickly, and then consider the information you may need to answer it properly. Do not be afraid to ask yourself questions like:
i. What is the focus of the question?
ii. Does it require a formula calculation?
iii. What are the variables?
iv. Do I have all of the values?
2. Next, as we have done with the reading part of the exam, we have to split everything up and look at it separately. Look at everything and try and determine again what you may need to answer it. You will want to go over the question twice before moving on.
3. Look at the statements and make sure that you understand them. Focus on them and think about what you just read in the passage. By this time, you should be able to focus on what answers can remain and what answers you can eliminate. You can then begin to answer the question.
4. The last step is to answer the question to the best of your ability. Remember, it is better to get it wrong than to skip it, so be sure to answer it.
That is about all there is to data sufficiency questions. For questions that make up a third of your math grade, they are pretty straightforward. Don’t worry, we aren’t going to throw you to the wolves yet; we’ll look at a couple of questions here before moving on to the practice section.
A Couple of Sample Questions
As I mentioned, first, you are presented with a question stem:
What is the value of w if w and z are two distinct integers and w x z = 60?
Then, you are given the following statements:
1. w is an odd integer
2. w > z
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
The correct answer in this choice is E, the value of w cannot be determined from the information provided*.* Did you get it? Here’s why it’s the right answer:
We were given enough information to know that the two variables added together is 60. By looking at simple multiplication, we can determine that the following numbers conform to this:
1 × 60
2 × 30
4 × 15
3 × 20
5 × 12
6 × 10
Their negative values also conform (–1 ×–60, etc).
We know that w is odd because of the statement, and that means w can be 1, 3, or 5, along with –1, –3, or –5. As a result, we cannot determine which of these will answer the question. From that data alone, we know that the first statement is automatically eliminated. You can cross off answer A, but the cool thing is that you can also cross off answer D. Remember that D means both statements independently can answer the question, and you have just prove that A independently cannot answer the question.
Also, since w has more than one value, we cannot use statement 2, which will not allow us to find the value of w. When you look at statement 2, be sure to look at it independently. You don’t want to apply any information you learned from statement 1 right away because then you might mistakenly choose answer B when you really mean answer C. Answer C means that you are using the two statements together to limit each other.
Since we cannot get the value of w, the next two statements are also eliminated because they do not provide sufficient data to answer any of the questions. This is why the last statement is correct, because with statements 1 and 2 together, we are not able to answer the question and we need more information to do so.
How was that? Let’s try one more before moving onto the practice section.
How many people are members of both a certain town’s softball team and bowling team?
1. The softball team has 24 members and the bowling team has 9 members.
2. 31 softball and bowling team members went to the town’s annual picnic last year and no team members were absent.
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E.** Statements (1) and (2) TOGETHER are NOT sufficient.**
Looking at the five answers, we can determine that answer C is the best choice for this question, which is Both statements are required to answer the given question*.*
We know from statement 1 how many members each individual team has, but we don’t know how many people play on both teams. This statement does not give us enough information, which eliminates answers A and D.
The second statement tells us that 31 members from both teams were at the picnic, and that 31 represents the total number of softball and bowling players. If there are only 31 players altogether, rather than 33 (24 + 9), 2 people must play on both the softball and bowling teams. Therefore, answer C is correct because we have the information to answer the question, but we need both statements together to do so.
Two Main Data Sufficiency Question Types
Now that you’ve got the basic understanding of the structure of the Data Sufficiency section and a couple of general strategies for handling these types of questions, let’s take a deeper look at the two main question types and some ways to tailor your approach to fit these questions.
The two question types that we’ll be looking at are concrete value and yes/no questions. Although these questions may initially appear to be easier than other question types, the test makers usually add hidden wrinkles into the question stem that will need to be identified and handled in order to get the question right. Let’s take a look at some ways of doing just that.
Question Type: Concrete Value
One common question type is called a concrete value question. This question type won’t be new to you. It’s asking for you to find the value of a particular variable that’s provided in the question stem. When the GMAT test-makers ask for a variable’s value in the Data Sufficiency section, it means the one and only value.
What is the value of x?
1. x2 - 9 = 16
2. 2x (x - 5) = 0
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Taking a look at the question stem in this example doesn’t take long. No tricks to be found here – you’re looking for the value of x. Taking a look at each statement that you’re given in the question takes a little more time. Statement (1) looks simple but you have to remember that x2 = 25 can mean that x is either +5 or -5. This is a good lesson because if you’re able to solve the equation that simply, you’re probably falling into a trap! Eliminate answers A and D.
For Statement (2), you could also have either 0 or +5 as possible values for x – so (2) is insufficient on its own as well.
Since neither of these statements were able to give us the value of x alone, we should try to look at them together and see what we can get.
Statement (1) tells us that the value of x is either +5 or -5; (2) says that x is either 0 or +5.
When they’re combined, BOTH must be true and be satisfied by one value – in this case +5 works for both. The answer can’t be 0 because that contradicts statement (1) and it can’t be -5 because that contradicts statement (2). The bottom line is if the statements share just one value, they are sufficient (when combined) for answering the question.
Therefore C is the correct answer.
Ø More Practice from the GMAT**®** Review 13****th Edition: Questions 1, 15, 46, 58, 147
Question Type: Yes/No
Yes/no questions generally represent about a third of the questions that you’ll encounter in the Data Sufficiency section. That’s both good news and bad news. The bad news is that questions generally appear to be fairly simple but you may have to brush up on some numbers properties or memorize a few basic mathematical rules in order to allow yourself to work through these problems in a reasonable amount of time. The good news is that if you can spend your time before the test figuring out these details, you’ll have a much more organized approach to these problems during the actual test – and your score will show it.
While concrete value questions look for one value and one value only, yes/no questions look for one answer – yes or no – to the question posed.
Let’s take a look at a basic yes/no question stem to clarify:
Is the product of x, y, and z equal to 6?
1. x + y + z = 6
2. x, y, and z are each greater than 0
The standard answer choices for data sufficiency apply to this problem:
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Looking closely at the question stem, it’s pretty clear that what you’ll need to determine is the value of the product of xyz**.** Keep in mind that when you’re looking for a product, you’ll either need to know the value of all of these variables or you can use a rule or property of multiplication to help you along. For example, if the product is 0, you know that at least one of these variables must be zero.
Taking a look at the question stem and using some of the techniques that we’ve discussed previously, it should be fairly obvious that statement (2) is not sufficient to provide the answer for us alone – the numbers that make up all of the values greater than 0 are just too broad to provide us with an answer.
This means that if the values are 1, 2, and 3, you will have an answer of 1, 2, and 3, you will have an answer of yes to the question stem. If the values are 4, 5, and 6, you will have an answer of no to the question stem. Since we only want one of those answers, you can eliminate B right away, and if you can eliminate B, you can eliminate D. You’ve already increased your chances of getting this answer correct by 40% - great!
Next, pick some numbers to satisfy statement 1. Again, choosing simple numbers like x = 1, y = 2, z = 3 is a good place to start. In this case, the product does equal 6. When you plug in some different numbers to test the properties of this equation (maybe x= -5, y = 0, z = 12) the product is 0 and the product is not equal to 6 – you’ve now eliminated answer A.
At this point, we’re left with the possibility that the two statements combined will either be enough for us to get the yes/no answer that we’re seeking or that they will still be insufficient. Going back to picking numbers is easy enough. This time, we’ll just adjust our previous values so that they fit both rules – say x = 1, y = 1, z = 4. Even though the problem uses two different variables, x and y, you can assign them the same value if the problem doesn’t say they must be distinct.
Remember, with these yes/no questions, it will only take one example that doesn’t give you the desired output in order to show that the statement is not sufficient. In this case, the values that we substituted fit the rules of both statements and the resulting product is not 6 – C is not the answer. We’ve eliminated all other possibilities so choice E is our answer.
Although walking through the details of this process may seem somewhat lengthy, in reality these steps should take very little time for you to execute – especially if you are comfortable with this type of question stem and the way to methodically work through it for a solution. Always keep in mind that picking numbers to substitute for variables is a great technique but don’t forget to pick strategically – include positive numbers, negative numbers, and fractions in order to get a better sense for where things stand.
Important Tip!
If you simply go for the obvious selections, you’ll be playing right into the test maker’s hands. Part of what the GMAT is trying to identify is which test takers are capable of complex thinking and problem solving. Even if this isn’t your natural strength or if some of these approaches seem difficult initially, building good habits by practicing them now will pay off time and time again during the test.
Here’s another yes/no question type that will take a slightly different approach to get to the solution:
Is 6 + x/8 an integer?
1. x is between 80 and 90
2. x has exactly one factor pair
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient
The mathematical properties involved in this question stem are pretty straightforward. We need to know whether x is a multiple of 8 because if x/8 is an integer, it will remain an integer when we add it to 6. Let’s take a look at the choices to see where things stand.
First, we know that A is insufficient because there are numbers between 80 and 90 that will give us a yes and no answer. 88 is a multiple of 8 and 85 is not. Eliminate answers A and D.
Now look at statement (2). This statement is telling us in a roundabout way that x is a prime number. If x is a prime number, it will never be divisible by 8 and therefore the answer to the question will always be no. This means that B is the correct answer.
You may be confused at this point because you have been conditioned your whole life to think that no is a bad answer. But on yes/no Data Sufficiency, no is a good answer! Remember that we want a definite yes or a definite no. Either one is fine because it provides an answer to the question.
This question is also a reminder that you won’t always have to work through your entire problem-solving process in order to arrive at a solution. We don’t actually care what the value of x is. We just needed a response of yes or no. In fact, once you are proficient in using all of these techniques, you should rarely have to work through an entire problem from start to finish. Shaving a few seconds off the easier and moderate problems may help give you the time you need to crack the really difficult “stumper” questions that you’re bound to encounter.
Ø More Practice from the GMAT**®** Review 13****th Edition: Questions 7, 13, 14, 27, 32
Core Topics
Let’s look now at the most commonly tested concepts on Data Sufficiency. If you have already read through the whole Problem Solving section, you’ll see that there aren’t any new topics here. But what is different is the way you will apply the information you learned previously.
Core Topic 1: Linear Equations
While most of the techniques that we’ve discussed are solid and detailed approaches to certain types of problems, it’s sometimes nice to have a quick tip that will allow you to get certain questions out of the way and move on to something more difficult – this is one such tip.
You will probably encounter at least one Data Sufficiency question that will provide you with a couple of linear equations. If you know enough about the nature of these equations, you might be able to recognize that a solution is possible without working to solve a part of it. Since that’s all you need in a Data Sufficiency question, it’s perfect.
Here’s the tip: Solving for x variables requires x distinct, linear equations containing those variables. What this means is if you have two variables (say, x and y), you will need two distinct linear equations to solve both variables.
For example, given:
*x+y=*4
*x– y=*2
You can solve for both x and y. Although it’s not difficult to solve for x and y in this example, you can imagine that things get considerably more difficult on the test. A good example is when the equations are disguised as sentences as in this example:
Peter took a trip from his parents’ house to his grandmother’s house. If he did not stop along the way, how long did it take Peter to finish his trip?
1. He traveled a total of 240 miles.
2. He traveled half the distance at 30 miles per hour, and half the distance at 60 miles per hour.
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
Translate each sentence into an equation using distance = rate × time. Statement 1 will give you 240 = rate × time. Statement 2 will give you distance / 2 = 30 × time and* distance* / 2 = 60 × time. Notice there you can substitute the distance given in statement 1 into the equations in statement 2, which will leave you with one variable. Once you have gotten to that point, you can quickly select the corresponding answer (C) and move on to the next question.
A couple of notes about this tip. First, you have to make sure that the equations can’t be simplified to the same equation. If that’s the case, there are actually fewer distinct equations than it might appear and your final answer might be totally different. Second, this tip will only work if no variables are raised to exponents (e.g. no x2, y3...etc). Overall, you should continue to practice all of the other techniques that have been provided but if knowing this tip helps you shave time off just one Data Sufficiency question, it will have been worth reviewing.
Ø More Practice from the GMAT**®** Review 13****th Edition: Questions 9, 17, 34, 36, 60
Core Topic 2: Simple Geometry
It would probably be useful at this point to take a look at a totally different type of Data Sufficiency problem as a reminder of some of different issues that you might run into during your actual exam. This one is based on simple geometry:
What is the area of isosceles triangle XYZ?
1. The length of the side opposite the largest angle in the triangle is 6cm.
2. The perimeter of triangle XYZ is 16cm.
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
This question does require some basic knowledge of geometry but you have likely done a little brushing-up on these basic rules by this point. As a reminder, in a triangle the largest angle will be opposite the longest side. Similarly, the side opposite the smallest angle will be the shortest. We also know from the question stem that this is an isosceles triangle. This tells us several things – most importantly for this question, we know that two of the sides and two of the angles are equivalent.
Since statement (1) refers to a “largest angle”, we know that the side opposite this angle must be the longest in the triangle. The alternative in an isosceles triangle would be to have two equal angles that are equivalently large. Since we know that this largest side is 6, we know that the other two sides must be equivalent and that they measure no longer than 3 each (or they wouldn’t be able to join to form the triangle. Take a look at the diagram below to get an idea of what you should be able to take from the question at this point:
Although we know the measure of the base and have some idea about the other sides, we have no idea about the height at this point and can’t calculate the area of a triangle without it – statement (1) is NOT sufficient. You can eliminate A and D.
Taking a look at statement (2) alone, we not have to forget everything that we learned while looking at statement (1). We know that calculating the perimeter is going to require us to sum the values of each side of this triangle. We can express this as a + b + c = perimeter. From the question stem, however, we know that this triangle is an isosceles triangle and has two equivalent sides. This allows us to simplify our equation to calculate the perimeter into: 2a + b = perimeter.
Since we know the value of the perimeter, we can further simplify to:
2a + b = 16. At this point, we know that there’s no way we’ll be able to solve this equation without the help of another since we’ve discussed that two linear equations are necessary in order to solve for two variables. Statement (2) is NOT sufficient. This allows you to eliminate B. To get down to our final answer, it’s time to evaluate the two statements together and see if C or E is the correct choice.
Since we’ve already essentially come up with an equation from looking at each statement individually, we’ll just need to translate them into common variables to see if we’ll be able to solve for each when they’re combined. From statement (1), we know that:
The longest side = 6cm
From statement (2), we know that:
2a + b = perimeter
Since we know that the single longest side is also a distinct value from the other two sides (which are equivalent), we can substitute like this:
2a + (longest side) = perimeter
2a + (6cm) = 16cm
2a + 6 = 16
2a = 10
a = 5
This gives us the measure of the two equivalent sides of the triangle – so we know that the measures of all sides are 5cm, 5cm, and 6cm as in this diagram:
Since we ultimately want to know if we can find the area of the triangle (1/2bh), we must just calculate height knowing that the base is bisected by the height which intersects it at a right angle – giving a 3-4-5 special right triangle. Since we now know the height is 4, we know that statement (1) and (2), when taken together are SUFFICIENT to answer this question – answer C is correct.
Keep in mind that this question is one of those that is much easier to work through graphically. Remembering a couple of geometric ideas will have got you far with this one.
It is a good reminder that you’ll see MANY different question types and there is potential for any of them to be more difficult . Using a consistent approach and not getting bogged down unnecessarily will keep you moving ahead regardless of the question type – you may even be hoping for some of the more difficult questions on this computer adaptive test (CAT) because it means that you’re within striking distance of the higher scores that you’re seeking. More difficult questions also mean that there’s a better possibility that your fellow test takers will be tripped up – and your score will be higher as a result.
Ø More Practice from the GMAT**®** Review 13****th Edition: Questions 11, 30, 35, 56, 73
Core Topic 3: Mean, Median, and Mode
Let’s review a problem that requires some very basic knowledge about a common topic that comes up often in the Data Sufficiency section – mean/median/mode:
How many students scored more than the average (arithmetic mean) of the class on Monday’s test?
1. The average (arithmetic mean) of the class was 78
2. Ten students scored below the arithmetic mean of the class
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
In this case, it is VERY clear what this question is looking for – how many students scored higher than the average?
The first statement provides us with the average (as a reminder, that is the sum of all scores divided by the number of scores). This doesn’t tell us anything about the individual scores. With an arithmetic mean (as opposed to a median or mode), there could be many students who are above average or only a few. Statement (1) is clearly insufficient to solve this problem.
Statement (2) still tells us nothing about the number of students that we’re trying to determine. Statement (2) is insufficient to solve this problem.
Combining the two statements doesn’t get us to the answer either. Even when combined, these statements fail to provide us with enough information to get the answer. The properties of an arithmetic mean inherently leave room for an outlier at the top or the bottom of the range that would pull the average score up or down. Since we are still unable to answer the question, our answer is E.
Keep in mind that although this question required you to do some reasoning through the question stem and statements, the only real outside information that you had to bring to the process was the knowledge of how to calculate an average. You probably learned and understood this years ago – the tough part is figuring out how to apply that 7th grade knowledge to a much more abstract concept. Keep this in mind. You’ve got the basics covered. Now use that noggin of yours to work out when and where to apply them!
Ø More Practice from the GMAT**®** Review 13****th Edition: Questions 20, 37, 70, 84, 95
What Else do I Need to Know to Do Well?
By now, you undoubtedly can see why Data Sufficiency questions, though intimidating at first, are easier than problem solving. Let’s talk about two more tips that will help you work through these questions efficiently and accurately.
Quick Tip 1: Diagrams Are Your Friend!
One part of the GMAT Data Sufficiency section that isn’t unique is the diagrams that are provided with some of the questions. It’s worth reviewing some key details about these diagrams and also a little bit about how these diagrams might be different from others that you may have encountered before.
First, there are some key things to keep in mind when working your way through a problem that includes a diagram.
It is important to realize that these diagrams are not intended to be accurately drawn or scaled representations of the information in the problem. Really, they are largely intended to help you with the relation between different points or figures. For instance, if there is an angle in a triangle that appears to be a right angle, you can’t assume that that’s the case unless you’re told so by some other source in the question.
In fact, it’s probably safe to assume that it’s not a right angle if it’s not marked as such. If a diagram of a line segment with several points spaced equally along the segment, it’s probably a mistake to assume that these points are actually evenly-spaced and so on.
You’ll always want to keep in mind that part of what the test makers are testing is your ability to move forward with a problem using only what you are given. Sometimes it’s helpful to purposely imagine (and draw) the diagram with skewed proportions on your scratch sheet in order to remind yourself that you’re only dealing with the relationships that have been provided.
Patience and flexibility in your approach to problems with diagrams will ensure that you don’t fall for the distracting answer choices that are provided for the test takers who don’t understand these ideas.
Quick Tip: Abstract Thinking
One of the higher-level skills that the GMAT is trying to measure is the test taker’s ability to think about concepts in an abstract way. You should keep this in mind and use this fact to your benefit when working with all of the other techniques that we have discussed up to this point.
What does it mean to think about concepts in an abstract way? It means that, for instance, when you’re choosing numbers to substitute in to an equation, you might want to recognize that there are certain boundaries that define groups of numbers. For instance, in the following question stem, think about how y changes when you substitute x for a positive number, negative number, or fraction:
y = (2/x)2
You can see that the resulting relative value of y is different in each case. A test taker looking at this problem for the first time with no preparation might choose numbers like 0, 1, 5 for x. That would certainly be a good starting point. Looking a little closer at this problem shows that choosing a larger, positive value for x means that the value of y actually gets smaller.
Choosing a negative value for x means that the sign of y will still be positive since the base fraction is multiplied by itself. Using a fractional value for x gives you still another result based on the type of fraction.
Becoming familiar with these number properties and being able to substitute strategically and determine what your likely answer choice will be is a great skill that only takes practice and close attention.
Thinking abstractly about the different groups of numbers that would affect the outcome is something that will allow you to reach those three results more quickly than blindly picking numbers. As a result, taking a little time up front to look at the question in a more abstract way will ultimately help you save time by getting to the correct answer more often and saving you time on the way there. Since this isn’t the easiest approach to take initially, it may take a little work to get in the habit of taking a step back to consider the problem before diving in more deeply**. Pushing yourself this way can really be beneficial – even small improvements in abstract thinking and approach can gain extra points for you on the Quantitative section of the GMAT – and those are definitely extra points we are looking for!**
Bonus Question: The Stumper
Even if you’re thoroughly prepared and as familiar as possible with each question type, you’re likely to run into at least one question during the course of the Data Sufficiency section of the GMAT that throws you off balance.
Maybe it’s the particular construction of the question. Maybe the question is based on a subject matter with which you’re not familiar (this shouldn’t matter). Regardless of how you arrive at a position of helplessness (!), there are things that you can do – when you don’t know what to do, your “plan B”.
In data sufficiency, all of the answer choices are based on the two statements that are provided in the question stem. That makes things difficult, but it also provides you with a great opportunity to narrow down the choices in many cases. If you’ve tried to attack the question with most of the tips that we’ve discussed to this point and haven’t had any luck, take the statements individually. We’ll discuss how you move forward with that approach.
Many times, the test makers will provide one statement that is fairly straightforward and another that is trickier. If you can evaluate the simpler statement using the tools that we’ve discussed in order to knock out some of the potential choices, it will increase your odds of choosing the correct answer – even if it’s a complete guess – dramatically.
If you can get it down to two remaining answers, you’ve got a 50/50 shot at getting a “stumper” question right – that’s a much better scenario than blindly guessing at a question with a 20% chance of success initially. It might be easier for us to look directly at a problem that will demonstrate this approach.
For the sake of this exercise, don’t try to solve this problem traditionally until we’ve worked through the process as if you didn’t know how to move forward.
What was the maximum temperature in swimming pool A on Sunday, July 23?
1. The average (arithmetic mean) of the maximum daily temperatures in pool A from Sunday, July 23 to Saturday, July 29 was 72 degrees Fahrenheit, which was two degrees less than the average (arithmetic mean) of the maximum daily temperatures in pool A from Monday, July 24 to Friday, July 28.
2. The maximum temperature on Saturday, July 29 was 5 degrees Fahrenheit greater than the maximum temperature in pool A on Sunday, July 23.
A. Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
As we approach this problem, we want to remember the approach that we’ve successfully been practicing to this point – just because this one looks complicated, doesn’t mean that an organized approach will not be beneficial here. Concentrating on the question stem gives us some good information. We’re essentially looking for one number – the maximum temperature of the pool on a specific date. Reading carefully through the statements that follow the question stem gives us a great deal of information. Maybe these statements give us too much information. Statement (1) alone seems like a very detailed set of circumstances to work through – let’s skip it for now and take a look at statement (2) to see if things can be narrowed down first.
This statement essentially gives us a comparison of the maximum temperature on two different dates but never gives us a concrete reference temperature to start with. We can tell that this statement will not be sufficient on its own. If not, that eliminates answer B and D. We’ve already increased or odds of selecting the correct answer 1/5 from to 1/3.
We’ll work through how to actually solve this problem but even if you could get no farther, you’ve still improved your odds significantly by working through the easier of the two statements. There is no golden key that will unlock a higher GMAT Data Sufficiency score, but by constantly chipping away at the questions, you will get better bit by bit. Before you know it, you’re looking at a much higher score!
Now let’s take a look at the solution for this problem (in case you were wondering!) Starting with the first part of Statement 1, the average maximum temperature from July 23 to July 29 was 72. This means that the sum of the maximum temperatures for those days is 7 × 72=504. If the average maximum temperature from July 24 to July 28 was two degrees warmer than the average maximum of 72 for the other time period, we know that it is 72 + 2 or 74.
The sum of the average maximum temperatures for those days (5 × 74 = 370). Since we now have concrete values for each of these two sums, it would make sense to try to relate these two values in a way that would allow us to bring in what we know from statement (2) in order to make our way to a solution. Since statement (2) is essentially telling us that the temperature on Saturday was 5 degrees warmer that that on the earlier Sunday, we can express that as y– x= 5.
From our earlier strategies, we know that if we have two unknown variables, we can solve for those values if we have two corresponding linear equations. Using the variables that we extracted from statement (2), we know that we’re looking for another equation that involves x and y. We can see from the values provided in statement (1) that adding together Sunday and Saturday will be the same as if we subtracted the five-day period from the seven-day period (also leaving us with Sunday and Saturday). Thus, we can translate these into an equation:
Saturday + Sunday = (seven-day period) – (five day period)
Substituting the concrete values that we know gives us:
Saturday + Sunday = 504 - 370
Next, we substitute in the variables that were established in our first equation:
y + x = 504 - 370
And perform the simple arithmetic:
y + x = 134
Thus, we’ve reduced all of that down to a linear equation with two variables that are common with the other equation. We know from our previous discussions that we will now be able to solve for both variables using these two equations. As such, the two statements TOGETHER allow us to solve the problem – C is the correct answer.
The good news is that we don’t even have to solve both equations to know that C is the answer since the Data Sufficiency section isn’t testing your ability to actually solve these equations but, rather, to know whether the equations CAN be solved using the statements provided. Sometimes, knowing when to stop before working through a problem on the GMAT can be as important as being able to actually work through the entire thing – this is definitely one of those cases.
As you’re moving forward, keep in mind what each statement can tell you individually. In addition to a complete solution to the problem:
• If statement (1) is sufficient, you can eliminate (B), (C), and (E). You’ve got a 50/50 shot at getting the answer right with a guess!
• If statement (1) is insufficient, you can eliminate (A) and (D). You’ve increased your odds from 1/5 to 1/3 already.
• If statement (2) is sufficient, you can eliminate (A), (C), and (E).
• If statement (2) is insufficient, you can eliminate (B) and (D).
Things to Remember…
Know that you do NOT need to know the solutions to the questions; you just need to know whether you can answer the question with the given information. Most data sufficiency questions do not require mathematical calculations and you can usually answer them faster than problem-solving questions. You need some practice to become familiar with data sufficiency questions because they are quite different. But once you are familiar with them, you’ll find them easier than a lot of the problem solving questions.
Here’s an overview of how I answer data sufficiency questions and how you can run through them efficiently too:
1. Read the question quickly and decide what information is required to solve it. How many variables are in the equation? How many of them are unknown? Think before you look at the two statements, as this will help you quickly decide how relevant they are.
2. Read the two statements carefully and independently. Keep in mind that the information contained in each statement is unique and does not involve the other statement. Do not mix them up!
3. If both statements are insufficient individually to solve the question, look at them together and see if the information contained in both statements, taken together, is sufficient to solve the problem.
4. Finally, do NOT try to solve the question! As soon as you know whether the question can be solved, move on the next question and don’t waste your time doing calculations.
5. For questions on number properties and algebra, you can come up with numbers and assign them to the variables and unknowns in the questions/ statements to help you understand them better.
Also remember some of the concepts that we’ve covered in this section:
Basic Question Types:
• Concrete Value
• Yes/No
Core Topics:
• Linear Equations
• Simple Geometry
• Mean, Median, and Mode
Quick Tips:
• Diagrams are Your Friend
• The Stumper
Bonus Question :
• The Stumper
Is this a lot of information? Absolutely! If it were easy to ace the Data Sufficiency section of the GMAT, everyone would be able to do it. But you’re already at a huge advantage - now that you know these basic techniques and question structure, the complexity of Data Sufficiency questions will work in your favor. Remember that these sections are always graded on a curve – the harder the questions, the better you will do in comparison to the others who are taking the test.
For each trick that you can avoid, many of the others will take the bait. (Sounds mean, but unfortunately with it being a standardized test, the GMAT is a little bit dog-eat-dog). For every question type that you recognize immediately from your practice, many other test takers will have no idea what to do. Start this section with the confidence that you’ve done your homework and that you can handle any surprises that come your way.