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If you are new to the Executive Assessment, you may be researching the types of quant questions you will encounter. The first type, Problem Solving, is a traditional multiple-choice question, with answer choices A, B, C, D, and E. However, there is also another quant question type: “Data Sufficiency.”
Unlike in Problem Solving, in Data Sufficiency (DS) questions, your goal is to determine whether you have enough information to answer a given question. While this problem type may seem intimidating at first glance, you can actually learn to enjoy answering DS questions. Reading this article will be the first step in establishing a love of DS questions!
Here are the topics we’ll cover:
- Key Facts About Executive Assessment Data Sufficiency Questions
- The Answer Choices of an EA Data Sufficiency Question
- A Nifty Way of Eliminating DS Answer Choices
- Basic DS Questions
- The Yes/No Data Sufficiency Question
- The Value Data Sufficiency Question
- Don’t Solve; Determine Sufficiency
- Key Takeaways
- What’s Next?
Let’s start with some key facts about EA Data Sufficiency questions.
Key Facts About Executive Assessment Data Sufficiency Questions
First, it’s important to know that 6 of the 14 quant questions on the EA are Data Sufficiency.
The makeup of a Data Sufficiency question is such that it contains the following elements:
- A question
- Optional given information (in the problem stem)
- Two statements
The goal in any DS question is for you to determine, using the given information and the information provided by the statements, whether you can answer the question definitively. So, although your math skills are tested in a DS question, so are your analytical skills.
KEY FACT:
Data Sufficiency questions on the Executive Assessment test both your math skills and your analytical skills.
Now, let’s look at a very basic DS sample question. You don’t need to answer it now; we will analyze this question later in detail.
DS Sample Question
If x + y = 8, what is the value of x?
(1) x = 4
(2) y = 4
We see the following:
- The given information is that x + y = 8.
- The question we are to answer is, “what is the value of x?”.
- The two statements are given as (1) x = 4 and (2) y = 4.
Now that we have a solid sense of the elements of DS questions, let’s discuss the Data Sufficiency answer choices.
The Answer Choices of an EA Data Sufficiency Question
Like Problem Solving questions, Data Sufficiency questions have 5 answer choices. However, unlike Problem Solving questions, which have different answer choices in each new question, the answer choices in Data Sufficiency questions are always the same. Thus, I recommend that all EA students memorize the DS answer choices, to save time on test day. These answer choices are below:
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
(C) BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
(D) EACH statement ALONE is sufficient to answer the question asked.
(E) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
TTP PRO TIP:
Memorizing the DS answer choices will save you time on test day.
Now, let’s discuss how to eliminate Data Sufficiency answer choices.
A Nifty Way of Eliminating DS Answer Choices
A cool component of DS questions is that we can systematically eliminate answer choices as we evaluate statements (1) and (2). Being able to systematically eliminate DS answer choices will save you time on test day. Let’s refer to the flowchart below.
TTP PRO TIP:
Being able to systematically eliminate DS answer choices will save you time on test day.
Let’s go through the paths on the flowchart in more detail.
Scenario 1: When A Is the Correct Answer
Step 1:
We evaluate statement (1) and determine it’s sufficient to answer the question. So, we eliminate answers B, C, and E.
Step 2:
We then evaluate statement (2) and determine it’s not sufficient to answer the question.
So, the answer is A.
Scenario 2: When B Is the Correct Answer
Step 1:
We evaluate statement (1) and determine it’s not sufficient to answer the question. So, we eliminate answers A and D.
Step 2:
We then evaluate statement (2) and determine it’s sufficient to answer the question.
So, the answer is B.
Scenario 3: When C Is the Correct Answer
Step 1:
We evaluate statement (1) and determine it’s not sufficient to answer the question. So, we eliminate answers A and D.
Step 2:
We then evaluate statement (2) and determine it’s not sufficient to answer the question. So, we eliminate answer B.
Step 3:
We then evaluate statements (1) and (2) together and determine that both of them together are sufficient to answer the question.
So, the correct answer is C.
Scenario 4: When D Is the Correct Answer
Step 1:
We evaluate statement (1) and determine it’s sufficient to answer the question. So, we eliminate answers B, C, and E.
Step 2:
We then evaluate statement (2) and determine it’s sufficient to answer the question.
Each statement, independent of the other, is sufficient to answer the question.
So, the correct answer is D.
Scenario 5: When E Is the Correct Answer
Step 1:
We evaluate statement (1) and determine it’s not sufficient to answer the question. So, we eliminate answers A and D.
Step 2:
We then evaluate statement (2) and determine it’s not sufficient to answer the question. So, we eliminate answer B.
Step 3:
We then evaluate statements (1) and (2) together and determine that together they are not sufficient to answer the question.
So, the correct answer is E.
Let’s now put this theory into practice with some basic DS questions.
Basic DS Questions
Example 1:
If x + y = 8, what is the value of x?
(1) x = 4
(2) y = 4
Solution:
We may first notice that we have given information and a question. The given information is x + y = 8. The question is, “what is the value of x?”
Once we have noted this information, we can move on to statement (1). Our goal in analyzing statement (1) is to determine whether statement (1), on its own, provides enough information to determine the value of x. So, let’s do that now.
Statement (1) Alone:
x = 4
Since we need to determine x and know that x = 4, statement (1) alone is sufficient to answer the question. Thus, we can eliminate answers B, C, and E.
Let’s now look at statement (2).
Statement (2) Alone:
y = 4
Although at first glance you may think that statement (2) does not answer the question, we can’t forget about the given information! Since we know that x + y = 8 and that y = 4, we can deduce that x = 4. Thus, statement (2) alone is also sufficient to answer the question.
Since both statement (1) and statement (2) are sufficient independently, the answer is D. EACH statement ALONE is sufficient to answer the question asked.
Let’s now look at one more basic example.
Example 2:
Example 2:
What is the value of x?
(1) x + y = 8
(2) y = 4
Solution:
In this question, unlike in the previous one, we see no given information. That’s totally fine! Some DS question stems contain given information while others do not. So, we can move to our statements.
Statement (1) Alone:
x + y = 8
Although we have an equation, we need more information to determine the value of x. Thus, we know that statement (1) is not sufficient to answer the question. Therefore, we can eliminate answers A and D.
Let’s now move to statement (2).
Statement (2) Alone:
y = 4
The value of y is not enough information to determine the value of x. Thus, the answer cannot be B.
Because each statement did not work independently, we can use the statements together to see whether we can get an answer.
Statements (1) and (2) Together:
Using the two statements, we see that x + y = 8 and that y = 4. Thus, it’s clear that x = 4. Therefore, the answer is C because we have found an answer using statements (1) and (2) together. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Next, let’s discuss the 2 types of Data Sufficiency questions: “yes/no” DS questions and “value” DS questions.
The Yes/No Data Sufficiency Question
The first type of Data Sufficiency question you can see on the Executive Assessment is the yes/no Data Sufficiency question. A statement is sufficient in this type of DS question when we can use it to conclusively answer yes to the question or conclusively answer no to the question. On the other hand, if we can answer yes sometimes and no other times, the statement is not sufficient to answer the question.
Let’s look at a few examples of yes/no DS questions and focus on which answers (yes or no) will provide sufficiency.
Is x + 2 even?
If x + 2 is always even, then we can respond with an answer of YES. If x + 2 is never even, then we can respond with an answer of NO.
Is x positive?
If x is always positive, then we can respond with an answer of YES. If x is never positive, then we can respond with an answer of NO.
Was the profit greater than $10,000?
If the profit was greater than $10,000, then we can respond with an answer of YES. If the profit was not greater than $10,000, then we can respond with an answer of NO.
KEY FACT:
In a yes/no Data Sufficiency question, a statement is sufficient if the information it provides is sufficient for conclusively answering yes to the question or conclusively answering no to the question.
Let’s practice a yes/no Data Sufficiency example question.
Example 3:
Is x divisible by 3?
(1) x is divisible by 5.
(2) x is divisible by 6.
Solution:
We do not have any given information in the question stem.
The question is: Is x divisible by 3? If we can determine that x is always divisible by 3, we can conclusively answer yes. If we can determine that x is never divisible by 3, we can conclusively answer no. If we cannot determine that x is always or never divisible by 3, then we don’t have sufficient information for answering the question.
Let’s evaluate each statement.
Statement (1) Alone:
x is divisible by 5.
Although we know x is divisible by 5, we cannot answer conclusively whether x is also divisible by 3. For example, if x = 5, the answer to the question is NO. However, if x = 15, the answer to the question is YES. Therefore, both of these values for x satisfy statement (1). Thus, statement (1) is NOT SUFFICIENT to answer the question, and as we learned above, we can eliminate answers A and D.
Statement (2) Alone:
x is divisible by 6.
Since x is divisible by 6, x is also divisible by all factors of 6. In particular, since 3 is a factor of 6, x must be divisible by 3. Thus, we can conclusively answer YES to the question. Therefore, statement (2) alone is SUFFICIENT to answer the question.
The answer is B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Let’s consider another example.
Example 4:
Is y a prime number?
(1) y is a solution of the equation x2 – 7x + 12 = 0.
(2) y is a solution of the equation x2 – 9x + 18 = 0.
Solution:
We do not have any given information in the question stem.
The question is: Is y a prime number? If we can determine that y must be a prime number, we can conclusively answer YES. If we can determine that y is sometimes or never a prime number, we can conclusively answer NO. If the answer is yes for certain values of y and no for other values of y, then the statement or statements are insufficient. Let’s evaluate each statement.
Statement (1) Alone:
y is a solution of the equation x2 – 7x + 12 = 0.
Let’s go ahead and find the solutions of the given quadratic equation.
⇒ x2 – 7x + 12 = 0
⇒ (x – 3)(x – 4) = 0
⇒ x = 3 or x = 4
Thus, the solutions of the given quadratic equation are 3 and 4. It follows that y is equal to either 3 or 4.
However, this information is not sufficient to answer the question. If y = 3, y is a prime number, and the answer to the question is YES. If, on the other hand, y = 4, then y is not a prime number, and the answer to the question is NO. Statement (1) alone is not sufficient. We eliminate answer choices A and D.
Statement (2) Alone:
y is a solution of the equation x2 – 9x + 18 = 0.
We will follow the same steps we followed in the analysis of the previous statement and determine the solutions of the given quadratic equation.
⇒ x2 – 9x + 18 = 0
⇒ (x – 3)(x – 6) = 0
⇒ x = 3 or x = 6
We see that the solutions of the given quadratic equation are 3 and 6. So y is equal to either 3 or 6.
However, as with the previous statement, this information is not sufficient to determine an answer to the question. If y = 3, y is a prime number, and the answer to the question is YES. However, if y = 6, y is not a prime number, and the answer to the question is NO. Statement (2) alone is not sufficient. Eliminate answer choice B.
Statements (1) and (2) Together:
Using the first statement, we could conclude that y equals 3 or 4. Using the second statement, we concluded that y equals 3 or 6. These results can only hold at the same time if y = 3. Thus, we can conclusively answer YES to the question. Therefore, statements (1) and (2) together are SUFFICIENT to answer the question.
The answer is C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Now, let’s discuss value Data Sufficiency questions.
The Value Data Sufficiency Question
In a value DS question, a statement is sufficient if it provides information we can use to solve for one unique value.
Let’s check out a few examples of sufficiency in value DS questions:
What is Tom’s current age?
If we can determine a definitive value of Tom’s current age, we have sufficiency.
What is the value of p/q?
If we can determine a definitive value of p/q, we have sufficiency.
What is the tens digit of integer y?
If we can determine a definitive value of the tens digit of y, we have sufficiency.
KEY FACT:
In a value Data Sufficiency question, a statement is sufficient if it enables us to solve for one unique value.
Now, let’s practice some value Data Sufficiency questions.
Example 5:
What is the value of x?
(1) x2 = 1
(2) |x| = 1
Solution:
We need to determine a definitive value of x. Let’s analyze each statement.
Statement (1) Alone:
x2 = 1
We should be careful not to overlook that x = -1 satisfies this equation in addition to x = 1. Without more information, we cannot determine a definitive value for x. Thus, statement (1) alone is not sufficient. Therefore, we eliminate answer choices A and D.
Statement (2) Alone:
|x| = 1
There are two numbers whose absolute value is equal to 1, namely 1 and -1. We know for sure that x is either 1 or -1, but we need more information to choose between the two values. Statement (2) alone is not sufficient. Eliminate answer choice B.
Statements (1) and (2) Together:
Even when we use both statements, it is still possible for x to equal either 1 or -1. We cannot determine a definitive value for x. Statements (1) and (2) together are not sufficient.
Therefore, the answer is E. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question, and additional data specific to the problem are needed.
Example 6:
If x is an integer, what is the value of x?
(1) x < 7
(2) x > 5
Solution:
We know that x is an integer, and we must determine whether we can determine the value of x.
Statement (1) Alone:
x < 7
While we know that x is less than 7, we cannot determine the exact value of x without additional information. There are an infinite number of integers less than 7, and x could equal any of them. Since we cannot determine a unique value for x, statement (1) alone is not sufficient. Eliminate answer choices A and D.
Statement (2) Alone:
x > 5
All we know is that x is greater than 5, but an infinite number of integers are greater than 5. We need more information about x to determine an exact value for x. Statement (2) alone is not sufficient, so we eliminate answer choice B.
Statements (1) and (2) Together:
The question stem tells us that x is an integer. From the first statement, we know that x is less than 7, and from the second one, we know that x is greater than 5. There is only one integer that satisfies both conditions, namely 6. Therefore, assuming both statements, we can conclude with certainty that x must be equal to 6. Therefore, statements (1) and (2) together are sufficient.
The answer is C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Let’s now discuss a key move in answering Data Sufficiency questions.
Don’t Solve; Determine Sufficiency
Hopefully, at his point, you are starting to like DS questions. If not, I have some good news that may change your mind. In Data Sufficiency questions, you do not necessarily need to calculate a value to get an answer.
For example, let’s say you need to determine the fourth root of x. Then, using statement (1), you determine that x is 1,055. The good news is that you know you have enough information to determine the fourth root of x, so you can stop! It’s not necessary to actually calculate the fourth root of 1,055; all you need is to determine that you could calculate it.
TTP PRO TIP:
Calculating an actual numerical answer to a value DS question is unnecessary. Rather, you need to know whether a statement is sufficient to answer the question conclusively.
Let’s practice this concept with a couple of examples.
Example 7:
What is the value of n64?
1) n is a prime number and n is even.
2) n is a positive integer and n2 = 4.
Solution:
We need to determine whether we have enough information to calculate n64. There is no other information in the question stem.
Statement (1) Alone:
n is a prime number and n is even.
The only even prime number is 2, so we know that statement (1) is SUFFICIENT. That’s all we need to say! There is no need to evaluate 264. We simply need to determine whether we have all the information we need to determine the value of 264, and we do. We can eliminate answer choices B, C, and E.
Statement (2) Alone:
n is a positive integer and n2 = 4.
The only two numbers satisfying n2 = 4 are 2 and -2. Also, we know that n is a positive integer, meaning that n cannot be equal to -2. Therefore, we know that n = 2, from which we can conclude that statement (2) is SUFFICIENT.
Again, we should not spend any time trying to evaluate 264 (it is a huge number with 20 digits). We should notice that we have all the information we need to answer the question. Therefore, we eliminate answer choice A.
The answer is D. EACH statement ALONE is sufficient to answer the question asked.
Example 8:
Is y one of the solutions to the equation x3 – 2x2 – 2x + c = 0, where c is a constant?
(1) c = -3
(2) y = 3
Solution:
We need to figure out whether we have enough information to determine whether y is a solution to the given equation. Remember that we don’t have to answer the question; we need to know whether we have sufficient information to do so.
Statement (1) Alone:
c = -3
With the value of c, we know everything about the given equation, but without the value of y, we cannot answer the question. It is possible that y is one of the solutions, or it is possible that y is not among the solutions. Statement (1) alone is not sufficient. Eliminate answer choices A and D.
Statement (2) Alone:
y = 3
Given this statement, we know the value of y. However, without the value of c, we cannot answer the question. Depending on the value of c, y may or may not be a solution to the given equation.
Thus, statement (2) alone is not sufficient. Eliminate answer choice B.
Statements (1) and (2) Together:
From statement (1), we know everything about the equation, and from statement (2), we know the value of y. Using the two statements together, we can answer the question.
Notice that it would be tedious (and unnecessary) to substitute x = 3 in the equation x3 – 2x2 – 2x – 3 = 0, let alone factor this equation and find its solutions. However, we know that if we did, we would either get an equality and answer YES to the question or we would not get an equality, and then we would answer NO. Thus, even though we do not know the actual answer, we know that we have enough information to determine the answer.
The answer is C. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Key Takeaways
Data Sufficiency (DS) questions comprise nearly 50% of the quant questions on the Executive Assessment (EA). Therefore, it is imperative that you become very familiar and comfortable with this question type.
A DS question presents you with a question stem which, at a minimum, asks a question. It may also present some information that can be used to help answer the question. Following the question stem are two statements, each of which must be evaluated. One, both, or neither of the statements, along with the additional information presented in the question stem, may lead to a unique answer to the question.
There are two types of DS questions:
- A “yes/no” DS question asks you to give a definitive yes or no answer, if possible, to the question asked in the question stem.
- A “value” DS question asks you to definitively state, if possible, that a unique value can be obtained from the given information.
Every DS question has the same 5 answer choices, which you should memorize.
Practicing many DS questions will allow you to feel confident in the structure and logic of these questions.
What’s Next?
We have covered a lot in this short article and still have seen only the tip of the iceberg when it comes to Data Sufficiency questions. Now that you feel more comfortable with them, read our article about getting faster at answering quant questions.
