Overview: Data Sufficiency | Data Insights for GMAT PDF Download

Data sufficiency problems on the GMAT can be strange. They're made specifically for this test, so even if you've been studying for a while, they might still feel unfamiliar. The tricky part is you could make a mistake and still end up with one of the answer choices, not realizing you messed up. It's a weird feeling during a test. Let's make understanding data sufficiency less confusing.

What is Data Sufficiency 

Data Sufficiency is not really a math test on the GMAT. It's more about testing how well we make decisions and prioritize when we have too much to do in too little time. It's like your boss giving you a bunch of information and asking, "Is this what Sam needs to decide whether to raise the product price?" Here, you're not doing the actual calculations; you're just figuring out if the data is enough for Sam to do them.

Now, this is a part of Data Insights, not the regular math section. It's about quickly analyzing data to see if it's sufficient for a task, and you can get away with doing less math compared to other types of problems if you know what you're doing.

How does Data Sufficiency Work?

Alright, let's break it down in a simpler way:
First, you get a question like, "How tall is Sam?" Sometimes they add more info, like "If Sam's height is even, how tall is Sam?" If they tell you Sam is either 5 or 6 feet tall, you'd know Sam must be 6 because that's the only even option.

Then, they give you two statements, like:
(1) Sam is 3 years older than Alex.
(2) Alex will be 8 years old in 3 years.

Now, these are just facts. From each fact, can you figure out Sam's height? Statement (1) doesn't help because it doesn't say how old Alex is. Statement (2) doesn't help either as it doesn't say anything about Sam.

Combine both statements. Using both (1) and (2) together, you can figure out Sam's height. So, the answer is (C) in GMAT language.

But here's the trick: you don't need to actually calculate Sam's height. You just need to know you could if you used both statements. And that's the habit for Data Sufficiency: only calculate what you really need to.
There are five possible answers:
(A) Only statement 1 is enough.
(B) Only statement 2 is enough.
(C) Both statements together are enough.
(D) Each statement alone is enough.
(E) Nothing works, even if you use both statements together. Remember it as "Twelve-Ten": 1, 2, Together, Either one, or Nothing.

Value vs. Yes/No on Data Sufficiency

Imagine you're asked, "How old is Oliver?" That's called a value question because you're finding a specific number. If a statement gives you exactly one answer, it's enough. But if a statement gives you no answer or more than one, it's not enough.

Now, think of a question like, "Is Oliver 13 years old?" This is a Yes/No question. If you can definitely say yes or no, that's enough. For example, if Oliver is in his twenties, the answer is a clear no. That's sufficient because you can confidently answer the question.

However, if someone says, "Oliver is either 13 or 22," now you have a "maybe, maybe not" situation. Sometimes it's yes, sometimes it's no. That's not enough to answer the question.

In short, a clear yes or no is enough. But if it's a "maybe, maybe not" situation, it's not enough.

Remember, whether it's a value question or a yes/no question, a clear, definite answer is what makes the information sufficient. If it's uncertain or depends on the situation, it's not enough.

Solved Examples

Q1: Did Rahul solve more questions than Yami in a 2-hour test?
Statement 1: Thrice the number of questions that Rahul solved in the test was greater than 6 less than thrice the number of questions that Yami solved in the test.
Statement 2: Twice the number of questions that Rahul solved in the test was greater than 4 less than twice the number of questions that Yami solved in the test.
Answer Choices:
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.
Solution Explanation: We have to find out whether Rahul solved more questions than Yami.
Say Rahul solved x number of questions, while Yami solved y number of questions in the 2-hour test.
So, we need to determine whether x > y
Statement 1: We are given that "Thrice the number of questions that Rahul solved in the test was greater than 6 less than thrice the number of questions that Yami solved in the test."
⇒ 3x > 3y − 6
⇒ x > y − 2
We cannot determine whether x>y, since x is greater than a quantity y, which is reduced by a certain amount, 2.
Let us take an example.
Say y = 10, thus x > 10 − 2 ⇒ x > 8.
If x = 9, then x > y and the answer is No. However, if x = 11, then x > y and the answer is Yes. There is no unique answer, so Statement 1 alone is insufficient.
Statement 2: We are given that Twice the number of questions that Rahul solved in the test was greater than 4 less than twice the number of questions that Yami solved in the test.
⇒ 2x > 2y − 4
⇒ x > y − 2 ⇒ x
This is the same inequality that we got in Statement 1, making it insufficient.
Statement 1 & 2: Since each statement renders the same inequality, even combining both the statements cannot help. Finally, even combingin Statement 1 and 2 is insufficient.
Conclusion: You may have deduced a wrong conclusion with the inequality x > y − 2.
We see that x is greater than a number y minus 2; thus, x may or may not be greater than y.
Had the situation been x > y + 2, then it's for certain that x > y; since x is greater than a number (y + 2), then x must be greater than a relatively smaller number y.

Q2: How many ewes (female sheep) in a flock of 50 sheep are black?
Statement 1: There are 10 rams (male sheep) in the flock.
Statement 2: Forty percent of the animals are black.
A. statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question
B. statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
C. both statements taken together are sufficient to answer the question, but neither statement alone is sufficient
D. each statement alone is sufficient
E. statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
Correct Answer: E
Explanation:
From (1) we know the ratio of male to female sheep, but nothing about the color distribution. So the answer cannot be A or D. From (2) we know that forty percent of the animals are black but nothing about whether they are male of female. So the answer cannot be B. Even putting the information together does not help because there is no way to tell what fraction of the female sheep are black. And so C cannot be correct, and the answer is E.