Easy GRE Data Sufficiency Questions Practice Questions

Concept Explanation

GRE Data Sufficiency questions are a specific format of quantitative reasoning problems that ask you to determine if the provided information is enough to answer a given question. Unlike standard multiple-choice math problems where you must calculate a final numerical value, these tasks require you to evaluate two distinct statements and decide if either, both, or neither provide a definitive answer. This format tests logical reasoning and your ability to identify the minimum necessary data to solve a problem. It is a staple of graduate-level entrance exams, similar to those found in the GRE Quantitative Reasoning section. To succeed, you must understand the five standard answer choices, which remain the same for every question:

• (A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
• (B) Statement (2) ALONE is sufficient, but statement (1) alone 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 goal is to stop calculating as soon as you know a unique answer can be found. For more foundational practice, you can explore Free GRE Practice Questions Practice Questions with Answers to build your confidence. Utilizing an AI MasterPlan can also help organize your study schedule to cover these logic-heavy questions effectively.

Solved Examples

Reviewing these worked examples will help you internalize the process of elimination used in Data Sufficiency.

1. Question: What is the value of $x$?
   Statement (1): $2x + 4 = 10$
   Statement (2): $x^2 = 9$
   Solution:
   1. Analyze Statement (1): Solving $2x + 4 = 10$ gives $2x = 6$, so $x = 3$. This provides a single, unique value. Statement (1) is sufficient.
   2. Analyze Statement (2): Solving $x^2 = 9$ gives $x = 3$ or $x = -3$. Because there are two possible values, we do not have a unique answer. Statement (2) is not sufficient.
   3. Conclusion: Statement (1) alone is sufficient. Answer: (A).
2. Question: Is integer $n$ even?
   Statement (1): $n + 1$ is odd.
   Statement (2): $n/2$ is an integer.
   Solution:
   1. Analyze Statement (1): If $n + 1$ is odd, then $n$ must be even (Even + Odd = Odd). This answers the question with a definitive "Yes." Statement (1) is sufficient.
   2. Analyze Statement (2): If $n/2$ is an integer, then $n$ is divisible by 2, which is the definition of an even number. This also answers the question with a definitive "Yes." Statement (2) is sufficient.
   3. Conclusion: Each statement alone is sufficient. Answer: (D).
3. Question: What is the area of rectangle $R$?
   Statement (1): The perimeter of $R$ is 20.
   Statement (2): The length of $R$ is 6.
   Solution:
   1. Analyze Statement (1): Many rectangles have a perimeter of 20 (e.g., 5x5 area=25, or 6x4 area=24). Not sufficient.
   2. Analyze Statement (2): Knowing only the length (6) tells us nothing about the width. Not sufficient.
   3. Combine Statements: If perimeter is 20 and length is 6, then $2(6) + 2w = 20$. This solves to $12 + 2w = 20$, so $2w = 8$, meaning $w = 4$. Area = $6 \times 4 = 24$. Combined, they are sufficient.
   4. Conclusion: Both statements together are sufficient. Answer: (C).

Practice Questions

Test your skills with these Easy GRE Data Sufficiency Questions Practice Questions. Remember to evaluate each statement independently first.

1. What is the value of $y$?
(1) $3y = 12$
(2) $y > 0$

2. Is $a > b$?
(1) $a = b + 2$
(2) $a + b = 10$

3. A shirt costs $25. If the price is reduced by $x$ percent, what is the new price?
(1) $x = 20$
(2) The reduction in price is $5.

4. What is the average (arithmetic mean) of $m$ and $n$?
(1) $m + n = 14$
(2) $m = 6$

5. Is the product $xy$ positive?
(1) $x < 0$
(2) $y < 0$

6. What is the radius of circle $C$?
(1) The circumference of $C$ is $10\pi$.
(2) The area of $C$ is $25\pi$.

7. If $z$ is an integer, is $z$ a multiple of 6?
(1) $z$ is a multiple of 3.
(2) $z$ is a multiple of 2.

8. What is the value of $x + y$?
(1) $2x + 2y = 20$
(2) $x = 4$

9. Is triangle $T$ equilateral?
(1) All three angles of $T$ are equal.
(2) The perimeter of $T$ is 15.

10. How many students are in the class?
(1) There are 12 boys in the class.
(2) The ratio of boys to girls is 3:4.

Answers & Explanations

1. Answer: (A). Statement (1) allows us to solve for $y$ directly: $y = 4$. Statement (2) only tells us $y$ is positive, which could be any number. Thus, (1) alone is sufficient.
2. Answer: (A). Statement (1) tells us $a$ is 2 more than $b$, so $a$ must be greater than $b$. Statement (2) tells us the sum is 10, but $a$ could be 7 and $b$ could be 3, or vice versa. Thus, (1) alone is sufficient.
3. Answer: (D). Statement (1) gives the specific percentage, allowing us to calculate the discount and new price. Statement (2) gives the dollar amount of the discount, which also allows us to find the new price ($25 - $5 = $20). Each alone is sufficient.
4. Answer: (A). The average of two numbers is $\frac{m+n}{2}$. Statement (1) gives the sum $m+n = 14$, so the average is 7. Statement (2) only gives one variable, which is not enough to find the sum.
5. Answer: (C). Statement (1) tells us $x$ is negative, but we don't know $y$. Statement (2) tells us $y$ is negative, but we don't know $x$. Together, we know both are negative, and a negative times a negative is a positive. Combined, they are sufficient.
6. Answer: (D). Circumference is $2\pi r$, so $10\pi = 2\pi r$ gives $r = 5$. Area is $\pi r^2$, so $25\pi = \pi r^2$ also gives $r = 5$. Each alone is sufficient.
7. Answer: (C). Statement (1) includes 3, 6, 9... (not all are multiples of 6). Statement (2) includes 2, 4, 6... (not all are multiples of 6). Together, the number must be a multiple of both 2 and 3, which means it must be a multiple of 6.
8. Answer: (A). Dividing both sides of the equation in Statement (1) by 2 gives $x + y = 10$. This is the exact value we need. Statement (2) only gives one variable.
9. Answer: (A). If all angles are equal, the triangle must be equilateral. Statement (2) gives the perimeter, but without knowing the side relationships, the triangle could be isosceles or scalene.
10. Answer: (C). Statement (1) only gives the number of boys. Statement (2) only gives the ratio. Combined, if there are 12 boys and the ratio is 3:4, then $3x = 12$, so $x = 4$. There are $4(4) = 16$ girls, totaling 28 students.

1. If a question asks for the value of "x", and Statement (1) results in x = 5 or x = -5, is Statement (1) sufficient?

• AYes
• BNo
• COnly if x is a distance
• DOnly if Statement (2) is also insufficient

Frequently Asked Questions

What is the main goal of GRE Data Sufficiency?

The main goal is to determine if you have enough information to solve a problem, rather than finding the actual numerical solution. This tests your efficiency and quantitative logic under timed conditions.

Do I need to calculate the final answer in Data Sufficiency?

No, you should stop calculating as soon as you are certain a unique answer exists. For more tips on saving time, check out GRE Practice Questions with Explanations Practice Questions with Answers.

Can the two statements in a GRE question contradict each other?

On the actual GRE, the two statements will never provide contradictory information. If Statement (1) says $x=5$, Statement (2) will not say $x=10$; they will always be mathematically consistent.

Is Data Sufficiency harder than standard multiple-choice?

It is often considered trickier because of the logical traps, but it can be faster since you don't always need to complete complex calculations. Practicing with an AI Question Generator can help you get used to the unique logic required.

What is the most common mistake in Data Sufficiency?

The most common mistake is carrying over information from Statement (1) when evaluating Statement (2). You must clear your mind and look at the second statement in total isolation first.

How does the scoring work for these questions?

Data Sufficiency questions are scored the same as other quantitative reasoning questions. To improve your performance, you might try a Retrieval Challenge to sharpen your memory of math rules and formulas.