GRE Data Sufficiency Questions Practice Questions with Answers

Concept Explanation

GRE Data Sufficiency questions are a specific quantitative reasoning format designed to evaluate your ability to determine if provided information is adequate to solve a problem without requiring you to actually calculate the final numerical result. Unlike standard multiple-choice math problems where the goal is to find a specific value, these questions ask you to analyze two statements and decide which of them—if any—provides enough data to answer the question. This format tests logical reasoning, mathematical properties, and efficiency. To succeed, you must understand the five standard answer choices used in this format: Statement 1 alone is sufficient; Statement 2 alone is sufficient; Both statements together are sufficient; Each statement alone is sufficient; or Statements 1 and 2 together are still not sufficient. Utilizing GRE Prep resources helps students recognize that the objective is to prove sufficiency or insufficiency through counter-examples or algebraic manipulation rather than long-form computation.

Solved Examples

1. Example 1: Number Properties
   Is $n$ an even integer?
   (1) $3n + 2$ is an even integer.
   (2) $n^2$ is an even integer.
   Solution:
   1. Analyze Statement 1: If $3n + 2$ is even, then $3n$ must be even (since even - even = even). For $3n$ to be even, $n$ must be even. Statement 1 is sufficient.
   2. Analyze Statement 2: If $n^2$ is even, then its square root $n$ must also be even because the square of an odd number is always odd. Statement 2 is sufficient.
   3. Conclusion: Each statement alone is sufficient.
2. Example 2: Geometry
   What is the area of rectangle $ABCD$?
   (1) The perimeter of rectangle $ABCD$ is 20.
   (2) The diagonal of rectangle $ABCD$ is $\sqrt{52}$.
   Solution:
   1. Analyze Statement 1: $2(l + w) = 20$, so $l + w = 10$. Multiple pairs of $l$ and $w$ (like 6,4 or 7,3) give different areas. Insufficient.
   2. Analyze Statement 2: $l^2 + w^2 = 52$. Again, multiple pairs (like 6,4 or 4,6) could work, but without another constraint, we cannot find the product $l \times w$. Insufficient.
   3. Combine Statements: We have $l + w = 10$ and $l^2 + w^2 = 52$. Since $(l+w)^2 = l^2 + 2lw + w^2$, we can substitute: $100 = 52 + 2lw$. Thus $48 = 2lw$, and $lw = 24$. Sufficient.
   4. Conclusion: Both statements together are sufficient.
3. Example 3: Rates
   How long did it take John to drive 150 miles?
   (1) John drove at an average speed of 50 miles per hour for the first 100 miles.
   (2) John’s average speed for the entire trip was 60 miles per hour.
   Solution:
   1. Analyze Statement 1: We know the time for the first 100 miles (2 hours), but we don't know the speed for the final 50 miles. Insufficient.
   2. Analyze Statement 2: Speed = Distance / Time. So, $60 = 150 / t$. Solving for $t$ gives $2.5$ hours. Sufficient.
   3. Conclusion: Statement 2 alone is sufficient.

Practice Questions

1. Is $x > y$?
(1) $x^2 > y^2$
(2) $x - y > 0$

2. What is the value of $z$?
(1) $2z + 4y = 12$
(2) $y = 3 - 0.5z$

3. If $a$ and $b$ are integers, is $ab$ odd?
(1) $a + b$ is even.
(2) $2a + b$ is odd.

4. A jar contains only red and blue marbles. What is the probability of picking a red marble?
(1) The ratio of red marbles to blue marbles is 3:2.
(2) There are 30 red marbles in the jar.

5. Is the integer $k$ divisible by 6?
(1) $k$ is divisible by 3.
(2) $k$ is divisible by 2.

6. What is the value of $x + y$?
(1) $x^2 - y^2 = 24$
(2) $x - y = 4$

7. Is triangle $ABC$ equilateral?
(1) Angle $A = 60^\circ$.
(2) Side $AB = Side BC$.

8. What is the average (arithmetic mean) of $a, b,$ and $c$?
(1) $a + b = 14$
(2) $c = 7$

Answers & Explanations

1. Answer: Statement 2 alone is sufficient.
   Statement 1 is insufficient because if $x = -3$ and $y = 2$, $x^2 > y^2$ but $x < y$. Statement 2 is $x - y > 0$, which simplifies directly to $x > y$.
2. Answer: Statements 1 and 2 together are still not sufficient.
   Statement 1 is an equation with two variables. Statement 2 is actually the same equation rewritten: $y = 3 - 0.5z \rightarrow 2y = 6 - z \rightarrow z + 2y = 6$. Since both statements represent the same line, we have infinite solutions for $z$.
3. Answer: Statement 2 alone is sufficient.
   For $ab$ to be odd, both $a$ and $b$ must be odd. Statement 1: $a+b$ is even means both are odd OR both are even. Insufficient. Statement 2: $2a$ is always even. For $2a + b$ to be odd, $b$ must be odd. However, we don't know if $a$ is odd. Wait—re-evaluating Statement 2: If $b$ is odd, but $a$ is even, $ab$ is even. If both are odd, $ab$ is odd. Both together: If $b$ is odd (from St. 2) and $a+b$ is even (from St. 1), then $a$ must be odd. Thus $ab$ is odd. Correct answer: Both together are sufficient.
4. Answer: Statement 1 alone is sufficient.
   Probability of red is $\frac{ \text{Red}}{ \text{Total}}$. If the ratio is 3:2, probability is $\frac{3}{3+2} = 0.6$. Statement 2 only gives the count of red, not the total.
5. Answer: Both statements together are sufficient.
   Divisibility by 6 requires divisibility by both 2 and 3. Statement 1 only covers 3; Statement 2 only covers 2. Together they satisfy the rule for 6.
6. Answer: Both statements together are sufficient.
   Factor Statement 1: $(x - y)(x + y) = 24$. Substitute Statement 2: $4(x + y) = 24$. Therefore $x + y = 6$.
7. Answer: Both statements together are sufficient.
   Statement 1: Only one angle is 60. Statement 2: Two sides are equal (isosceles). Together, an isosceles triangle with one 60-degree angle must have all angles equal to 60 degrees.
8. Answer: Both statements together are sufficient.
   Mean is $\frac{a+b+c}{3}$. Statement 1 gives $a+b$, Statement 2 gives $c$. Together, $\frac{14+7}{3} = 7$.

To master these logic-heavy problems, many students use an AI Question Generator to drill specific quantitative topics like geometry or algebra. You can also simulate the full test experience with an AI Exam Simulator to adapt to the pressure of timed sections.

1. If a question asks for the value of x, and Statement 1 allows x to be either 5 or -5, is Statement 1 sufficient?

• AYes
• BNo
• COnly if x is a distance
• DOnly if Statement 2 is the same

Frequently Asked Questions

Do I need to solve for the exact number in a Data Sufficiency question?

No, the goal is only to determine if you have enough information to find the number, not to perform the actual calculation. This saves time and prevents calculation errors.

What is the most common mistake on these questions?

The most common error is carrying over information from Statement 1 when evaluating Statement 2. Each statement must be evaluated in total isolation before considering them together.

Can the two statements contradict each other?

According to official ETS guidelines, the two statements in a Data Sufficiency question will never provide contradictory information. If they seem to contradict, you have likely made a calculation error.

How should I guess if I am stuck?

If one statement is very complex and the other is simple, and the simple one is clearly insufficient, often the complex one is sufficient or they work together. Use the Retrieval Challenge tool to practice common math properties so you can spot these patterns faster.

Is Data Sufficiency harder than standard Multiple Choice?

Many students find it harder because it requires a higher level of abstract logic and a deep understanding of mathematical sufficiency. However, it can be faster to solve once you master the process of elimination.