Data Sufficiency: Practice Questions & Notes

Data Sufficiency questions test your ability to determine whether the provided information (data) is enough to answer a question decisively. The goal is not to solve the problem fully, but to decide if you have enough information to do so.

In these problems, you are given:

A question or problem statement
Two or more statements or data points

Your task is to analyze whether the information from the statements is sufficient to answer the question.

What is Data Sufficiency?

It is about evaluating the adequacy of information rather than finding the answer itself.
You must decide if the data provided alone or combined can answer the question with certainty.
The question remains the same; only the data provided changes.

Key Concepts

Term	Meaning
Sufficient	Enough information to answer the question uniquely and definitely
Insufficient	Not enough information; cannot answer uniquely
Independent Statements	Statements that can be considered separately
Combined Statements	Statements considered together for sufficiency

Approach to Solve Data Sufficiency Questions

Understand the question carefully: Know exactly what is being asked.
Evaluate Statement 1 alone: Is it sufficient to answer the question?
Evaluate Statement 2 alone: Is it sufficient to answer the question?
Evaluate both statements together: Are they sufficient when combined?
Choose the correct option based on sufficiency, not on actually solving the problem.

Standard Options in Data Sufficiency

Typically, the answer choices are:

(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 alone is sufficient.
(D) Each statement alone is sufficient.
(E) Statements together are not sufficient.

Tips and Common Mistakes

Do not try to solve the problem fully unless needed; focus on sufficiency.
Sometimes a statement seems useful but is ambiguous or incomplete.
Avoid assumptions beyond what the statements provide.
Remember, sufficiency means one unique answer only.
Check for cases where data could give multiple answers — that means insufficient.

Examples

Example 1

Question: What is the value of $x$ ?

Statements:

$x + y = 10$
$y = 4$

Analysis:

Statement 1 alone: $x + y = 10$ — no unique $x$ because $y$ is unknown. Insufficient.
Statement 2 alone: $y = 4$ — no info about $x$ . Insufficient.
Both together: Using $y=4$ , $x + 4 = 10 \Rightarrow x = 6$ . Sufficient.

Answer: (C)

Example 2

Question: Is $x$ greater than 10?

Statements:

$x > 5$
$x < 15$

Analysis:

Statement 1 alone: $x > 5$ — $x$ can be greater or less than 10. Insufficient.
Statement 2 alone: $x < 15$ — $x$ can be greater or less than 10. Insufficient.
Both statements together: $5 < x < 15$ — $x$ can be less than or greater than 10. Insufficient.

Answer: (E)

Example 3

Question: Is the number $n$ even?

Statements:

$n$ is divisible by 4.
$n$ is divisible by 2.

Analysis:

Statement 1 alone: Divisible by 4 → must be even. Sufficient.
Statement 2 alone: Divisible by 2 → even number. Sufficient.
Both statements also sufficient individually.

Answer: (D)