GMAT Math : Data-Sufficiency Questions
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Example Questions
Example Question #2 : Dsq: Understanding Intersecting Lines
Lines p and q are parallel. What's the value of x?
(1)
(2)
EACH statement ALONE is sufficient to answer the question asked.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
Although the question itself tells us that lines p and q are parallel, the iinformation in statement 1 is insufficient to determine a definitive value for either y or z.
With the information from the question that lines p and q are parallel, and the added information from statement 2 that 
Example Question #1 : Dsq: Calculating The Angle Of An Intersection
Note: Figure NOT drawn to scale.
Refer to the above diagram. Evaluate 
Statement 1:
Statement 2:
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 alone gives insufficient information. It only gives a relationship between 
Statement 2 alone gives insufficient information; 
Now assume both statements are true. Again, from Statement 1, 
Therefore, both statements together are sufficient to answer the question.
Example Question #2 : Dsq: Calculating The Angle Of An Intersection
Note: Figure NOT drawn to scale.
Refer to the above diagram. Evaluate 
Statement 1:
Statement 2:
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Assume Statement 1 alone. From the diagram, the three angles of measure 
From Statement 1,
so by the subtraction property of equality,
Assume Statement 2 alone. 
Example Question #3 : Dsq: Calculating The Angle Of An Intersection
Note: Figure NOT drawn to scale. Do not assume lines are parallel or perpendicular simply by appearance.
Evaluate 
Statement 1:
Statement 2:
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Assume Statement 1 alone. 
Assume Statement 2 alone. 
Example Question #4 : Dsq: Calculating The Angle Of An Intersection
Note: Figure NOT drawn to scale.
Refer to the above diagram. Evaluate 
Statement 1:
Statement 2:
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Assume Statement 1 alone. 
Assume Statement 2 alone. Again, 
Since the angles of measures 
Example Question #1 : Dsq: Calculating The Angle Of An Intersection
Note: Figure NOT drawn to scale.
Refer to the above diagram. Evaluate 
Statement 1:
Statement 2:
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
We show that both statements together give insufficient information. Assume both statements together. Consider the following two cases:
Case 1:
Since the angles of measures 
The angle of measure 
From Statement 1,
Since 
These values are therefore consistent with the diagram and with both statements.
Case 2:
We can find the values of the other variables as before:
Again, all values are consistent with the diagram and both statements.
Since at least two different values of 
Example Question #6 : Dsq: Calculating The Angle Of An Intersection
Note: Figure NOT drawn to scale. Do not assume lines are parallel or perpendicular simply by appearance.
Evaluate 
Statement 1:
Statement 2:
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 alone gives us that 
Assume both statements are true. From Statement 1, 
Example Question #5 : Dsq: Calculating The Angle Of An Intersection
Note: Figure NOT drawn to scale.
Give the measure of 
Statement 1: 
Statement 2: 
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
If two chords of a circle intersect inside it, then the measure of an angle formed is equal to the arithmetic mean of the measures of arc it intercepts and the arc its vertical angle intercepts. In other words, in this diagram,
Both arc measures are needed to find the measure of the angle. Neither statement alone give both; the two together do.
Example Question #1 : Squares
Find the length of the diagonal of square G.
I) The area of G is 
II) The side length of G is 
Statement 1 is sufficient to solve the question, but statement 2 is not sufficient to solve the question.
Both statements taken together are sufficient to solve the problem.
Neither statement is sufficient to solve the question. More information is needed.
Statement 2 is sufficient to solve the question, but statement 1 is not sufficient to solve the question.
Each statement alone is enough to solve the question.
Each statement alone is enough to solve the question.
We can use the side length and the Pythagorean Theorem to find the diagonal of a square.
We can find side length from area, so we could solve this with either I or II.
Example Question #1 : Squares
The circle with center 
(1) The area of the circle is 
(2) The side of the square is 
Statement 1 alone is sufficient.
Statements 1 and 2 together are not sufficient.
Both statements together are sufficient.
Statement 2 alone is sufficient.
Each statement alone is sufficient.
Each statement alone is sufficient.
The diagonal of the square can be calculated as long as we have any information about the lengths or area of the circle or of the square.
Statement 1, by giving us the area of the circle, allows us to find the radius of the circle, which is half the length of the side. Therefore statement 1 alone is sufficient.
Statement 2, by telling us the length of a side of the square is also sufficient, and would allow us to calculate the length of the diagonal.
Therefore, each statement alone is sufficient.
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