GMAT Math : GMAT Quantitative Reasoning
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Example Questions
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 #2271 : Gmat Quantitative Reasoning
Find the length of the diagonal of square G.
I) The area of G is 
II) The side length of G is 
Both statements taken together are sufficient to solve the problem.
Each statement alone is enough to solve the question.
Statement 2 is sufficient to solve the question, but statement 1 is not sufficient to solve the question.
Statement 1 is sufficient to solve the question, but statement 2 is not sufficient to solve the question.
Neither statement is sufficient to solve the question. More information is needed.
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 #2 : Dsq: Calculating The Length Of The Diagonal Of A Square
The circle with center 
(1) The area of the circle is 
(2) The side of the square is 
Statement 2 alone is sufficient.
Each statement alone is sufficient.
Statements 1 and 2 together are not sufficient.
Statement 1 alone is sufficient.
Both statements together are 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.
Example Question #161 : Data Sufficiency Questions
On your college campus there is a square grassy area where people like to hangout and enjoy the sun. While walking with some friends, you decide to take the shortest distance to the corner of the square opposite from where you are. Find the distance you traveled.
I) The perimeter of the square is 
II) The square covers an area of 
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Neither statement is sufficient to answer the question. More information is needed.
Both statements are needed to answer the question.
Either statement is sufficient to answer the question.
Either statement is sufficient to answer the question.
We are asked to find the length of a diagonal of a square.
We can do this if we have the side length. We can find side length from either perimeter or area.
From Statement I)
In this case, our side length is 15 meters.
We can use this and Pythagorean Theorem or 45/45/90 triangles to find our diagonal.
From Statement II)
From here, we can plug the side length into the Pythagorean Theorem like before and solve for the diagonal.
Therefore, either statement alone is sufficient to answer the question.
Example Question #4 : Quadrilaterals
Find the length of the diagonal of square A if the diagonal of square B is 
- The perimeter of square B is
- The area of square A is
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Each statement alone is sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statement 1: The information provided would only be useful if the ratio of square A to square B was known.
Statement 2: We need the length of the square's side to find the length of the diagonal and we can use the area to solve for the length of the side.
Now we can find the diagonal:
Example Question #5 : Dsq: Calculating The Length Of The Diagonal Of A Square
What is the length of the diagonal of the square?
- The area of the square is
.
- The perimeter is
.
Each statement alone is sufficient to answer the question.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Each statement alone is sufficient to answer the question.
The length of the diagonal of a square is given by 
Statement 1:
Statement 2:
Both statements provide us with the length of the square's side.
Example Question #5 : Quadrilaterals
The diagonal bracing of a square pallet measures 
To solve this problem, we must recognize that the diagonal bisector creates identical 45˚ - 45˚ - 90˚ right triangles. This means that, if the sides of the square are 
If 
Example Question #2271 : Gmat Quantitative Reasoning
Is Rectangle 
Statement 1:
Statement 2:
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 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.
EITHER statement ALONE is sufficient to answer the question.
A rectangle, by definition, is a parallelogram. Statement 1 asserts that the diagonals of this parallelogram are perpendicular. Statement 2 asserts that adjacent sides of the parallelogram are congruent, so, since opposite sides are also congruent, this makes all four sides congruent. From either statement alone, it can be deduced that Rectangle 
Example Question #2 : Squares
Find the side length of square R.
I) The area of square R is 
II) The perimeter of square R is 
Each statement alone is enough to solve the question.
Both statements taken together are sufficient to solve the question.
Statement 2 is sufficient to solve the question, but statement 1 is not sufficient to solve the question.
Neither statement is sufficient to solve the question. More information is needed.
Statement 1 is sufficient to solve the question, but statement 2 is not sufficient to solve the question.
Each statement alone is enough to solve the question.
Consider the following equations:
Where a is area, p is perimeter, and s is side length
We can find the side length with either our area or our perimeter.
Thus, we only need one statment or the other.
Example Question #2272 : Gmat Quantitative Reasoning
What is the length of the side of square 
(1)
(2)
Statements 1 and 2 together are not sufficient
Statement 2 alone is sufficient
Statement 1 alone is sufficient
Each statement alone is sufficient
Both statements together are sufficient
Statement 1 alone is sufficient
Since ABCD is a square, we just need to know the length of the diagonale to find the length of the side. BE is half the diagonal, therefore knowing its length would help us find the length of the sides.
Statement 1 tells us the length of BE, therefore, with the formula 
Statement 2 tells us that triangle AEB is isoceles, but it is something we could already have known from the beginning since we are told that E is the midpoint of the diagonal.
Therefore, statement 1 alone is sufficient.
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