GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #571 : Geometry

The graph of the equation

$(x-A)^{2} + (y-A)^{2} = B$ ,

where B > 0 , is a circle. In which quadrant is the center of the circle located?

Statement 1: A < 0

Statement 2: A + B = 0

Possible Answers:

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.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

The center of the circle of the equation $(x-A)^{2} + (y-A)^{2} = B$ is the point (A,A) .

If Statement 2 is assumed, then A = -B ; since is known to be positive, is negative, which is the same as Statement 1.

From either statement, we know to be negative, and, subsequently, that both coordinates of the center (A,A) are negative, putting it in Quadrant III.

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Example Question #2 : Dsq: Calculating The Equation Of A Circle

Find the equation of circle T.

I) Circle T is centered at the point (5,5) .

II) Circle T touches the axis at the point (7,0) .

Possible Answers:

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.

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.

Neither statement is sufficient to solve the question. More information is needed.

Correct answer:

Both statements taken together are sufficient to solve the question.

Explanation:

The equation of a circle is given by:

$\small r^2=(x-h)^2+(y-k)^2$

Where r is the radius and (h,k) are the center of the circle

I) gives us (h,k)

By using II) and distance formula, we can find r

Thus, both statements are needed!

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Example Question #1 : Circles

Write the equation for circle , a circle in the standard x-y plane.

I) is centered at (7,7) .

II) The line y=0 is tangent to the circle at the point (7,0) .

Possible Answers:

Either statement alone is sufficient to answer the question.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Both statements together are needed to answer the question.

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Correct answer:

Both statements together are needed to answer the question.

Explanation:

To write the equation of a circle we need the coordinates of its center and the length of its radius.

I) Gives us the center.

II) Tells us that the circle just touches the x-axis at the point (7,0), which is exactly 7 units below our center. This makes our radius 7.

Thus, we need both statements.

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Example Question #5 : Dsq: Calculating The Equation Of A Circle

Consider Circle L.

I) The radius of Circle L is twice the value of the third prime number when counting the prime numbers and increasing after zero.

II) The x-coordinate of Circle L is four times the y-coordinate of L. The y-coordinate is equal to the radius.

Find the equation of Circle L.

Possible Answers:

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Either statement is sufficient to answer the question.

Both statements are needed to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Correct answer:

Both statements are needed to answer the question.

Explanation:

The equation of a circle is as follows:

(x-h)^2+(y-k)^2=r^2

Where (h,k) is the center of the circle and is the radius.

Statement I gives us the radius.

Statement II gives us clues to find (h,k) .

So, by using both, we can find the equation. Both are needed.

Recap:

Consider circle L.

I) The radius of L is twice the value of the third prime number.

II) The x-coordinate of L is four times the y-coordinate of L. The y-coordinate is equal to the radius.

Find the equation of circle L.

Using Statement I, the third prime number is 5, so our radius is 10.

Using Statement II, k=10 , so must be 40.

Putting it all into the equation of a circle:

(x-40)^2+(y-10)^2=100

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Example Question #2 : Dsq: Calculating The Equation Of A Circle

Find the equation of Circle X.

I) The x-coordinate of Circle X's center is twice the y-coordinate of Circle X's center.

II) Circle X has a radius of 16 units.

Possible Answers:

Both statements are needed to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

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.

Either statement is sufficient to answer the question.

Correct answer:

Neither statement is sufficient to answer the question. More information is needed.

Explanation:

The equation of a circle is as follows:

(x-h)^2+(y-k)^2=r^2

Where (h,k) is the center of the circle and is the radius.

Statement I tells us how to relate and , but doesn't tell us how to find either one.

Statement II gives us .

We almost have enough information here, but we can't tell for certain where the circle's center is, so more information is needed.

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Example Question #7 : Dsq: Calculating The Equation Of A Circle

Circle T is plotted in Euclidean space. Find its equation.

I) The diameter of Circle T is twice the square of the y-coordinate of its center.

II) Circle T is centered at the point (5,3) .

Possible Answers:

Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.

Both statements are needed to answer the question.

Either statement is sufficient to answer the question.

Neither statement is sufficient to answer the question. More information is needed.

Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.

Correct answer:

Both statements are needed to answer the question.

Explanation:

The equation of a circle is as follows:

(x-h)^2+(y-k)^2=r^2

Where (h,k) is the center of the circle and is the radius.

Statement I gives us a clue to find the diameter, which can be used to find the radius.

Statement II gives us the center of the circle.

Use Statement II and Statement I to find the radius, then plug it all into the equation to find the equation of Circle T.

Recap:

Circle T is plotted in Euclidean space. Find its equation.

I) The diameter of circle T is twice the square of the y-coordinate of its center.

II) Circle T is centered at the point (5,3) .

Statement II gives us (h,k) .

Use Statement I and Statement II to write the following equation:

$d=2\cdot 3^2=2 \cdot 9=18$

So, if the diameter is 18, the radius must be 9. This makes our equation of the circle:

(x-5)^2+(y-3)^2=81

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Example Question #691 : Data Sufficiency Questions

What is the area of the circle $(x+5)^{2}+(y-2)^{2}=32?$

Possible Answers:

$16\pi^{2}$

$32\pi$

$32\pi^{2}$

$16\pi$

$\sqrt{32}\pi$

Correct answer:

$32\pi$

Explanation:

Circle equations are written in the form $(x-h)^{2}+(y-k)^2=r^{2},$ where (h,k) are the coordinates for the center of the circle. When dealing with the area of a circle, the formula is $\pi r^2.$ Since, the circle equation already gives us the squared radius, we only need to multiply that number by $\pi.$ Therefore, the area is $32\pi.$

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Example Question #571 : Geometry

What is the -intercept of a line with equation Ax + By = 15?

1) A = 6

2) B = 3

Possible Answers:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are NOT sufficient to answer the question.

EITHER Statement 1 or Statement 2 ALONE is sufficient to answer the question.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.

Explanation:

The -intercept is the point at which x = 0 . To find the -coordinate of the -intercept, just substitute 0 for :

Ax + By = 15

$A \cdot 0 + By = 15$

By = 15

$y = \frac{15}{B}$

Therefore, you need only know ; knowing is neither necessary nor helpful.

If you are given that since B = 3 . the -intercept is easily determined to be $\left (0, 5 \right )$ .

The answer is that Statement 2 alone is sufficient, but not Statement 1 alone.

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Example Question #581 : Geometry

Give the -intercept of the graph of the equation $f(x) = x^{2}+Ax+B$ .

Statement 1: A = 8

Statement 2: B = 10

Possible Answers:

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.

Correct answer:

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Explanation:

The -intercept of the graph of an equation is the point at which x = 0 , so we evaluate f(0) :

$f(x) = x^{2}+Ax+B$

$f(0) = 0^{2}+A\cdot 0+B$

f(0) =B

The -intercept is simply the point (0,B) , so knowing is necessary, and knowing is neither necessary nor helpful.

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Example Question #582 : Geometry

Find the -intercept and y-intercept of the following straight line.

1. The line has a slope of 0.6.

2. The line passes through point (10,2)

Possible Answers:

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

Statement (1) ALONE is sufficient, but statement (2) alone is not 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.

EACH statement ALONE is sufficient to answer the question asked.

Correct answer:

BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.

Explanation:

To find the - and y-intercepets, we need both statements of information.

Statement 1 is not enough information because we don't have a reference point for the slope. A slope by itself is not enough to define the line. There are an infinite amount of lines with a slope of 0.6.

Statement 2 is not enough information by itself since it only tells us about 1 point on the line. Again, there are an infinite number of lines that pass through the point (10,2).

Only by using both statements can we find the - and y-intercepts. Solving, we see the line is actually

y=0.6x-4

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GMAT Math : GMAT Quantitative Reasoning

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #571 : Geometry

Example Question #2 : Dsq: Calculating The Equation Of A Circle

Example Question #1 : Circles

Example Question #5 : Dsq: Calculating The Equation Of A Circle

Example Question #2 : Dsq: Calculating The Equation Of A Circle

Example Question #7 : Dsq: Calculating The Equation Of A Circle

Example Question #691 : Data Sufficiency Questions

Example Question #571 : Geometry

Example Question #581 : Geometry

Example Question #582 : Geometry

All GMAT Math Resources

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