GMAT Math : Data-Sufficiency Questions

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Example Questions

Example Question #2 : Dsq: Calculating The Area Of A Right Triangle

Find the area of the right triangle.

Statement 1): The hypotenuse is $2\sqrt2$ .

Statement 2): Both legs have a side length of .

Possible Answers:

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

EACH statement ALONE is sufficient.

BOTH statements TOGETHER are NOT sufficient, and additional data is needed to answer the question.

Correct answer:

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

Explanation:

Statement 1) only provides the hypotenuse of the triangle, but it does not imply that both legs of the right triangle are congruent sides. Of the three interior angles, only the right angle is known with the other 2 unknown interior angles.

Statement 1) does not have enough information to solve for the area of the triangle.

Statement 2) provides the lengths of both legs. The formula $A=\frac{bh}{2}$ can be used to solve for the area of the triangle.

Statement 2) can be used by itself to solve for the area of the triangle.

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Example Question #3 : Dsq: Calculating The Area Of A Right Triangle

The lobby of a building is in the shape of a right triangle. The shortest side of the room is meters long. Find the number of tiles needed to cover the floor.

I) Each tile covers square centimeters.

II) The longest side of the lobby is five less than three times the shortest side.

Possible Answers:

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.

Correct answer:

Both statements are needed to answer the question.

Explanation:

To find the number of tiles needed, we need to find the area of the lobby and the area of one tile.

I) Gives us the area of one tile.

II) Gives us the length of the hypotenuse of the lobby.

Use II) along with the info given in the question to find the last side (Pythagorean Theorem).

$H=3SS-5 \rightarrow H=3(14)-5$

H=37

SS^2+MS^2=H^2 , where SS is the short side, MS is the middle side, and H is the hypotenuse.

14^2+MS^2=37^2

$MS=\sqrt{37^2-14^2}=\sqrt{1173}=34.2$

From there you can find the area of the lobby.

$A=\frac{1}{2}b\cdot h \rightarrow A=\frac{1}{2}34.2\cdot 14=239.4m^2$

Use I) along with the area of the lobby to find the number of tiles needed.

10,000cm^2=1m^2

$239.4m^2\cdot\frac{10,000cm^2}{1m^2}=2394000cm^2$

$\frac{2394000cm^2}{20cm^2}=119700 \text{ tiles}$

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Example Question #421 : Geometry

What is the area of the right triangle?

The hypotenuse measures .
The height measures .

Possible Answers:

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Each statement alone is 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.

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

Correct answer:

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Explanation:

Neither statement provides us with sufficient information to answer the question but both statements taken together are sufficient to answer the question.

In order to find the area of the right triangle we need both the height and base. We can use the Pythagorean Theorem to solve for the base.

c^2=a^2+b^2

b^2=5^2-4^2

$b=\sqrt{25-16}=\sqrt{9}=3cm$

Now we can find the area:

$\frac{1}{2}(3)(4)=6cm^2$

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Example Question #1 : Dsq: Calculating The Perimeter Of A Right Triangle

What is the perimeter of isosceles triangle ABC?

(1) AB=32

(2) BC=40

Possible Answers:

BOTH statements TOGETHER are not sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but the other statement alone is not sufficient.

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

EACH statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but the other statement alone is not sufficient.

Correct answer:

BOTH statements TOGETHER are not sufficient to answer the question.

Explanation:

(1) This statement gives us the length of one side of the triangle. This information is insufficient to solve for the perimeter.

(2) This statement gives us the length of one side of the triangle. This information is insufficient to solve for the perimeter.

Additionally, since we don't know which one of the sides ( or ) is one of the equal sides, it's impossible to determine the perimeter given the information provided.

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Example Question #2 : Dsq: Calculating The Perimeter Of A Right Triangle

Find the perimeter of right triangle $\Delta XLC$ .

I) XL=CL

II) $CX=5\sqrt{2}$

Possible Answers:

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.

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.

Correct answer:

Both statements are needed to answer the question.

Explanation:

If the two shorter sides of a right triangle are equal, that means our other two angles are 45 degrees. This means our triangle follows the ratios for a 45/45/90 triangle, so we can find the remaining sides from the length of the hypotenuse.

I) Tells us we have a 45/45/90 triangle. The ratio of side lengths for a 45/45/90 triangle is $x:x:x\sqrt2$ .

II) Tells us the length of the hypotenuse.

Together, we can find the remaining two sides and then the perimeter.

$CX=5\sqrt2\rightarrow XL=5, CL=5$

$P=5\sqrt2 +5+5$

$P=10+5\sqrt2$

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Example Question #3 : Dsq: Calculating The Perimeter Of A Right Triangle

Find the perimeter of the right triangle.

The product of the base and height measures .
The hypotenuse measures .

Possible Answers:

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.

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

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

Correct answer:

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Explanation:

Statement 1: We need additional information.

$b \times h =48$

But this can mean our base and height measure 2 and 24, 4 and 12, or 6 and 8.

We cannot determine which one based solely on this statement.

Statement 2: We're given the length of the hypotenuse so we can narrow down the possible base and height values.

c^2=a^2+b^2

We have to see which pair of values makes the statement 100=a^2 + b^2 true.

The only pair that does is 6 and 8.

We can now find the perimeter of the right triangle:

a+b+c=6+8+10=24

or, if you're more familiar with the equation $perimeter=a+b+\sqrt{a^2+b^2}$ , then:

$6+8+\sqrt{6^2+8^2}=24$

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Example Question #4 : Dsq: Calculating The Perimeter Of A Right Triangle

Calculate the perimeter of the triangle.

The hypotenuse of the right triangle is .
The legs of the right triangle measure and .

Possible Answers:

Each statement alone is sufficient to answer the question.

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

Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.

Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.

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

Correct answer:

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

Explanation:

Statement 1: In order to find the perimeter of a right triangle, we need to know the lengths of the legs, not the hypotenuse.

Statement 2: Since we have the values to both of the legs' lengths, we can just plug it into the equation for the perimeter:

$p=a+b+\sqrt{a^2+b^2}$

$p=3+4+\sqrt{9+16}=3+4+\sqrt{25}=12cm$

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Example Question #1 : Circles

You are given a circle and a square. Which one has the larger area?

Statement 1: The radius of the circle is two-thirds the sidelength of the square.

Statement 2: The circumference of the circle is $\frac{\pi }{3}$ times the perimeter of the square.

Possible Answers:

EITHER statement ALONE is 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.

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

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Let be the sidelength of the square. Then its area is $s^{2}$ .

From Statement 1, it follows that the radius of the circle is $r = \frac{2}{3}s$ .

From Statement 2, it follows that , since the perimeter of the square is , the circumference of the circle is $\frac{\pi }{3} \cdot 4s = \frac{4\pi }{3} \cdot s$ , and the radius is $\frac{ \frac{4\pi }{3} \cdot s}{2\pi } = \frac{2}{3} s$ - the same fact given in Statement 1.

Either way, it follows that the area of the circle in terms of is

$A = \pi r ^{2} =\pi \cdot \left ( \frac{2}{3} s \right )^{2} = \frac{\pi 4}{9} s ^{2}$ ,

so all we have to do is compare $\frac{\pi 4}{9}$ to 1 in order to determine whether the square or the circle is larger in area.

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Example Question #431 : Geometry

You are given a circle and an equilateral triangle. Which one has the greater area?

Statement 1: The sidelength of the triangle is three times the radius of the circle.

Statement 2: The perimeter of the triangle is 99 inches.

Possible Answers:

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

Correct answer:

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

Explanation:

From Statement 2, we can calculate the area of the triangle, but we are given no clues about the area of the circle, actual or relative.

From Statement 1, we know that if we call the radius of the circle , we know the sidelength of the triangle is s = 3r .

The area of the circle is $A = \pi r^{2}$ .

The area of the triangle is $A =\frac{ s^{2} \sqrt{ 3}}{4} = \frac{ (3r)^{2} \sqrt{ 3}}{4} = \frac{ 9 \sqrt{ 3}}{4} r^{2}$ .

All we have to do is compare $\pi$ to $\frac{ 9 \sqrt{ 3}}{4}$ to determine whether the circle or the triangle has the greater area.

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Example Question #1 : Circles

Data Sufficiency Question

Calculate the area of a circle.

1. The radius of the circle is 4.

2. The circumference of the circle is 24.

Possible Answers:

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

Each statement alone is sufficient

Statements 1 and 2 together are not sufficient, and additional data is needed to answer the question

Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question

Correct answer:

Each statement alone is sufficient

Explanation:

The area of a circle can be calcuated using the equation:

$A=r^2\pi$

and the circumference calculated using:

$C=2r\pi$

The radius is the only information required for calculating the area of a circle and that can be obtained from the circumference, therefore, either statement is sufficient.

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GMAT Math : Data-Sufficiency Questions

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #2 : Dsq: Calculating The Area Of A Right Triangle

Example Question #3 : Dsq: Calculating The Area Of A Right Triangle

Example Question #421 : Geometry

Example Question #1 : Dsq: Calculating The Perimeter Of A Right Triangle

Example Question #2 : Dsq: Calculating The Perimeter Of A Right Triangle

Example Question #3 : Dsq: Calculating The Perimeter Of A Right Triangle

Example Question #4 : Dsq: Calculating The Perimeter Of A Right Triangle

Example Question #1 : Circles

Example Question #431 : Geometry

Example Question #1 : Circles

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