GMAT Math : GMAT Quantitative Reasoning

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Example Questions

Example Question #4 : Dsq: Calculating The Length Of The Side Of An Acute / Obtuse Triangle

Is $\Delta ABC$ isosceles?

Statement 1: $\Delta ABC \sim \Delta DEF$

Statement 2: DE = EF

Possible Answers:

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.

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.

Correct answer:

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

Explanation:

Statement 1 alone does not tell us anything unless we know the relative lengths of the sides of $\Delta DEF$ ; Statement 2 only gives us information about another triangle.

Suppose we assume both statements. Then by similarity,

$\frac{AB}{DE} = \frac{BC}{EF}$ .

Since DE = EF , then

$\frac{AB}{DE} \cdot DE = \frac{BC}{EF} \cdot EF$ , or

AB = BC .

This makes $\Delta ABC$ isosceles.

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Example Question #5 : Dsq: Calculating The Length Of The Side Of An Acute / Obtuse Triangle

Which of the three sides of $\Delta ABC$ is the longest?

Statement 1: $m \angle A =m \angle B + 20^{\circ }$

Statement 2: $m \angle C = m \angle A + 100^{\circ }$

Possible Answers:

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.

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.

Correct answer:

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

Explanation:

The longest side of a triangle is opposite the angle of greatest measure.

From Statement 1 alone, we can find two possible scenarios with different answers:

Case 1:

$m \angle B = 20 ^{\circ }, m \angle A = 40 ^{\circ }, m \angle C = 120 ^{\circ }$

Case 2:

$m \angle C = 20 ^{\circ }, m \angle B = 70 ^{\circ }, m \angle A = 90 ^{\circ }$

In both cases, $m \angle A =m \angle B + 20^{\circ }$ , but in Case 1, $\overline{AB}$ is the longest side, and in Case 2, $\overline{BC }$ is the longest side.

From Statement 2 alone, however, we know that $m \angle C > 100^{\circ }$ , so $\angle C$ is obtuse and the other two angles are acute. That makes $\overline{AB}$ the longest side.

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Example Question #295 : Geometry

True or false: $\Delta ABC$ is scalene.

Statement 1: $\angle A \ncong \angle B$

Statement 2: $\overline{AB} \ncong \overline{BC}$

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 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.

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.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements are true.

By definition, a scalene triangle has three noncongruent sides. Sides opposite noncongruent angles of a triangle are noncongruent, so as a consequence of Statement 1, $\overline{AC} \ncong \overline{BC}$ . Statement 2 alone establishes that $\overline{AB} \ncong \overline{BC}$ . However, the two statements together do not establish whether or not $\overline{AB} \ncong \overline{AC}$ , so it is not clear whether $\Delta ABC$ is scalene or isosceles.

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Example Question #5 : Dsq: Calculating The Length Of The Side Of An Acute / Obtuse Triangle

True or false: $\Delta ABC$ is scalene.

Statement 1: $\overline{AC} \ncong \overline{BC}$

Statement 2: $\angle B \cong \angle C$

Possible Answers:

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.

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.

Correct answer:

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

Explanation:

By definition, a scalene triangle has three noncongruent sides.

Statement 1 alone states that two sides are noncongruent, but no information is given about whether or not third side $\overline{AB}$ is congruent to either of the other sides.

Assume Statement 2 alone. In a triangle, sides opposite congruent angles are congruent, so it follows that $\overline{AB} \cong \overline{AC}$ . The triangle cannot be scalene.

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Example Question #292 : Geometry

True or false: $\Delta ABC$ is scalene.

Statement 1: AB > AC

Statement 2: BC > AC

Possible Answers:

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.

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.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

By definition, a scalene triangle has three noncongruent sides.

If AB = 7, AC = 5, BC = 6 , then AB > AC and BC > AC , and the triangle is scalene.

If AB = 7, AC = 5, BC = 7 , then AB > AC and BC > AC , but AB = BC , so the triangle is not scalene.

The two statements together are insufficient.

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Example Question #1 : Equilateral Triangles

Is $\Delta ABC$ an equilateral triangle?

Statement 1: $m\angle A =m\angle B = 60^{\circ }$

Statement 2: $\Delta ABC \sim \Delta DEF$ , and $\Delta DEF$ is equiangular.

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 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.

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.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

If $m\angle A =m \angle B = 60^{\circ }$ , then

$m\angle C = 180 - \left (m\angle A + m \angle B \right )=180 - \left (60 +60 \right ) = 60^{\circ }$ .

This makes $\Delta ABC$ an equiangular triangle.

If $\Delta ABC \sim \Delta DEF$ , and $\Delta DEF$ is equiangular, then, since corresponding angles of similar triangles are congruent, $\Delta ABC$ has the same angle measures, and is itself equiangular.

From either statement, since all equiangular triangles are equilateral, we can draw this conclusion about $\Delta ABC$ .

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Example Question #52 : Triangles

True or false: $\Delta ABC$ is equilateral.

Statement 1: The perimeter of $\Delta ABC$ is .

Statement 2: AB= 4 .

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

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

The two statements together provide insufficient information. A triangle with sides , , and is equilateral and has perimeter ; A triangle with sides , , and is not equilateral and has perimeter .

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Example Question #53 : Triangles

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$\overline{DC}$ is the height of $\bigtriangleup ABC$ . What is the length of $\overline{AB}$ ?

(1) $\overline{DC}=4$

(2) $\overline{DB}=3$

Possible Answers:

Statements 1 and 2 together are not sufficient

Statement 2 alone is sufficient

Statement 1 alone is sufficient

Both statements together are sufficient

Each statement alone is sufficient

Correct answer:

Statements 1 and 2 together are not sufficient

Explanation:

To find the answer we should know more about the characteristics of the triangle, i.e. its angles, sides...

Statement 1 alone is obviously insufficient, since we don't know whether the triangle is equilateral, nothing can be said about AB.

Statement 2 is equally as unhelpful as statement 1, since we don't know whether ABC is of a specific type of triangle.

Taken together, these statements allow us to calculate the length of CB, but we can't go further, because we don't know what is AD.

Therefore statements 1 and 2 are not sufficient even taken together.

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Example Question #1 : Dsq: Calculating The Length Of The Side Of An Equilateral Triangle

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ABC is an equilateral triangle inscribed in the circle. What is the length of side AB?

(1) The area of the circle is $16\pi$

(2) The perimeter of triangle ABC is $\frac{36}{\sqrt{3}}$

Possible Answers:

Statment 2 alone is sufficient

Statements 1 and 2 together are not sufficient

Both statements together are sufficient

Statement 1 alone is sufficient

Each statement alone is sufficient

Correct answer:

Each statement alone is sufficient

Explanation:

To find the length of the side, we would need to know anything about the lengths in the circle or in the triangle.

From statement 1, we can find the radius of the circle, which allows us to calculate the height of the triangle, since the radius is $\frac{2}{3}$ of the height. And finally since the triangle is equilateral, we can also calculate the length of the sides from the height.

Therefore statement 1 is sufficient.

Statement 2 also gives us useful information, indeed the perimeter is simply three times the length of the sides.

Therefore the final answer is each statement alone is sufficient.

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Example Question #2 : Dsq: Calculating The Length Of The Side Of An Equilateral Triangle

Find the side length of $\Delta FHT$ .

I) $\Delta FHT$ has perimeter of 114 ft .

II) $\measuredangle F$ is equal to $\measuredangle T$ which is $60^\circ$ .

Possible Answers:

Either statement is sufficient to answer the question.

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

Both statements are needed to answer the question.

Correct answer:

Both statements are needed to answer the question.

Explanation:

I) Tells us the perimeter of the triangle.

II) Tells us that FHT is an equilateral triangle.

Taking these statements together we are able to find the side length by dividing the perimeter from statement I, by 3 since all side lengths of an equilateral are the same by statement II.

$s=\frac{P}{3} \rightarrow s=\frac{114}{3}=38ft$

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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 #4 : Dsq: Calculating The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #5 : Dsq: Calculating The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #295 : Geometry

Example Question #5 : Dsq: Calculating The Length Of The Side Of An Acute / Obtuse Triangle

Example Question #292 : Geometry

Example Question #1 : Equilateral Triangles

Example Question #52 : Triangles

Example Question #53 : Triangles

Example Question #1 : Dsq: Calculating The Length Of The Side Of An Equilateral Triangle

Example Question #2 : Dsq: Calculating The Length Of The Side Of An Equilateral Triangle

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