GMAT Math : Data-Sufficiency Questions

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Example Questions

Example Question #22 : Polygons

Thingy

Note: Figure NOT drawn to scale.

Refer to the above figure. What is the length of $\overline{CD}$ ?

Statement 1: DE = 4

Statement 2: AB = 7

Possible Answers:

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.

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.

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:

To find the length of $\overline{CD}$ , we can extend $\overline{BC}$ to meet $\overline{EF}$ at a point to form two rectangles, as seen below:

Thingy

Statement 1 gives no helpful information, since the length of $\overline{DE}$ , which is not parallel to $\overline{CD}$ , has no bearing on that side's length.

If we are given Statement 2 alone, then, as seen in the diagram, FG + GE = FE = 12 from segment addition, AB = 7 , from Statement 2, and from congruence of opposite sides of a rectangle, AB = FG and CD = GE . Therefore, AB + CD = 12 , 7 + CD = 12 , and CD = 5 .

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Example Question #1 : Dsq: Calculating The Length Of A Side Of A Polygon

Given a regular hexagon HEXAGN , what is the length of $\overline{HE}$ ?

Statement 1: The hexagon is circumscribed by a circle with circumference $12 \pi$ .

Statement 2: $\overline{HA }$ hs length 12.

Possible Answers:

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.

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:

Below is a regular hexagon HEXAGN , with its three diameters, its center , and its circumscribed circle, which also has center .

Hexagon_2

If Statement 1 is true. then the circle, with circumference $12 \pi$ , has as its diameter $12 \pi \div \pi = 12$ , which is 12; this makes the two statements equivalent, so we need only establish that one statement is sufficient or insufficient.

Either way, , the radius of the hexagon, is 6. The six triangles that are formed by the sides and diameters of a regular hexagon are all equilateral by symmetry, so each side of the hexagon - in particular, $\overline{HE}$ - has length 6.

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Example Question #5 : Dsq: Calculating The Length Of A Side Of A Polygon

Give the length of side $\overline{HE}$ of Hexagon HEXAGO .

Statement 1: EX= 7 .

Statement 2: Hexagon HEXAGO has perimeter 42.

Possible Answers:

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.

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

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements to be true, and examine these two scenarios:

Case 1: The hexagon could have six sides of length 7.

Case 2: The hexagon has four sides of length 7, one of which is $\overline{EX}$ , one side of length 6, and one side - $\overline{HE}$ - of length 8.

In both situations, EX= 7 and the perimeter of the hexagon is 42:

$7 \times 6= 7 \times 4+6+8 = 42$ .

The conditions of both statements would be met in both scenarios, so the two statements together are insufficient.

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Example Question #6 : Dsq: Calculating The Length Of A Side Of A Polygon

Give the length of side $\overline{PE}$ of Pentagon PENTA .

Statement 1: $\overline{PE} \cong\overline{PA} \cong \overline{NT}$

Statement 2: $\overline{NE}$ and $\overline{TN}$ both have length 10.

Possible Answers:

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.

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 sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

Statement 1 alone states that $\overline{PE}$ is congruent to two other sides, but gives no actual measurements. Statement 2 alone gives the actual measurements of two other segments, but without further information, such as how their lengths relates to that of $\overline{PE}$ , no information about $\overline{PE}$ can be inferred.

Now, assume both statements to be true. From Statement 2, $\overline{TN}$ has length 10, and from Statement 2, $\overline{NT}$ , which is the same line segment (which can be named after its endpoints in either order), has the same length as $\overline{PE}$ . Therefore, PE = 10 .

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Example Question #7 : Dsq: Calculating The Length Of A Side Of A Polygon

Give the length of side $\overline{PE}$ of Pentagon PENTA .

Statement 1: Pentagon PENTA has perimeter 50.

Statement 2: EP = 10

Possible Answers:

BOTH statements TOGETHER give sufficient information to answer the question, but neither statement ALONE gives sufficient information to answer the question.

BOTH statements TOGETHER do not give sufficient information to answer the question.

Statement 2 ALONE gives sufficient information to answer the question, but Statement 2 ALONE does NOT sufficient information to answer the question.

Statement 1 ALONE gives sufficient information to answer the question, but Statement 2 ALONE does NOT sufficient information to answer the question.

EITHER statement ALONE gives sufficient information to answer the question.

Correct answer:

Statement 2 ALONE gives sufficient information to answer the question, but Statement 2 ALONE does NOT sufficient information to answer the question.

Explanation:

Statement 1 alone only gives the perimeter - the sum of the lengths of the sides - but gives no information about the individual sidelengths. (In particular, there is no indication that the pentagon is regular).

Assume Statement 2 alone. $\overline{PE}$ and $\overline{EP}$ are two names for the same line segment, which can be named after its endpoints in either order. Therefore, PE = EP = 10 .

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Example Question #8 : Dsq: Calculating The Length Of A Side Of A Polygon

True or false: $\overline{NT}$ is the shortest side of Pentagon PENTA .

Statement 1: Pentagon PENTA has perimeter 65.

Statement 2: NT = 12 .

Possible Answers:

Statement 1 ALONE provides sufficient information to answer the question, but Statement 2 ALONE does NOT provide sufficient information to answer the question.

BOTH statements TOGETHER provide insufficient information to answer the question.

Statement 2 ALONE provides sufficient information to answer the question, but Statement 1 ALONE does NOT provide sufficient information to answer the question.

EITHER Statement ALONE provides sufficient information to answer the question.

BOTH statements TOGETHER provide sufficient information to answer the question, but NEITHER statement ALONE provides sufficient information to answer the question.

Correct answer:

BOTH statements TOGETHER provide insufficient information to answer the question.

Explanation:

Assume both statements are true. If the pentagon has sides of length 12, 13, 13, 13, and 14, with $\overline{NT}$ the side of length 12, then $\overline{NT}$ is the shortest side, and the perimeter is

12+13+13+13+14 = 65 .

On the other hand, if the pentagon has sides of length 11, 12, 13, 14, and 15,

with $\overline{NT}$ the side of length 12, then $\overline{NT}$ is not the shortest side, and the perimeter is

11+ 12+13+14 +15= 65 .

The two statements together are insufficient.

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Example Question #2383 : Gmat Quantitative Reasoning

True or false: $\overline{XA}$ is the longest side of Hexagon HEXAGO .

Statement 1: XA = 10

Statement 2: Hexagon HEXAGO has perimeter 66.

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.

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.

BOTH statements TOGETHER are insufficient 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 only gives information about one side of the hexagon, and Statement 2 gives only information about the perimeter without giving any clues as to the individual sidelengths; neither is sufficient to answer the question.

Assume both statements are true. If $\overline{XA}$ , with length 10, is the longest side of Hexagon HEXAGO , then

HE, EX, AG, GO, OH < 10

By the addition property of inequality,

HE+ EX+XA+ AG+ GO+ OH < 10 +10 +10 +10 +10 +10 = 60 < 66

This means the sum of the sidelengths of the hexagon, which is its perimeter, is less than 66, in contradiction to Statement 2. $\overline{XA}$ cannot be the longest side.

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Example Question #1 : Dsq: Calculating The Area Of A Polygon

What is the area of a parallelogram with four equal sides?

(1) Each side is $\dpi{100} \small 5cm$

(2) One diagonal is $\dpi{100} \small 6cm$

Possible Answers:

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

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

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

EACH statement ALONE is sufficient.

Correct answer:

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

Explanation:

$\dpi{100} \small S= \frac{1}{2}\times L1\times L2$ ( $\dpi{100} \small L1$ and $\dpi{100} \small L2$ are the diagonals of the rhombus). From statement (1) we cannot get to the lengths of diagonals. From statement (2) we only know the length of one diagonal, which is insufficient. However, putting the two statements together, we can use the Pythagorean Theorem to calculate the other diagonal, and then use the formula to calculate the area.

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Example Question #1 : Dsq: Calculating The Area Of A Polygon

What is the area of a regular hexagon?

Statement 1: The perimeter of the hexagon is 48.

Statement 2: The radius of the hexagon is 8.

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:

A regular hexagon can be viewed as the composite of six equilateral triangles. The sidelength of each of the triangles is equal to both the sidelength of the hexagon (one-sixth of the perimeter) and the radius of the hexagon. From either statement, it is possible to find the area of one triangle by substituting s = 8 in the area formula

$A = \frac{s^{2}\sqrt{3}}{4}$

and multiplying the result by 6.

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Example Question #162 : Geometry

What is the area of a trapezoid?

Statement 1: The length of its midsegment is 20.

Statement 2: The lengths of its bases are 18 and 22.

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:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

The area of a trapezoid can be found using the following formula:

$A = \frac{1}{2} (B + b) h$

Where B,b are the lengths of the bases and is the height. From either statement, B + b can be determined, but is not given in either statement.

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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 #22 : Polygons

Example Question #1 : Dsq: Calculating The Length Of A Side Of A Polygon

Example Question #5 : Dsq: Calculating The Length Of A Side Of A Polygon

Example Question #6 : Dsq: Calculating The Length Of A Side Of A Polygon

Example Question #7 : Dsq: Calculating The Length Of A Side Of A Polygon

Example Question #8 : Dsq: Calculating The Length Of A Side Of A Polygon

Example Question #2383 : Gmat Quantitative Reasoning

Example Question #1 : Dsq: Calculating The Area Of A Polygon

Example Question #1 : Dsq: Calculating The Area Of A Polygon

Example Question #162 : Geometry

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