GMAT Math : Data-Sufficiency Questions

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Example Questions

Example Question #5 : Dsq: Understanding Measurement

You are given a square metal sheet whose area can be given by a whole number of square yards. What is the length of each side?

Statement 1: Each side has length between 4 and 6 feet inclusive.

Statement 2: Each side has length between 44 and 54 inches inclusive.

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:

Assume Statement 1 alone. Since the length of one side is at minimum 4 feet, or equivalently, $4 \div 3 = 1\frac{1}{3}$ yards, its area is at least the square of this, or $\left ( 1\frac{1}{3} \right )^{2}= 1\frac{7}{9}$ square yards. Since the length of one side is at most 6 feet, or, equivalently, $6 \div 3= 2$ yards, its area is at most the square of this, or 4 square yards. Since the area must be equal to a whole number of yards, we can only narrow the area down to 2, 3, or 4 square yards.

Assume Statement 2 alone. Since the length of one side is at minimum 44 inches, or equivalently, $44 \div 36 = 1\frac{2}{9}$ yards, its area is at least the square of this, or $\left ( 1\frac{2}{9} \right )^{2}= 1\frac{40}{81}$ square yards. Since the length of one side is at most 54 inches, or, equivalently, $54 \div 36 = 1\frac{1}{2}$ yards, its area is at most the square of this, or $\left ( 1\frac{1}{2} \right )^{2}= 2\frac{1}{4}$ square yards. Since the area must be equal to a whole number of yards, the only possible area for the sheet is 2 square yards.

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Example Question #4 : Dsq: Understanding Measurement

The weight of a bag of oranges can be given by a whole number of ounces. What is its weight?

Statement 1: The bag of oranges weighs between 110 ounces and 130 ounces inclusive.

Statement 2: The weight of the bag of oranges can be given as a whole number of pounds.

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:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume both statements are true. Since, as known from Statement 2, the weight of the bag of oranges is given by a whole number of pounds, then the weight in ounces must be a multiple of 16. From Statement 1, this number is between 110 and 130 inclusive. However, there are two multiples of 16 - 112 and 128 - that fall in this range. Therefore, the question cannot be answered for certain.

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Example Question #111 : Data Sufficiency Questions

You are given a square metal sheet whose area can be given by a whole number of square yards. What is the length of each side?

Statement 1: The area of the sheet is less than 3,000 square inches.

Statement 2: The area of the sheet is less than 15 square feet.

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 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 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:

Assume Statement 1 alone. One yard is equal to 36 inches, so one square yard is equal to $36^{2}= 1,296$ square inches. The maximum area of 3,000 square inches is equal to $3,000 \div 1,296 \approx 2.3$ square yards; since the area is a whole number of square yards less than this, we can narrow the area down to 1 or 2 square yards. Without further information, we cannot narrow this down further.

Assume Statement 2 alone. One yard is equal to 3 feet, so one square yard is equal to $3^{2} = 9$ square feet. The maximum area of 15 square feet is equivalent to $15 \div 9 = 1 \frac{2}{3}$ square yards; since the area is a whole number of square yards less than this, the only possible area is one square yard.

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Example Question #114 : Word Problems

The length of a metal rod can be given by a whole number of inches. How long is the rod?

Statement 1: The length of the rod can be given by a whole number of feet.

Statement 2: The rod is between 40 and 50 inches long, inclusive.

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.

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.

Correct answer:

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

Explanation:

If Statement 1 alone is assumed, since the length of the rod is given by a whole number of feet, then the length in inches must be a multiple of 12 - 12 inches, 24 inches, etc. However, no other information can be found.

If Statement 2 alone is assumed, there are eleven possible lengths of the rod - 40 inches, 41 inches, and so on up to 50 inches.

Now assume both statements. The length of the rod in inches must be a multiple of 12 between 40 and 50; this narrows it down to one possibility, 48 inches.

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Example Question #115 : Word Problems

You are given a square metal sheet whose area can be given by a whole number of square meters. What is the length of each side?

Statement 1: The length of each side is between 250 and 280 centimeters, inclusive.

Statement 2: The length of each side is between 2,500 millimeters and 2,800 millimeters inclusive.

Possible Answers:

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.

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.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. Since one meter is equal to 100 centimeters, the minimum and maximum lengths in meters are $250 \div 100 = 2.5$ meters and $280 \div 100 = 2.8$ meters. The squares of these lengths provide the minimum and maximum areas of the sheet:

$2.5 \le s \le 2.8$

$2.5 ^{2} \le s^{2} \le 2.8 ^{2}$

$6.25 \le A\le 7.84$

From the main body of the problem, the area in square meters must be a whole number, so its area must be seven meters.

Assume Statement 2 alone. One meter is equal to 1,000 millimeters, so the minumum and maximum lengths are $2,500 \div 1,000 = 2.5$ meters and $2,800 \div 1,000 = 2.8$ meters. These are the same boundaries derived from Statement 1, so again, the area can be determined to be seven meters.

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Example Question #1 : Geometry

Data Sufficiency Question

Is Line A perpendicular to the following line?

$y=-\frac{1}{2}x+3$

Statement 1: The slope of Line A is 3.

Statement 2: Line A passes through the point (2,3).

Possible Answers:

Statement 1 alone is sufficient, but Statement 2 alone is not 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 together are not sufficient, and additional data is needed to answer the question.

Each statement alone is sufficient.

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

Correct answer:

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

Explanation:

To determine if two lines are perpendicular, only the slope needs to be considered. The slopes of perpendicular lines are the negative reciprocals of each other. Knowing a single point on the line is not sufficient, as an infinite number of lines can pass through and individual point.

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Example Question #1 : Geometry

Untitled

Refer to the above figure. True or false: $m \perp n$

Statement 1: $\triangle AXB$ is equilateral.

Statement 2: Line bisects $\angle AXB$ .

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.

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.

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 establishes nothing about the angle makes with , as it is not part of the triangle. Statement 2 alone only establishes that AY = YB .

Assume both statements are true. Then $\overleftrightarrow{XY}$ is an altitude of an equilateral triangle, making it - and - perpendicular with the base $\overline {AB}$ - and .

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Example Question #2 : Geometry

Untitled Statement 1:

Refer to the above figure. Are the lines perpendicular?

Statement 1: x = 9

Statement 2: x= y+1

Possible Answers:

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.

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.

Correct answer:

EITHER statement ALONE is sufficient to answer the question.

Explanation:

Assume Statement 1 alone. The measure of one of the angles formed is

$x^{2}+ 9 = 9^{2}+ 9= 81 + 9 = 90$ degrees.

Assume Statement 2 alone.

By substituting x-1 for , one angle measure becomes

11y + 2 = 11 (x-1) +2= 11x-11+2= 11x-9

The marked angles are a linear pair and thus their angle measures add up to 180 degrees; therefore, we can set up an equation:

$\left ( 11x-9 \right )+ \left ( x^{2}+9 \right ) = 180$

$x^{2}+11x = 180$

$x^{2}+11x - 180 = 0$

(x+20)(x-9) = 0

x= -20 or x= 9

x= -20 yields illegal angle measures - for example,

$x^{2}+ 9 = (-20)^{2}+ 9= 409$

x= 9 yields angle measures $90 ^{\circ }$ for both angles; the angles are right and the lines are perpendicular.

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Example Question #3 : Geometry

Transversal

Refer to the above figure.

True or false: $m \perp t$

Statement 1: $m \angle 2 = 89^{\circ }$

Statement 2: $\angle 3 \cong \angle 6$

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.

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.

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 establishes by definition that $l \perp \! \! \! \! \! / \; t$ , but does not establish any relationship between and .

By Statement 2 alone, since alternating interior angles are congruent, l || m , but no conclusion can be drawn about the relationship of , since the actual measures of the angles are not given.

Assume both statements are true. By Statement 2, l || m . $\angle 2$ and $\angle 6$ are corresponding angles formed by a transversal across parallel lines, so $m \angle 6 = m \angle 2 = 89^{\circ }$ . $\angle 6$ is not a right angle, so $m\perp \! \! \! \! \! / \; t$ .

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Example Question #2 : Dsq: Calculating Whether Lines Are Perpendicular

Untitled

Refer to the above figure. True or false: $m \perp n$

Statement 1: $\bigtriangleup XAY \cong \bigtriangleup XBY$

Statement 2: Line bisects $\angle AXB$ .

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 insufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER 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:

Assume Statement 1 alone. Then, as a consequence of congruence, $\angle XYA$ and $\angle XYB$ are congruent. They form a linear pair of angles, so they are also supplementary. Two angles that are both congruent and supplementary must be right angles, so $m \perp n$ .

Assume Statement 2 alone. Then $\angle AXY \cong \angle BXY$ , but without any other information about the angles that $\overleftrightarrow{AX}, \overleftrightarrow{BX},$ or make with , it cannot be determined whether $m \perp n$ or not.

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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 #5 : Dsq: Understanding Measurement

Example Question #4 : Dsq: Understanding Measurement

Example Question #111 : Data Sufficiency Questions

Example Question #114 : Word Problems

Example Question #115 : Word Problems

Example Question #1 : Geometry

Example Question #1 : Geometry

Example Question #2 : Geometry

Example Question #3 : Geometry

Example Question #2 : Dsq: Calculating Whether Lines Are Perpendicular

All GMAT Math Resources

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