Find the direction in which the parabola y = ax 2 + bx - 2 is facing. 1. a = b 2. a < 0

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

Statement (2) ALONE is sufficient, but statement (1) 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 ask

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

Find out if t < 0. 1. |t| > t 2. t 2 > 0

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

Statement (2) ALONE is sufficient, but statement (1) 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 ask

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

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GMAT Exam > GMAT Tests > Test: Data Sufficiency - 3 - GMAT MCQ

Test: Data Sufficiency - 3 - GMAT MCQ

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10 Questions MCQ Test - Test: Data Sufficiency - 3

Test: Data Sufficiency - 3 for GMAT 2024 is part of GMAT preparation. The Test: Data Sufficiency - 3 questions and answers have been prepared according to the GMAT exam syllabus.The Test: Data Sufficiency - 3 MCQs are made for GMAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Data Sufficiency - 3 below.

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Test: Data Sufficiency - 3 - Question 1

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Find the area of a right angle triangle whose base is 12 inches.
1. The hypotenuse is 13 inches.
2. The perpendicular height of the triangle is one less than half its base.

A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
D.
EACH statement ALONE is sufficient to answer the question asked.
E.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Detailed Solution for Test: Data Sufficiency - 3 - Question 1

Base = 12 inches.
In statement 1, hypotenuse = 13 inches. Using Pythagorean theorem, we have height = √(13² - 12²) = 5.
Area = 1/2 × 5 × 12 = 30 square inches. The statement is sufficient.
In statement 2, perpendicular height = 1/2 (base) - 1 = 1/2 × 12 -1 = 5 inches. Base = 12 inches.
Area =1/2 × 5 × 12 = 30 square inches. The statement is sufficient.

Test: Data Sufficiency - 3 - Question 2

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Is the number a prime number?
1. The number is divisible by a prime factor.
2. The number is positive

A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
D.
EACH statement ALONE is sufficient to answer the question asked.
E.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Detailed Solution for Test: Data Sufficiency - 3 - Question 2

In statement 1, the number is divisible by a prime factor, hence the number can be 2, 4, 6, -2, -4, -6, 8 , 9 . . . . Hence the statement is insufficient.
In statement 2, the number is positive. But there are infinitely many numbers that are positive but not prime, hence, the statement is not sufficient.
Combining the two statements, we have the numbers being positive, thus, 2,4,6,8,9,10,. . . . The numbers are infinitely many, hence Statements (1) and (2) TOGETHER are NOT sufficient.

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Test: Data Sufficiency - 3 - Question 3

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Find the direction in which the parabola y = ax²+ bx - 2 is facing.
1. a = b
2. a < 0

A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
D.
EACH statement ALONE is sufficient to answer the question asked.
E.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Detailed Solution for Test: Data Sufficiency - 3 - Question 3

The parabola y = ax² + bx - 2 faces upwards when a > 0 and downwards when a < 0.
In statement 1, a = b, this does not give the numerical equivalent to a, hence it is not sufficient.
In statement 2, a < 0, hence the parabola faces downwards. Thus the statement is sufficient.

Test: Data Sufficiency - 3 - Question 4

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Find the equation of a line.
1. Its x and y intercept is 2 and -2 respectively.
2. The slope of the line is 1.

A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
D.
EACH statement ALONE is sufficient to answer the question asked.
E.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Detailed Solution for Test: Data Sufficiency - 3 - Question 4

In statement 1, the x and y intercept is 2 and -2 respectively, hence the line passes through (2,0) and (0,-2). The slope is
(-2 - 0)/(2 - 0) = -1.
The equation is y/(x - 2) = -1 hence x = -x + 2.
The statement is sufficient.
In statement 2, the slope is 1. Since we are not given any point where the line is passing, the statement is insufficient. Thus, Statement (1) ALONE is sufficient but statement (2) is not sufficient.

Test: Data Sufficiency - 3 - Question 5

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Determine the size of an interior angle of the polygon.
1. The ratio of its interior angle to the exterior angle is 2:1.
2. The polygon is a regular hexagon

A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.
EACH statement ALONE is sufficient to answer the question asked.
C.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
D.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
E.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Detailed Solution for Test: Data Sufficiency - 3 - Question 5

Conclusion:

Since both statements independently lead to the determination that the interior angle is 120 degrees, each statement alone is sufficient.

The correct answer is:

EACH statement ALONE is sufficient to answer the question asked.

Test: Data Sufficiency - 3 - Question 6

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Find out if t < 0.
1. |t| > t
2. t² > 0

A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
D.
EACH statement ALONE is sufficient to answer the question asked.
E.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Detailed Solution for Test: Data Sufficiency - 3 - Question 6

In statement 1, |t| > t. But is |-t| = |t|. Hence t can be positive or negative. When |t| > t, it implies that t is a negative value, hence t < 0. The statement is sufficient.
In statement 2, t² > 0 , but when t is negative or positive, t² > 0 , hence the statement is not sufficient. Thus Statement (1) ALONE is sufficient but statement (2) is not sufficient.

Test: Data Sufficiency - 3 - Question 7

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Determine the value of t.
1. 2t + 6s = 8
2. t/2 - 2 = - 3s/4

A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
D.
EACH statement ALONE is sufficient to answer the question asked.
E.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask

Detailed Solution for Test: Data Sufficiency - 3 - Question 7

In statement 1, 2t + 6s = 8 is one equation is two unknowns, hence we cannot determine the value of t. The statement is insufficient.
In statement 2, t/2 - 2 = -3s/4 can be transformed to t - 4 = -6s/2. But this is an equation with two unknowns hence we cannot determine the value of t. The statement is insufficient.
Combining the two statements, we have 2, t/2 - 2 = -3s/4 which can be transformed to 2t - 8 = -3s. Thus, we can determine the value of t and s. Therefore, statements (1) and (2) TOGETHER are sufficient.

Test: Data Sufficiency - 3 - Question 8

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Find the percentage change in the volume of cylinder.
1. The diameter is increased by 20%.
2. The height is increased by 21%.

A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
D.
EACH statement ALONE is sufficient to answer the question asked.
E.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Detailed Solution for Test: Data Sufficiency - 3 - Question 8

The volume of the cylinder is given buy v = πr²h.
In statement 1, diameter (d) is increased by 20%, hence the radius is increased by 10%. The new radius is given by 1.1r. The new volume = π(1.1r)²h = 1.21πr²h
Percentage change in volume = (1.21πr²h - πr²h )/pr²h × 100% = 21%. The statement is sufficient.
In statement 2, height is increased by 21%, hence the new height is 1.21h. The new volume = 1.21πr²h.
Percentage change in volume = (1.21πr²h - πr²h )/πr²h × 100% = 21%. The statement is sufficient. Therefore, EACH statement ALONE is sufficient.

Test: Data Sufficiency - 3 - Question 9

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a < b. Is a positive?
1. b = 0.
2. √a < a

A.
EACH statement ALONE is sufficient to answer the question asked.
B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
D.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
E.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Detailed Solution for Test: Data Sufficiency - 3 - Question 9

In statement 1, b =0, when a < b and b = 0, it implies that a < 0, hence, a is negative and a is not positive. The statement is sufficient.
In statement 2, √a < a, the square root of a number is defined only when in √a a > 0 . Hence, the statement is sufficient. Thus, EACH statement ALONE is sufficient to answer the question asked.

Test: Data Sufficiency - 3 - Question 10

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Determine the equation of the circle passing through (-4,-2).
1. (1,-1) lies in the circle.
2. The center of the circle is the origin.

A.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
B.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
C.
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question ask
D.
EACH statement ALONE is sufficient to answer the question asked.
E.
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

Detailed Solution for Test: Data Sufficiency - 3 - Question 10

The circle passes through (-4,-2).
In statement 1, (1,-1) lies in the circle; since the statement does not specify if the point is the center, we cannot determine its radius and the center, hence, it is insufficient.
In statement 2, the center is the origin, using (-4,-2) the radius of the circle is √((-4 - 0)² + (-2 - 0)²) = √(16 + 4) = √20 units.
The equation is (x - 0)² + (y - 0)² = 20 ; x² + y² = 20. The statement is sufficient. Thus, Statement (2) ALONE is sufficient but statement (1) is not sufficient.

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Test: Data Sufficiency - 3 - GMAT MCQ

10 Questions MCQ Test - Test: Data Sufficiency - 3

Find the area of a right angle triangle whose base is 12 inches. 1. The hypotenuse is 13 inches. 2. The perpendicular height of the triangle is one less than half its base.

Is the number a prime number? 1. The number is divisible by a prime factor. 2. The number is positive

Find the direction in which the parabola y = ax2 + bx - 2 is facing. 1. a = b 2. a < 0

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Important Questions for Data Sufficiency - 3

Data Sufficiency - 3 MCQs with Answers

Online Tests for Data Sufficiency - 3

Find the area of a right angle triangle whose base is 12 inches.
1. The hypotenuse is 13 inches.
2. The perpendicular height of the triangle is one less than half its base.

Is the number a prime number?
1. The number is divisible by a prime factor.
2. The number is positive

Find the direction in which the parabola y = ax²+ bx - 2 is facing.
1. a = b
2. a < 0