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GMAT Quantitative University of Warwick 2017

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; Subject: ; Class: ; with 37 questions; test in 75 minutes; update 26/07/2017
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Subjects Update 26/07/2017
Class Number of questions 37
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Question 1.

The height of isosceles trapezoid ABDC is 12 units. The length of diagonal AD is 15 units. What is the area of trapezoid ABDC?

(A)

72

(B)

90

(C)

96

(D)

108

(E)

180

Question 2.

The combined area of the two black squares is equal to 1000 square units. A side of the larger black square is 8 units longer than a side of the smaller black square. What is the combined area of the two white rectangles in square units?

(A)

928

(B)

936

(C)

948

(D)

968

(E)

972

Question 3.

The perimeter of a rectangular yard is completely surrounded by a fence that measures 40 meters. What is the length of the yard if the area of the yard is 64 meters squared?

(A)

8

(B)

10

(C)

12

(D)

14

(E)

16

Question 4.

In the rhombus ABCD, the length of diagonal BD is 6 and the length of diagonal AC is 8. What is the perimeter of ABCD?

(A)

10

(B)

14

(C)

20

(D)

24

(E)

28

Question 5.

If 1/a2 + a2 represents the diameter of circle O and 1/a + a = 3, which of the following best approximates the circumference of circle O?

(A)

28

(B)

22

(C)

20

(D)

16

(E)

12

Question 6.

Two circular road signs are to be painted yellow. If the radius of the larger sign is twice that of the smaller sign, how many times more paint is needed to paint the larger sign (assuming that a given amount of paint covers the same area on both signs)?

(A)

2

(B)

3

(C)

π 

(D)

4

(E)

3π/2

Question 7.

In the diagram, points A, B, and C are on the diameter of the circle with center B. Additionally, all arcs pictured are semicircles. Suppose angle YXA = 105 degrees. What is the ratio of the area of the shaded region above the line YB to the area of the shaded region below the line YB? (Note: Diagram is not drawn to scale and angles drawn are not accurate.)

(A)

3/4

(B)

5/6

(C)

1

(D)

7/5

(E)

9/7

Question 8.

Two circles share a center at point C, as shown. Segment AC is broken up into two shorter segments, AB and BC, with dimensions shown. What is the ratio of the area of the large circle to the area of the small circle?
 

(A)

25/4

(B)

5/2

(C)

3/2

(D)

2/5

(E)

4/25

Question 9.

The length of minor arc AB is twice the length of minor arc BC and the length of minor arc AC is three times the length of minor arc AB. What is the measure of angle BCA?

(A)

20

(B)

40

(C)

60

(D)

80

(E)

120

Question 10.

In the figure, circle O has center O, diameter AB and a radius of 5. Line CD is parallel to the diameter. What is the perimeter of the shaded region?

(A)

(5/3)π + 5√3

(B)

(5/3)π + 10√3

(C)

(10/3)π + 5√3

(D)

(10/3)π + 10√3

(E)

(10/3)π + 20√3

Question 11.

The measures of the interior angles in a polygon are consecutive integers. The smallest angle measures 136 degrees. How many sides does this polygon have?

(A)

8

(B)

9

(C)

10

(D)

11

(E)

13

Question 12.

If x represents the sum of the interior angles of a regular hexagon and y represents the sum of the interior angles of a regular pentagon, then the difference between x and y is equal to the sum of the interior angles of what geometric shape?

(A)

Triangle

(B)

Square

(C)

Rhombus

(D)

Trapezoid

(E)

Pentagon

Question 13.

Regular hexagon ABCDEF has a perimeter of 36. O is the center of the hexagon and of circle O. Circles A, B, C, D, E, and F have centers at A, B, C, D, E, and F, respectively. If each circle is tangent to the two circles adjacent to it and to circle O, what is the area of the shaded region (inside the hexagon but outside the circles)?

(A)

108 – 18π

(B)

54√3 – 9π

(C)

54√3 – 18π

(D)

108 – 27π

(E)

54√3 – 27π

Question 14.

What is the ratio of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?

(A)

1/4

(B)

3/8

(C)

1/2

(D)

3/5

(E)

2

Question 15.

A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?

(A)

10(√3 – 1)

(B)

5

(C)

10(√2 – 1)

(D)

5(√3 – 1)

(E)

5(√2 – 1)

Question 16.

If the box shown is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C?

(A)

10%

(B)

20%

(C)

30%

(D)

40%

(E)

50%

Question 17.

A cylindrical tank of  radius R and  height H must  be redesigned to  hold approximately twice as much  liquid. Which of the following changes would be farthest from the new design requirements?

(A)

a 100% increase in R and a 50% decrease in H  

(B)

a 30% decrease in R and a 300% increase in H

(C)

a 10% decrease in R and a 150% increase in H

(D)

a 40% increase in R and no change in H

(E)

a 50% increase in R and a 20% decrease in H

Question 18.

A cylindrical tank, with radius and height both of 10 feet, is to be redesigned as a cone, capable of holding twice the volume of the cylindrical tank. There are two proposed scenarios for the new cone: in scenario (1) the radius will remain the same as that of the original cylindrical tank, in scenario (2) the height will remain the same as that of the original cylindrical tank. What is the approximate difference in feet between the new height of the cone in scenario (1) and the new radius of the cone in scenario (2)?

(A)

13

(B)

25

(C)

30

(D)

35

(E)

40

Question 19.

The figure represents a deflated tire (6 inches wide as shown) with a hub (the center circle). The area of the hub surface shown in the picture is 1/3 the area of the tire surface shown in the picture. The thickness of the tire, when fully inflated is 3 inches. (Assume the tire material itself has negligible thickness.) Air is filled into the deflated tire at a rate of 4π inches3 / second. How long (in seconds) will it take to inflate the tire?

(A)

24

(B)

27

(C)

48

(D)

81

(E)

108

Question 20.

When a cylindrical tank is filled with water at a rate of 22 cubic meters per hour, the level of water in the tank rises at a rate of 0.7 meters per hour. Which of the following best approximates the radius of the tank in meters?

(A)

√10/2

(B)

√10

(C)

4

(D)

5

(E)

10

Question 21.

A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the cylinder, which of the following must be true of the two possible cylinders that can be formed?

(A)

The volume of the cylinder with height 10 is 60/p cubic inches greater than the volume of the cylinder with height 6.

(B)

The volume of the cylinder with height 6 is 60/p cubic inches greater than the volume of the cylinder with height 10.

(C)

The volume of the cylinder with height 10 is 60p cubic inches greater than the volume of the cylinder with height 6.

(D)

The volume of the cylinder with height 6 is 60p cubic inches greater than the volume of the cylinder with height 10.

(E)

The volume of the cylinder with height 6 is 240/p cubic inches greater than the volume of the cylinder with height 10.

Question 22.

For any triangle T in the xy–coordinate plan, the center of T is defined to be the point whose x–coordinate is the average (arithmetic mean) of the x–coordinates of the vertices of T and whose y–coordinate is the average of the y–coordinates of the vertices of T. If a certain triangle has vertices at the points (0,0) and (6,0) and center at the point (3,2), what are the coordinates of the remaining vertex?

(A)

(3,4)

(B)

(3,6)

(C)

(4,9)

(D)

(6,4)

(E)

(9,6)

Question 23.

Line l is defined by the equation y – 5x = 4 and line w is defined by the equation 10y + 2x + 20 = 0. If line k does not intersect line l, what is the degree measure of the angle formed by line k and line w?

(A)

0

(B)

30

(C)

60

(D)

90

(E)

It cannot be determined from the information given.

Question 24.

In the xy-coordinate system, what is the slope of the line that goes through the origin and is equidistant from the two points P = (1, 11) and Q = (7, 7)?

(A)

2

(B)

2.25

(C)

2.50

(D)

2.75

(E)

3

Question 25.

What is the slope of the line represented by the equation x + 2y = 1?

(A)

-3/2

(B)

-1

(C)

-1/2

(D)

0

(E)

1/2

Question 26.

A certain square is to be drawn on a coordinate plane. One of the vertices must be on the origin, and the square is to have an area of 100. If all coordinates of the vertices must be integers, how many different ways can this square be drawn?

(A)

4

(B)

6

(C)

8

(D)

10

(E)

12

Question 27.

Line L contains the points (2,3) and (p,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L?

(A)

2x + y = px + 7

(B)

2x + y = –px

(C)

x + 2y = px + 7

(D)

y – 7 = x ÷ (p – 2)

(E)

2x + y = 7 – px

Question 28.

The (x, y) coordinates of points P and Q are (-2, 9) and (-7, -3), respectively. The height of equilateral triangle XYZ is the same as the length of line segment PQ. What is the area of triangle XYZ?

(A)

169/√3

(B)

84.5

(C)

75√3

(D)

169√3 /4 

(E)

225√3 /4

Question 29.

The line 3x + 4y = 8 passes through all of the quadrants in the coordinate plane except: 

(A)

I

(B)

II

(C)

III

(D)

IV

(E)

II and IV

Question 30.

The coordinates of points A and C are (0, -3) and (3, 3), respectively. If point B lies on line AC between points A and C, and if AB = 2BC, which of the following represents the coordinates of point B?

(A)

(1, -√5)

(B)

(1, -1)

(C)

(2, 1)

(D)

(1.5, 0)

(E)

(√5, √5)

Question 31.

In the xy-coordinate system, rectangle ABCD is inscribed within a circle having the equation x2 + y2 = 25.  Line segment AC is a diagonal of the rectangle and lies on the x-axis. Vertex B lies in quadrant II and vertex D lies in quadrant IV. If side BC lies on line y = 3x + 15, what is the area of rectangle ABCD?

(A)

15

(B)

30

(C)

40

(D)

45

(E)

50

Question 32.

The line represented by the equation y = 4 – 2x is the perpendicular bisector of line segment RP. If R has the coordinates (4, 1), what are the coordinates of point P?

(A)

(–4, 1)

(B)

(–2, 2)

(C)

(0, 1)

(D)

(0, –1)

(E)

(2, 0)

Question 33.

A certain computer program randomly generates equations of lines in the form    y = mx + b. If point P is a point on a line generated by this program, what is the probability that the line does NOT pass through figure ABCD?

(A)

3/4

(B)

3/5

(C)

1/2

(D)

2/5

(E)

1/4

Question 34.

In the rectangular coordinate system, a line passes through the points (0,5) and (7,0). Which of the following points must the line also pass through?

(A)

(-14, 10)

(B)

(-7, 5)

(C)

(12, -4)

(D)

(14, -5)

(E)

(21, -9)

Question 35.

Which of the following equations represents a line that is perpendicular to the line described by the equation 3x + 4y = 8?

(A)

3x + 4y = 18

(B)

3x – 4y = 24

(C)

4y – 3x = 26

(D)

1.5y + 2x = 18

(E)

8x – 6y = 24

Question 36.

How many units long is the straight line segment that connects the points (-1,1) and (2,6) on a rectangular coordinate plane?

(A)4 (B)

√26

(C)

√34

(D)

7

(E)

√58

Question 37.

Line A is drawn on a rectangular coordinate plane.  If the  coordinate  pairs (3,  2)  and  (-1,  -2) lie on line A, which of the following coordinate pairs does NOT lie on a line that is perpendicular to line A?

(A)

(5, 8) and (4, 9) 

(B)

(3, -1) and (4, -2)

(C)

(-1, 6) and (-4, 9)

(D)

(2, 5) and (-3, 2)

(E)

(7, 1) and (6, 2)

Question 1    Question 2    Question 3    Question 4    Question 5    Question 6    Question 7    Question 8    Question 9    Question 10    Question 11    Question 12    Question 13    Question 14    Question 15    Question 16    Question 17    Question 18    Question 19    Question 20    Question 21    Question 22    Question 23    Question 24    Question 25    Question 26    Question 27    Question 28    Question 29    Question 30    Question 31    Question 32    Question 33    Question 34    Question 35    Question 36    Question 37   
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