GRE_Math_Bible_eBook
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Geometry 101
34.In the figure, ABCD is a parallelogram. Which one of the following is true?
(A)x < y
(B)x > q
(C)x > p
(D)y > p
(E)y > q
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30° |
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31° |
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35.In the figure, the areas of parallelograms EBFD and AECF are 3 and 2, respectively. What is the area of rectangle ABCD ?
(A)3
(B)4
(C)5
(D)4
3
(E)7
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102GRE Math Bible
36.In the figure, the area of rectangle ABCD is 100. What is the area of the square EFGH ?
(A)256
(B)275
(C)309
(D)399
(E)401
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2x + 5 |
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37.In the figure, the area of rectangle EFGH is 3 units greater than the area of rectangle ABCD. What is the value of ab if a + b = 8?
(A)9
(B)12
(C)15
(D)18
(E)21
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x + a |
F |
x + 6 |
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Geometry 103
38.In the figure, the area of rectangle ABCD is 45. What is the area of the square EFGH ?
(A)20
(B)40
(C)50
(D)65
(E)70
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x + 5 |
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5 – x |
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39.In the figure, ABCD is a parallelogram, what is the value of b ?
(A)46
(B)48
(C)72
(D)84
(E)96
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48° |
b° |
48° |
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D C
104GRE Math Bible
40.In the figure, AB and CD are the diameters of the circle. What is the value of x ?
(A)16°
(B)18°
(C)26°
(D)32°
(E)58°
x°
D
A
32°
O
B
C
Geometry 105
41.In the figure, a, b, c, d, e, f, g, h, i, and j are chords of the circle. Which two chords are parallel to each other?
(A)a and f
(B)b and g
(C)c and h
(D)d and i
(E)e and j
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b |
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40° |
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35° |
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35° |
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a 30° |
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40°e |
35° |
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32° |
f |
32° |
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36° |
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45° |
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The figure is not drawn to scale.
106GRE Math Bible
42.A and B are centers of two circles that touch each other externally, as shown in the figure. What is the area of the circle whose diameter is AB ?
(A)4π
(B)25π/4
(C)9π
(D)16π
(E)25π
B A
2 3
43.In the figure, which one of the following angles is the greatest?
(A)A
(B)B
(C)C
(D)D
(E)CDB
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D 6
C
The figure is not drawn to scale.
Geometry 107
A B C D
44.In the figure, A, B, C, and D are points on a line in that order. If AC = 5, BD = 10, and AD = 13, then what is the length of BC ?
(A)2
(B)8
(C)15
(D)18
(E)28
45.The side length of a square inscribed in a circle is 2. What is the area of the circle?
(A)π
(B)
2π
(C)2π
(D)2
2π
(E)π2
46.In the figure shown, if A = 60°, B = C, and BC = 20, then AB =
(A)20
(B)10
2
(C)10
3
(D)20
2
(E)20
3
A
60°
C B
47.Which of the following could be the four angles of a parallelogram?
(I)50°, 130°, 50°, 130°
(II)125°, 50°, 125°, 60°
(III)60°, 110°, 60°, 110°
(A)I only
(B)II only
(C)I and II only
(D)I and III only
(E)I, II and III
108GRE Math Bible
48.In the figure,ABCD is a rectangle and E is a point on the side AB. If AB = 10 and AD = 5, what is the area of the shaded region in the figure?
(A)25
(B)30
(C)35
(D)40
(E)45
A E B
D C
49.What is the area of the equilateral triangle if the base BC = 6?
(A)9
3
(B)18
3
(C)26
3
(D)30
3
(E)36
3
A
C D B
Geometry 109
50.In the figure, ABCD is a square, and OB is a radius of the circle. If BC is a tangent to the circle and PC = 2, then what is the area of the square?
(A)16
(B)20
(C)25
(D)36
(E)42
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51.In the figure shown, AB is a diameter of the circle and O is the center of the circle. If A = (3, 4), then what is the circumference of the circle?
(A)3
(B)4
(C)4π
(D)5π
(E)10π
y-axis
A
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x-axis |
B
110GRE Math Bible
52.A, B, and C are three unequal faces of a rectangular tank. The tank contains a certain amount of water.
When the tank is based on the face A, the height of the water is half the height of the tank. The dimensions of the side B are 3 ft 4 ft and the dimensions of side C are 4 ft 5 ft. What is the measure of the height of the water in the tank in feet?
(A)2
(B)2.5
(C)3
(D)4
(E)5
53.In the figure, if line CE bisects ACB, then x =
(A)45
(B)50
(C)55
(D)65
(E)70
A
40°
D
E
90°
x°
x°
B C
54.In the figure, P =
(A)15°
(B)30°
(C)35°
(D)40°
(E)50°
B
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105° |
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