GRE_Math_Bible_eBook
.pdf
Geometry 111
55.The length of a rectangular banner is 3 feet 2 inches, and the width is 2 feet 4 inches. Which one of the following equals the area of the banner?
(A)5 sq. feet
(B)5 1/2 sq. feet
(C)6 1/3 sq. feet
(D)7 sq. feet
(E)7 7/18 sq. feet
56.In the figure, if A = C, then x =
(A)30
(B)60
(C)90
(D)150
(E)180
A
y°/2
x° O
C
y°
D
B
The dimensions in the figure may be different from what they appear to be.
57.Column A
The area of the rectangle when its length is decreased by 4 inches and its width is not changed
The width and length of a rectangle are 6 inches and 12 inches, respectively.
58. |
Column A |
|a| is the distance point a is from |
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the origin on the number line. x ≠ |
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|x| + |–2| |
0. |
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59. |
Column A |
A regular polygon of 24 sides is |
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The perimeter of the polygon |
inscribed in a circle. |
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Column B
The area of the rectangle when its width is decreased by 4 inches and its length is not changed
Column B
|x – 2|
Column B
The circumference of the circle
112 GRE Math Bible
Hard
60.In the figure, lines l and k are parallel. Which one of the following must be true?
(A)a < b
(B)a ≤ b
(C)a = b
(D)a ≥ b
(E)a > b
(b + 30)° |
l |
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O a°
b° |
k |
61.In the figure, lines l and k are parallel. If a is an acute angle, then which one of the following must be true?
(A)b > 10
(B)b > 15
(C)b < 20
(D)b < 30
(E)b > 45
(b + 30)° |
l |
O a°
b° |
k |
62.The diagonal length of a square is 14.1 sq. units. What is the area of the square, rounded to the nearest integer?
(A)96
(B)97
(C)98
(D)99
(E)100
Geometry 113
63.In the figure, ABC and ADC are right triangles. Which of the following could be the lengths of AD and DC, respectively?
(I)
3 and 
4
(II)4 and 6
(III)1 and 
24
(IV) 1 and 
26
(A)I and II only
(B)II and III only
(C)III and IV only
(D)IV and I only
(E)I, II and III only
A
4
B 
D
3
C
64.In the figure, what is the value of x ?
(A)15
(B)30
(C)45
(D)60
(E)75
x°
x°
x°
x°
114 GRE Math Bible
65.In the figure, what is the value of x ?
(A)10°
(B)30°
(C)45°
(D)60°
(E)75°
5 5
5√2
5
5
5
x°
66.If ABCD is a square and the area of ∆AFG is 10, then what is the area of ∆AEC ?
(A)5
(B)
10
2
(C)
10
3
(D)10
(E)20
A B
F
4
G
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Geometry 115
67.In the figure, ABCD is a rectangle, and F and E are points on AB and BC, respectively. The area of ∆DFB is 9 and the area of ∆BED is 24. What is the perimeter of the rectangle?
(A)18
(B)23
(C)30
(D)42
(E)48
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68.In the figure, ABCD is a rectangle. The area of quadrilateral EBFD is one-half the area of the rectangle ABCD. Which one of the following is the value of AD ?
(A)5
(B)6
(C)7
(D)12
(E)15
A B
4
F
E
3
D C
116GRE Math Bible
69.In the figure, ABCD is a rectangle, and the area of quadrilateral AFCE is equal to the area of ∆ABC. What is the value of x ?
(A)5
(B)6
(C)7
(D)12
(E)15
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70.In the figure, ABCD is a rectangle. Points E and F cut the sides BC and CD of the rectangle respectively such that EC = 3, FC = 4, and AD = 12, and the areas of the crossed and the shaded regions in the figure are equal. Which one of the following equals the perimeter of rectangle ABCD ?
(A)42
(B)50
(C)56
(D)64
(E)72
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Geometry 117
71.What is the perimeter of ∆ABC shown in the figure?
(A)2 + 4
2
(B)4 + 2
2
(C)8
(D)4 + 4
2
(E)4 + 4
3
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2z° |
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2 |
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z° |
y° |
y° C |
B x° |
72.In the figure, what is the value of x ?
(A)90
(B)95
(C)100
(D)105
(E)115
x°
4
1
5
1
3 |
1 |
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x° |
118GRE Math Bible
73.In the figure, ABCD is a rectangle. Points P, Q, R, S, and T cut side AB of the rectangle such that AP = 3, PQ = QR = RS = ST = 1. E is a point on AD such that AE = 3. Which one of the following line segments is parallel to the diagonal BD of the rectangle?
(A)EP
(B)EQ
(C)ER
(D)ES
(E)ET
15
A 3 P 1 Q 1 R 1 S 1 T |
B |
3
9 E
D C
The figure is not drawn to scale.
74.In the, figure A, B and C are points on the circle. What is the value of x ?
(A)45
(B)55
(C)60
(D)65
(E)70
B
x°
C
A
75° 35°
O
Geometry 119
75.In the figure, ABCD and PQRS are two rectangles inscribed in the circle as shown and AB = 4, AD = 3, and QR = 4. What is the value of l ?
(A)3/2
(B)8/3
(C)3
(D)4
(E)5
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76.In the figure, ABCD and PQRS are rectangles inscribed in the circle shown in the figure. If AB = 5, AD = 3, and QR = 4, then what is the value of l ?
(A)3
(B)4
(C)5
(D)
15
(E)3
2
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120GRE Math Bible
77.In the figure, ABCD is a rectangle inscribed in the circle shown. What is the length of the arc DC ?
(A)π/4
(B)2π/3
(C)π/2
(D)3π/4
(E)4π/3
A B
4
2
D C
78.Which one of the following relations is true regarding the angles of the quadrilateral shown in figure?
(A)A = C
(B)B > D
(C)A < C
(D)B = D
(E)A = B
3 B
A
4 |
5 |
D 6
C
The figure is not drawn to scale.
79. In a triangle with sides of lengths 3, 4, and 5, the smallest angle is 36.87°. In the figure, O is the center of the circle of radius 5. A and B are two points on the circle, and the distance between the points is 6. What is the value of x ?
(A)36.87
(B)45
(C)53.13
(D)116.86
(E)126.86