GRE_Math_Bible_eBook
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Geometry 121
80.Which of following indicates that ∆ABC is a right triangle?
(I)The angles of ∆ABC are in the ratio 1 : 2 : 3.
(II)One of the angles of ∆ABC equals the sum of the other two angles.
(III)∆ABC is similar to the right triangle ∆DEF.
(A)I only
(B)II only
(C)III only
(D)I and II only
(E)I, II, and III
81. In the figure, O is the center of the circle of radius 3, andABCD is a square. If PC = 3 and the side BC of the square is a tangent to the circle, then what is the area of the square ABCD ?
(A)25
(B)27
(C)36
(D)42
(E)56
A B O
P
D C
122GRE Math Bible
82.In the figure shown, ABCDEF is a regular hexagon and AOF is an equilateral triangle. The perimeter of ∆AOF is 2a feet. What is the perimeter of the hexagon in feet?
(A)2a
(B)3a
(C)4a
(D)6a
(E)12a
A B
F C
O
ED
83.The area of the base of a tank is 100 sq. ft. It takes 20 seconds to fill the tank with water poured at rate of 25 cubic feet per second. What is the height in feet of the rectangular tank?
(A)0.25
(B)0.5
(C)1
(D)5
(E)25
84.Point A is 10 miles West of Point B. Point B is 30 miles North of Point C. Point C is 20 miles East of Point D. What is the distance between points A and D?
(A)10
10 miles
(B)10
20 miles
(C)20
10 miles
(D)30
10 miles
(E)30
20 miles
85.Water is poured into an empty cylindrical tank at a constant rate. In 10 minutes, the height of the water increased by 7 feet. The radius of the tank is 10 feet. What is the rate at which the water is poured?
(A)11/8 π cubic feet per minute.
(B)11/3 π cubic feet per minute.
(C)7/60 π cubic feet per minute.
(D)11π cubic feet per minute.
(E)70π cubic feet per minute.
Geometry 123
86.The length of a rectangle is increased by 25%. By what percentage should the width be decreased so that the area of the rectangle remains unchanged?
(A)20
(B)25
(C)30
(D)33.33
(E)50
87.In the rectangular coordinate system shown, ABCD is a parallelogram. If the coordinates of the points A, B, C, and D are (0, 2), (a, b), (a, 2), and (0, 0), respectively, then b =
(A)0
(B)2
(C)3
(D)4
(E)5
B(a, b)
A(0, 2)
C(a, 2)
D(0, 0)
124 GRE Math Bible
88.In the figure, if AB = 10, what is the length of the side CD ?
(A)5
(B)5
3
(C)
10
3
(D)10
(E)10
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89.In the figure, what is the area of ∆ABC if EC/CD = 3 ?
(A)12
(B)24
(C)81
(D)121.5
(E)143
E
3
B
x°
9
x°
A C D
Geometry 125
90.AB and CD are chords of the circle, and E and F are the midpoints of the chords, respectively. The line EF passes through the center O of the circle. If EF = 17, then what is radius of the circle?
(A)10
(B)12
(C)13
(D)15
(E)25
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91. |
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Column A |
The perimeter of rectangle ABCD |
Column B |
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Length of side AB |
is 5/2 times as long as the side AB. |
Length of side BC |
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92.A closed rectangular tank contains a certain amount of water. When the tank is placed on its 3 ft by 4 ft side, the height of the water in the tank is 5 ft. When the tank is placed on another side of dimensions 4 ft by 5 ft, what is the height, in feet, of the surface of the water above the ground?
(A)2
(B)3
(C)4
(D)5
(E)6
93. |
Column A |
Column B |
The clockwise angle made by the hour hand and the minute hand at 12:15pm
The counterclockwise angle made by the hour hand and the minute hand at 12:45pm
94.AC, a diagonal of the rectangle ABCD, measures 5 units. The area of the rectangle is 12 sq. units. What is the perimeter of the rectangle?
(A)7
(B)14
(C)17
(D)20
(E)28
126GRE Math Bible
95.In the figure, ∆ABC is inscribed in the circle. The triangle does not contain the center of the circle O. Which one of the following could be the value of x in degrees?
(A)35
(B)70
(C)85
(D)90
(E)105
A
x°
C B
.O
96.In the figure, ABCD is a square, and BC is tangent to the circle with radius 3. If PC = 2, then what is the area of square ABCD ?
(A)9
(B)13
(C)16
(D)18
(E)25
A B O
P
2
D
C
Geometry 127
97.In the figure, ABCD is a square and BCP is an equilateral triangle. What is the measure of x ?
(A)7.5
(B)15
(C)30
(D)45
(E)60
A B
x° P
y°
D C
98.Column A
The percentage increase in the radius of the park due to the enlargement
A circular park is enlarged uniformly such that it now occupies 21% more land.
Column B
The percentage increase in the area of the park due to the enlargement
99.In the figure, ABCD and ABEC are parallelograms. The area of the quadrilateral ABED is 6. What is the area of the parallelogram ABCD ?
(A)2
(B)4
(C)4.5
(D)5
(E)6
A B
D C E
128GRE Math Bible
100.In the figure, lines l1, l2, and l3 are parallel to one another. Line-segments AC and DF cut the three lines. If AB = 3, BC = 4, and DE = 5, then which one of the following equals DF ?
(A)3/30
(B)15/7
(C)20/3
(D)6
(E)35/3
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C F
101.In the figure, AB is parallel to CD. What is the value of x ?
(A)36
(B)45
(C)60
(D)75
(E)Cannot be determined
E
A B
x° y°
y° |
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C |
D |
Geometry 129
102. |
Column A |
In the figure, P and Q are centers |
Column B |
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of the two circles of radii 3 and 4, |
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respectively. A and B are the |
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points at which a common |
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AB |
tangent touches each circle. |
PQ |
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A
B
Q P
103. |
Column A |
In the figure, ∆ABC is inscribed |
Column B |
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in the circle. The triangle does not |
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x |
contain the center of the circle O. |
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x°
C B
.O
104. |
Column A |
Column B |
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Measure of the largest angle (in |
60 |
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degrees) of a triangle with |
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sides of length 5, 6, and 7 |
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130 GRE Math Bible
Very Hard
105.In the figure, if y = 60, then what is the value of z ?
(A)20
(B)30
(C)55
(D)75
(E)90
x°
z° |
y° |
x°
106.In the figure, ABCD is a rectangle and AF is parallel to BE. If x = 5, and y = 10, then what is the area of ∆AFD ?
(A)2.5
(B)5
(C)12.5
(D)50
(E)50 + 5y
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