GMAT

1. Coordinate Geometry

3. Right triangle PQR is to be constructed in the xy-plane so that the
right angle is at P and PR is parallel to the x-axis. The x and Y
coordinates of P,Q and R are to be integers that satisfy the
inequalities -4≤ X≤ 5 and 6≤ y≤16. How many different triangles
with these properties could be constructed?
A. 110 B. 1100 C. 9900 D. 10000 E. 12100

4. Right triangle PQR is to be constructed in the xy-plane so that the
right angle is at P and PR is parallel to the x-axis. The x and Y
coordinates of P,Q and R are to be integers that satisfy the
inequalities -4≤ X≤ 5 and 6≤ y≤16. How many different triangles
with these properties could be constructed?
A. 110 B. 1100 C. 9900 D. 10000 E. 12100

5. What is the minimum distance between the point (3,4) and
points on the circle x2+y2=1?
A. 1 B. 2 C. 3 D. 4 E. 5

6. What is the minimum distance between the point (3,4) and
points on the circle x2+y2=1?
A. 1 B. 2 C. 3 D. 4 E. 5

7. The figure shows a square. The line y=mx divides the square
evenly. What is m?
A. ½ B. 1/3 C. 2/5 D. 5/6 E. 1

8. The figure shows a square. The line y=mx divides the square
evenly. What is m?
A. ½ B. 1/3 C. 2/5 D. 5/6 E. 1

9. In the coordinate axis above, line segment AC is three times as
long as line segment AB. In addition, segment AC is perpendicular
to segment BD. What is the area of triangle DOB?
A. 4 B. 4√2 C. 6 D. 8
E. It cannot be determined from the information given.

10. In the coordinate axis above, line segment AC is three times as
long as line segment AB. In addition, segment AC is perpendicular
to segment BD. What is the area of triangle DOB?
A. 4 B. 4√2 C. 6 D. 8
E. It cannot be determined from the information given.

11. In the x-y coordinate plane, line k passes through the point (5, -4)
and has a negative x-intercept. Which of the following COULD be
the equation of line k?
i) y = -0.4x – 2 ii) y = 2 - 1.2x iii) y = -0.7x - 1.5
A) i only B) ii only C) iii only D) i & ii only E) i & iii only

12. In the x-y coordinate plane, line k passes through the point (5, -4)
and has a negative x-intercept. Which of the following COULD be
the equation of line k?
i) y = -0.4x – 2 ii) y = 2 - 1.2x iii) y = -0.7x - 1.5
A) i only B) ii only C) iii only D) i & ii only E) i & iii only

13. In the figure above, all the marked angles are some multiple
of x (x is a positive integer). For which value of x must at least
two of the lines be parallel?
A) 8 B) 10 C) 15 D) 18 E) 20

14. In the figure above, all the marked angles are some multiple
of x (x is a positive integer). For which value of x must at least
two of the lines be parallel?
A) 8 B) 10 C) 15 D) 18 E) 20

15. In the rectangular coordinate system shown above, which
quadrant, if any, contains no point (x,y) that satisfies the
inequality 2x−3y≤−6 ?
(A) None (B) I (C) II (D) III (E) IV

16. In the rectangular coordinate system shown above, which
quadrant, if any, contains no point (x,y) that satisfies the
inequality 2x−3y≤−6 ?
(A) None (B) I (C) II (D) III (E) IV

17. What is the smallest possible distance between the point (0, 5)
and any point on the line y=−x+3?
A. 0 B.
1
2
C. 1 D. √2 E. 2

18. What is the smallest possible distance between the point (0, 5)
and any point on the line y=−x+3?
A. 0 B.
1
2
C. 1 D. √2 E. 2

19. Set T consists of all points (x, y) such that x2 + y2 = 1. If point (a, b)
is selected from set T at random, what is the probability that
b > a + 1 ?

20. Set T consists of all points (x, y) such that x2 + y2 = 1. If point (a, b)
is selected from set T at random, what is the probability that
b > a + 1 ?

21. What is the area of the figure bounded by lines described by the
following equations?
y+2=2x
𝑥3
−5
11
=2
𝑦−5
2
=x (x+2)5=0
A. 6 B. 12 C. 17 D. 35 E. 56

22. What is the area of the figure bounded by lines described by the
following equations?
y+2=2x
𝑥3
−5
11
=2
𝑦−5
2
=x (x+2)5=0
A. 6 B. 12 C. 17 D. 35 E. 56

23. What is the least possible distance between a point on the circle
x2+y2=1 and a point on the line y=
3
4
x−3?
A. 1.4 B. 2√2 C. 1.7 D. 3√3 E. 2.0

24. What is the least possible distance between a point on the circle
x2+y2=1 and a point on the line y=
3
4
x−3?
A. 1.4 B. 2√2 C. 1.7 D. 3√3 E. 2.0

25. What are the coordinates of point B in the xy-plane above ?
(A) (6, 12) (B) (6, 28) (C) (8, 20)
(D) (12, 20) (E) (14, 28)

26. What are the coordinates of point B in the xy-plane above ?
(A) (6, 12) (B) (6, 28) (C) (8, 20)
(D) (12, 20) (E) (14, 28)

27. Given the points 𝐴 (2, 9), 𝐵 (−3, 1) and 𝐶 (10, −2), Which of the
following points could be the fourth vertex of parallelogram 𝐴𝐵𝐶
𝐷?
A. (8,−11) B. ( 5,8 ) C. (15,6 )
D. (5,−6) E. None of these.

28. Given the points 𝐴 (2, 9), 𝐵 (−3, 1) and 𝐶 (10, −2), Which of the
following points could be the fourth vertex of parallelogram 𝐴𝐵𝐶
𝐷?
A. (8,−11) B. ( 5,8 ) C. (15,6 )
D. (5,−6) E. None of these.

29. If the coordinates of point A are (2,2) and the coordinates of
point B are (0,-2), what is the equation of the perpendicular
bisector of line segment AB?
(A) y=
1
2
x+5 (B) y= -
1
2
x+3 (C) y= 2x+
3
2
(D) y= -
1
2
x+
1
2
(E) y=
3
2
x -
1
2

30. If the coordinates of point A are (2,2) and the coordinates of
point B are (0,-2), what is the equation of the perpendicular
bisector of line segment AB?
(A) y=
1
2
x+5 (B) y= -
1
2
x+3 (C) y= 2x+
3
2
(D) y= -
1
2
x+
1
2
(E) y=
3
2
x -
1
2

31. In the rectangular coordinate system, points (4, 0) and (– 4, 0)
both lie on circle C. What is the maximum possible value of the
radius of C ?
(A) 2 (B) 4 (C) 8 (D) 16 (E) None of the above

32. In the rectangular coordinate system, points (4, 0) and (– 4, 0)
both lie on circle C. What is the maximum possible value of the
radius of C ?
(A) 2 (B) 4 (C) 8 (D) 16 (E) None of the above

33. In a coordinate system, P = (2, 7) and Q = (2, –3). Which could be
the coordinates of R if PQR is an isosceles triangle?
I. (12, –3) II. (–6, –9) III. (–117, 2)
(A) I only (B) I and II only (C) I and III only
(D) II and III only (E) I, II, and III

34. In a coordinate system, P = (2, 7) and Q = (2, –3). Which could be
the coordinates of R if PQR is an isosceles triangle?
I. (12, –3) II. (–6, –9) III. (–117, 2)
(A) I only (B) I and II only (C) I and III only
(D) II and III only (E) I, II, and III

35. Which of the following points could lie in the same quadrant of
the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?
A. (–b, –a) B. (–a, –b) C. (b, –a) D. (a, –b) E. (–b, a)

36. Which of the following points could lie in the same quadrant of
the xy-coordinate plane as the point (a, b), where ab ≠ 0 ?
A. (–b, –a) B. (–a, –b) C. (b, –a) D. (a, –b) E. (–b, a)

37. A square is drawn in the coordinate plane with its vertices at the points (–2, –2),
(–2, 6), (6, 6), and (6, –2), and a non-vertical line is drawn that passes through the
point (0, 4). The portion of the coordinate plane that lies within the square, but
above the line, is then shaded as shown above. If A is the area of the shaded region
in square units, which of the following specifies all the possible values of A ?
(A) 8 ≤ A ≤ 16 (B) 8 ≤ A < 48 (C) 16 ≤ A< 48
(D) 8 < A ≤ 32 (E) 16 < A ≤ 32

38. A square is drawn in the coordinate plane with its vertices at the points (–2, –2),
(–2, 6), (6, 6), and (6, –2), and a non-vertical line is drawn that passes through the
point (0, 4). The portion of the coordinate plane that lies within the square, but
above the line, is then shaded as shown above. If A is the area of the shaded region
in square units, which of the following specifies all the possible values of A ?
(A) 8 ≤ A ≤ 16 (B) 8 ≤ A < 48 (C) 16 ≤ A< 48
(D) 8 < A ≤ 32 (E) 16 < A ≤ 32

39. 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)

40. 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)

41. 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

42. 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

43. The equation of line n is y =
4
3
x - 100. What is the smallest
possible distance in the xy-plane from the point with coordinates
(0, 0) to any point on line n?
A. 48 B. 50 C. 60 D. 75 E. 100

44. The equation of line n is y =
4
3
x - 100. What is the smallest
possible distance in the xy-plane from the point with coordinates
(0, 0) to any point on line n?
A. 48 B. 50 C. 60 D. 75 E. 100

45. In the xy-plane, what is the area of the region bounded by y +2x
≥ 3, y –x ≥ -6 and the line, that is perpendicular to x = 0 and
passes through the origin?
A.
9
4
B.
27
4
C. 9 D.
27
2
E. Cannot be determined

46. In the xy-plane, what is the area of the region bounded by y +2x
≥ 3, y –x ≥ -6 and the line, that is perpendicular to x = 0 and
passes through the origin?
A.
9
4
B.
27
4
C. 9 D.
27
2
E. Cannot be determined

47. In the figure below, points P and Q lie on the circle with center O.
What is the value of s?
A.
1
2
B. 1 C. √2 D. √3 E.
2
2

48. In the figure below, points P and Q lie on the circle with center O.
What is the value of s?
A.
1
2
B. 1 C. √2 D. √3 E.
2
2

49. Given line L (illustrated in graph), and a parallel line that runs
through point (-1,5), what is the perimeter of a rectangle whose
sides run along the two lines and has a length of 9?
A. 28 B. 9√15 C. 18+2√20 D. 36 E. 45

50. Given line L (illustrated in graph), and a parallel line that runs
through point (-1,5), what is the perimeter of a rectangle whose
sides run along the two lines and has a length of 9?
A. 28 B. 9√15 C. 18+2√20 D. 36 E. 45

51. In a rectangular coordinate system, what is the area of a
quadrilateral whose vertices have the coordinates (2,-2), (2, 6),
(15, 2), (15,-4)?
A. 91 B. 95 C. 104 D. 117 E. 182

52. In a rectangular coordinate system, what is the area of a
quadrilateral whose vertices have the coordinates (2,-2), (2, 6),
(15, 2), (15,-4)?
A. 91 B. 95 C. 104 D. 117 E. 182

53. 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)

54. 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)

55. 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

56. 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

57. If the line ax+by=1, where ab ≠ 0, has its y-intercept greater than
its x-intercept, then which of the following must be true?
I. ab>1 II. a>b III. a>−b
A. I only B. II only C. I and II only D. II and III only E. None

58. If the line ax+by=1, where ab ≠ 0, has its y-intercept greater than
its x-intercept, then which of the following must be true?
I. ab>1 II. a>b III. a>−b
A. I only B. II only C. I and II only D. II and III only E. None

59. A total of m different points are selected on a particular line, and
a total of n different points are selected on another line parallel
to the first, where each of m and n is greater than 1. In how
many different ways can a triangle be made with its vertices at
three of the selected points?
A) m2n+mn2 B) mn(m+n-2) C)
mn(m+n−2)
2
D)
(m+n)(m+n−1)(m+n−2)
6
E)
(m+n)!
m!n!

60. A total of m different points are selected on a particular line, and
a total of n different points are selected on another line parallel
to the first, where each of m and n is greater than 1. In how
many different ways can a triangle be made with its vertices at
three of the selected points?
A) m2n+mn2 B) mn(m+n-2) C)
mn(m+n−2)
2
D)
(m+n)(m+n−1)(m+n−2)
6
E)
(m+n)!
m!n!

61. In the coordinate plane, one of the vertices of a square is the
point (-3, -4). If the diagonals of that square intersect at point (3,
2), what is the area of that square?
A. 36 B. 72 C. 108 D. 144 E. 180

62. In the coordinate plane, one of the vertices of a square is the
point (-3, -4). If the diagonals of that square intersect at point (3,
2), what is the area of that square?
A. 36 B. 72 C. 108 D. 144 E. 180

63. A square is drawn on the xy coordinate plane as shown:
Its center lies at (0, 0). If it is rotated clockwise by 45° around the
center point, what will be the (x, y) coordinates of point D?
A. (−2,0) B. (2,2) C. (−2,2) D. (−√2,−√2) E. (−√2,√2)

64. A square is drawn on the xy coordinate plane as shown:
Its center lies at (0, 0). If it is rotated clockwise by 45° around the
center point, what will be the (x, y) coordinates of point D?
A. (−2,0) B. (2,2) C. (−2,2) D. (−√2,−√2) E. (−√2,√2)

65. Which of the following is NOT a point on the circle of radius 5
and center O as graphed above?
(A) (-1, 2) (B) (8, -1) (C) (0, -5) (D) (6, 3) (E) (7, -6)

66. Which of the following is NOT a point on the circle of radius 5
and center O as graphed above?
(A) (-1, 2) (B) (8, -1) (C) (0, -5) (D) (6, 3) (E) (7, -6)

67. What is the area of the quadrilateral bounded by the lines and
y=
3
4
x+6, y=
3
4
x−6, y=−
3
4
x+6, y=−
3
4
x−6?
(A) 48 (B) 64 (C) 96 (D) 100 (E) 140

68. What is the area of the quadrilateral bounded by the lines and
y=
3
4
x+6, y=
3
4
x−6, y=−
3
4
x+6, y=−
3
4
x−6?
(A) 48 (B) 64 (C) 96 (D) 100 (E) 140

69. The vertices of a rectangle in the standard (x,y) coordinate
place are (0,0), (0,4), (7,0) and (7,4). If a line through (2,2)
partitions the interior of this rectangle into 2 regions that have
equal areas, what is the slope of this line?
A. 0 B.
2
5
C.
4
7
D. 1 E.
7
4

70. The vertices of a rectangle in the standard (x,y) coordinate
place are (0,0), (0,4), (7,0) and (7,4). If a line through (2,2)
partitions the interior of this rectangle into 2 regions that have
equal areas, what is the slope of this line?
A. 0 B.
2
5
C.
4
7
D. 1 E.
7
4

71. A circle is drawn in the xy-coordinate plane. If there are n
different points (x, y) on the circle such that xy = 0, then the
possible values of n are:
a) 0, 1, or 2 b) 0, 2, or 4 c) 0 or 4
d) 0, 2, 3, or 4 e) 0, 1, 2, 3, or 4

72. A circle is drawn in the xy-coordinate plane. If there are n
different points (x, y) on the circle such that xy = 0, then the
possible values of n are:
a) 0, 1, or 2 b) 0, 2, or 4 c) 0 or 4
d) 0, 2, 3, or 4 e) 0, 1, 2, 3, or 4

73. If on the coordinate plane (6,2) and (0,6) are the endpoints of
the diagonal of a square, what is the distance between point
(0,0) and the closest vertex of the square?
A.
1
2
B. 1 C. √2 D. √3 E. 2√3

74. If on the coordinate plane (6,2) and (0,6) are the endpoints of
the diagonal of a square, what is the distance between point
(0,0) and the closest vertex of the square?
A.
1
2
B. 1 C. √2 D. √3 E. 2√3

75. Point P lies on the equation y=x2−1 and Point Q lies on the
equation y=−x2+1. Find the difference between the minimum y
coordinate value of Point P and the maximum y coordinate
value of Point Q.
A. -2 B. -1 C. 0 D. 1 E. 2

76. Point P lies on the equation y=x2−1 and Point Q lies on the
equation y=−x2+1. Find the difference between the minimum y
coordinate value of Point P and the maximum y coordinate
value of Point Q.
A. -2 B. -1 C. 0 D. 1 E. 2

77. A circle centered at (4,-1) intersects the x-axis and y-axis at 2
points each. Three points out of the four intercept points are
taken to form a triangle. If two vertices of the triangle are (0,-8)
and (12,0), which of the following could be the third vertex?
I. (-4,0) II. (0,-6) III. (0,6)
A. I only B. II only C. III only D. I&III only E. I,II & III

78. A circle centered at (4,-1) intersects the x-axis and y-axis at 2
points each. Three points out of the four intercept points are
taken to form a triangle. If two vertices of the triangle are (0,-8)
and (12,0), which of the following could be the third vertex?
I. (-4,0) II. (0,-6) III. (0,6)
A. I only B. II only C. III only D. I&III only E. I,II & III

79. The two adjacent vertices of a quadrilateral are (2, 3), (8, 3). If
the third and the fourth vertices of the quadrilateral are (x, y)
and (a, b), for how many pairs of non negative integer values of
(x, y) and (a, b), the quadrilateral will be a rectangle of area at
least 12 sq. units and at most 30 sq. units?
A. 2 B. 4 C. 5 D. 6 E. >6

80. The two adjacent vertices of a quadrilateral are (2, 3), (8, 3). If
the third and the fourth vertices of the quadrilateral are (x, y)
and (a, b), for how many pairs of non negative integer values of
(x, y) and (a, b), the quadrilateral will be a rectangle of area at
least 12 sq. units and at most 30 sq. units?
A. 2 B. 4 C. 5 D. 6 E. >6

81. Out of all the points on line 3x + 2y = 6, where x & y are integers
and |y| < 12. What is the probability |x| = |y|?
A.
1
3
B.
1
7
C.
2
7
D.
1
2
E.
2
3

82. Out of all the points on line 3x + 2y = 6, where x & y are integers
and |y| < 12. What is the probability |x| = |y|?
A.
1
3
B.
1
7
C.
2
7
D.
1
2
E.
2
3

83. The following figure shows line l: y=2x. If the area of ∆BOC is 8,
what is the area of triangle ∆AOB?
A. 4 B. 6 C. 8 D. 11 E. 13

84. The following figure shows line l: y=2x. If the area of ∆BOC is 8,
what is the area of triangle ∆AOB?
A. 4 B. 6 C. 8 D. 11 E. 13

85. How many points on line with equation
x
13
+
y
52
= 1 have both
non-negative integer coordinates?
(A) 10 (B) 12 (C) 13 (D) 14 (E) Infinite

86. How many points on line with equation
x
13
+
y
52
= 1 have both
non-negative integer coordinates?
(A) 10 (B) 12 (C) 13 (D) 14 (E) Infinite

87. A rectangle ABCD must be constructed on the xy plane so that
the side AB is parallel to the y axis. If the x and y coordinates of
A, B, C, and D are integers between -3 and 6, inclusively, how
many different rectangles can be constructed that satisfy these
properties?
A. 81 B. 100 C. 2,025 D. 10,000 E. 12,100

88. A rectangle ABCD must be constructed on the xy plane so that
the side AB is parallel to the y axis. If the x and y coordinates of
A, B, C, and D are integers between -3 and 6, inclusively, how
many different rectangles can be constructed that satisfy these
properties?
A. 81 B. 100 C. 2,025 D. 10,000 E. 12,100

89. In a rectangular coordinate system, point A has coordinates (d,
d), where d > 0. Point A and the origin form the endpoints of a
diameter of circle C. What fraction of the area of circle C lies
within the first quadrant?
A.
π
π+ 2
B.
π
π+1
C.
2
π
D.
π+2
π
E.
π
π+1

90. In a rectangular coordinate system, point A has coordinates (d,
d), where d > 0. Point A and the origin form the endpoints of a
diameter of circle C. What fraction of the area of circle C lies
within the first quadrant?
A.
π
π+ 2
B.
π
π+1
C.
2
π
D.
π+2
π
E.
π
π+1

91. The equation y=ax2+bx+c represents a parabola in the xy-
plane. If a < 0 and the x-intercepts of the parabola are – 1
and 3, which of the following could be the vertex of the
parabola?
(A) (2,5) (B) (1,-3) (C) (2,3) (D) (1,4) (E) (4,5)

92. The equation y=ax2+bx+c represents a parabola in the xy-
plane. If a < 0 and the x-intercepts of the parabola are – 1
and 3, which of the following could be the vertex of the
parabola?
(A) (2,5) (B) (1,-3) (C) (2,3) (D) (1,4) (E) (4,5)

93. x=3, x=9, x=12−3y, y=−
𝑥
3
+10
The lines created by the four equations above intersect at
four points. What is the area of the quadrilateral created
by those intersections?
A) 12 B) 21 C) 36 D) 49 E) 63

94. x=3, x=9, x=12−3y, y=−
𝑥
3
+10
The lines created by the four equations above intersect at
four points. What is the area of the quadrilateral created
by those intersections?
A) 12 B) 21 C) 36 D) 49 E) 63

95. Rectangle ABCD is constructed in the coordinate plane
parallel to the x- and y-axes. If the x- and y-coordinates of
each of the points are integers which satisfy 3 ≤ x ≤ 11
and -5 ≤ y ≤ 5, how many possible ways are there to
construct rectangle ABCD?
A. 396 B. 1260 C. 1980 D. 7920 E. 15840

96. Rectangle ABCD is constructed in the coordinate plane
parallel to the x- and y-axes. If the x- and y-coordinates of
each of the points are integers which satisfy 3 ≤ x ≤ 11
and -5 ≤ y ≤ 5, how many possible ways are there to
construct rectangle ABCD?
A. 396 B. 1260 C. 1980 D. 7920 E. 15840

97. In the figure above, how many of the points on line
segment PQ have coordinates that are both integers?
(A) 5 (B) 8 (C) 10 (D) 11 (E) 20

98. In the figure above, how many of the points on line
segment PQ have coordinates that are both integers?
(A) 5 (B) 8 (C) 10 (D) 11 (E) 20

99. The set P contains the points (x, y) on the coordinate
plane that are in or on circle O. The values of x and y are
integers. Circle O is centered at the origin and has a radius
of 3. If a point from set P is randomly selected, what is the
probability that the point is located on the circumference
of circle O?
A.
4
29
B.
4
28
C.
4
27
D.
4
19
E.
2
9

100. The set P contains the points (x, y) on the coordinate
plane that are in or on circle O. The values of x and y are
integers. Circle O is centered at the origin and has a radius
of 3. If a point from set P is randomly selected, what is the
probability that the point is located on the circumference
of circle O?
A.
4
29
B.
4
28
C.
4
27
D.
4
19
E.
2
9

101. A rectangle ABCD is to be constructed on the XY plane so
that AB is || to the y axis ; if the X and Y co-ordinates of
A,B,C & D are integers between -3 to 6 ; How many
different rectangles can be constructed ?
A) 81 B) 100 C) 2025 D) 10000 E) 12100

102. A rectangle ABCD is to be constructed on the XY plane so
that AB is || to the y axis ; if the X and Y co-ordinates of
A,B,C & D are integers between -3 to 6 ; How many
different rectangles can be constructed ?
A) 81 B) 100 C) 2025 D) 10000 E) 12100

103. Line k passes through the points (6,2) and P and has a
slope of −
3
5
, . If the line that passes through the origin and
point P has a slope of –2, which of the following are the
xy-coordinates for point P ?
A. (−
40
7
,
80
7
) B. (-4,8) C. (-3,6) D. (
11
5
,−
22
5
) E. (
28
13
,−
56
13
)

104. Line k passes through the points (6,2) and P and has a
slope of −
3
5
, . If the line that passes through the origin and
point P has a slope of –2, which of the following are the
xy-coordinates for point P ?
A. (−
40
7
,
80
7
) B. (-4,8) C. (-3,6) D. (
11
5
,−
22
5
) E. (
28
13
,−
56
13
)

105. Line M has a y-intercept of –4, and its slope must be an
integer-multiple of
1
7
. Given that Line M passes below
(4, –1) and above (5, –6), how many possible slopes could
Line M have?
(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

106. Line M has a y-intercept of –4, and its slope must be an
integer-multiple of
1
7
. Given that Line M passes below
(4, –1) and above (5, –6), how many possible slopes could
Line M have?
(A) 6 (B) 7 (C) 8 (D) 9 (E) 10

107. How many points (x, y) lie on the line segment between
(22, 12
2
3
) and (7, 17
2
3
) such that x and y are both integers?
A. 4 B. 5 C. 7 D. 8 E. 9

108. How many points (x, y) lie on the line segment between
(22, 12
2
3
) and (7, 17
2
3
) such that x and y are both integers?
A. 4 B. 5 C. 7 D. 8 E. 9

109. The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a
triangle. If angle ABC = 90, what is the area of triangle
ABC?
A. 102 B. 120 C. 132 D. 144 E. 156

110. The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a
triangle. If angle ABC = 90, what is the area of triangle
ABC?
A. 102 B. 120 C. 132 D. 144 E. 156

111. In the coordinate plane, a circle with its center on the
negative x-axis has a radius of 12 units, and passes
through (0, 6) and (0, – 6). What is the area of the part of
this circle in the first quadrant?
(A) 6π−12√3 (B) 12π−12√3 (C) 12π−18√3
(D) 24π−18√3 (E) 24π−36√3

112. In the coordinate plane, a circle with its center on the
negative x-axis has a radius of 12 units, and passes
through (0, 6) and (0, – 6). What is the area of the part of
this circle in the first quadrant?
(A) 6π−12√3 (B) 12π−12√3 (C) 12π−18√3
(D) 24π−18√3 (E) 24π−36√3

113. In the coordinate plane, a circle with its center on the negative x-
axis has a radius of 12 units, and passes If coordinates of two of
the vertices of a square are (6, 6) and (12, 0), the other two
coordinates Can be.
I. (0, 0) and (6, -6) II. (18, 6) and (12, 12) III. (6, 0) and (12, 6)
A. I Only B. I and II only C. I and III only
D. II and III only E. I, II, and III

114. In the coordinate plane, a circle with its center on the negative x-
axis has a radius of 12 units, and passes If coordinates of two of
the vertices of a square are (6, 6) and (12, 0), the other two
coordinates Can be.
I. (0, 0) and (6, -6) II. (18, 6) and (12, 12) III. (6, 0) and (12, 6)
A. I Only B. I and II only C. I and III only
D. II and III only E. I, II, and III

115. Line P is described by the equation 3x+2y−4=0. Which of the
following lines is parallel to P and has the same x-intercept as the
line 5x−y+10=0?
A. 6x=−4y+8 B. −y=
3
2
x+5 C. 3y=(−
9
2
)x−9
D. 4x+6y+8=0 E. 6x−4y=−12

116. Line P is described by the equation 3x+2y−4=0. Which of the
following lines is parallel to P and has the same x-intercept as the
line 5x−y+10=0?
A. 6x=−4y+8 B. −y=
3
2
x+5 C. 3y=(−
9
2
)x−9
D. 4x+6y+8=0 E. 6x−4y=−12