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Problem Solving #3
Question #1: In the x,y plane, which of the following statements are true?
I. Line y + x = 5 is perpendicular to line y - x = 5.
II. Lines y + x = 5 and y - x = 5 intersect each other on the y axis.
III. Lines y + x = 5 and y - x = 5 intersect each other on the x axis.
I and III are both true.
I is the only true statement.
II is the only true statement.
I and II are both true.
Question #2: If
a
is an integer chosen randomly from the set {3, 5, 6, 9} and
b
is an integer chosen randomly from the set {2, 3, 4}, what is the probability that a/b is an integer?
.125
.250
.333
.5
.55
Question #3: What is the value of integer
a
, if x = 2 is a solution of the equation √(a + x) = 2·x?
a = 10
a = 12
a = 14
a = 16
a = 18
Question #4: What is the value of (3
x + 1
- 3
x
) / (3
x
- 3
x - 1
)?
6
3
x
3
x + 1
3
x - 1
3
Question #5:Two diameters of a circle create an angle AOB of 45
o
between them. What is the length of arc AB if the radius of the circle is 10/¶?
5/2
3/2
2
4
6
Question #6: A bus travels from town A to town B for 2 hours at a speed of 60 miles/hour. The bus stops in town B for 2 hours and then travels from town B to town C for 1 hour, at a speed of 50 miles/hour. What is the average speed of the bus?
30miles/hour
31miles/hour
32miles/hour
34miles/hour
40miles/hour
Question #7: If a·b + b·c + c·a = 0, what is (a + b)
2
+ (b + c)
2
+ (c + a)
2
?
a
2
+ b
2
+ c
2
2·(a
2
+ b
2
+ c
2
)
(a
2
+ b
2
+ c
2
)/2
a
2
+ a + b
2
+ b + c
2
+c
(a + b + c)/2
Question #8:
Column A
Column B
x
2
+ 1
x + 1
The quantity in Column A is greater then the quantity in Column B.
The quantity in Column B is greater then the quantity in Column A.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question #9:
2·m - n = 4
m + 2·n = 12
Column A
Column B
(m + n)
2
61
The quantity in Column A is greater then the quantity in Column B.
The quantity in Column B is greater then the quantity in Column A.
The two quantities are equal.
The relationship cannot be determined from the information given.
Question #10: If a and b are positive integers and a·b = 200, which of the following can be the sum a + b?
40
46
33
55
50
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