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Problem Solving #5
Question #1: If a, b and c are consecutive integers, a < b < c, and a + b + c = 96, what is the value of b?
b = 30
b = 31
b = 32
b = 33
b = 34
Question #2: The price of wheat was $5/bushel on January 2007 and $9/bushel on January 2008. By what percentage did the price change?
10%
40%
60%
80%
90%
Question #3: In the figure below, angle AMB is 100
^{o}
, angle BMD is 40
^{o}
and angle CME is 60
^{o}
. What is the value of angle CMD?
Figure not drawn to scale.
20
^{o}
30
^{o}
40
^{o}
50
^{o}
80
^{o}
Question #4: A vehicle runs from town A to town B at a speed of 20 miles/hour while another vehicle runs from town B to town A at a speed of 60 miles/hour. Both vehicles start their trips at the same time and the distance between towns is 100 miles. How long does it take from the time they start running to the moment they are at the same point on the road?
1 hour
1 hour and 15 minutes
1 hour and 30 minutes
1 hour and 45 minutes
2 hours and 15 minutes
Question #5: Given the list of integers: -2, 2, 0, 6, 8, 0, -5, 9, 10, 4, which of the following statements is true?
mode < median < average
median < mode < average
median < average < mode
mode = median < average
average < median < mode
Question #6: What are the solutions x of the equation a
^{x}
·a
^{1/x}
= 1, x ≠ 0 and a ≠ 1?
x = -1
x = 1
x
_{1}
= 1 and x
_{2}
= -1
The equation does not have real solutions.
x = a
Question #7: If f(x) = |x| and g(x) = x
^{2}
, how many solutions has f(x) = g(x)?
1
2
3
4
The equation does not have real solutions.
Question #8: If a, b and c are the sides of any triangle, which of the following inequalities is not true?
ab > 0
a + b > c
a + c/2 >b
b + c > a
(a + b)·(b + c) > a·c
Question #9: If x + 4y = 6 and x - 2y = 3, which of the following statements is not true?
y = 1/2
x = 4
y = 2
xy = 2
x + y = 9/2
Question #10: Prizes totaling $60,000 were awarded unequally between 3 contestants. Which of the following choices could be the highest prize?
$5,000
$10,000
$15,000
$25,000
$65,000