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Question 1
The sum of three consecutive integers is four times the
first integer. What is the last of the three integers?
A 5
B 4
C 3
D 2
E 1
Question 2
What is the value of 1/2 + 1/4 + 1/8?
A 3/8
B 2/4
C 5/8
D 3/4
E 7/8
Question 3
What is the average (arithmetic mean) of the following
five numbers: -8, -6, 3, 7, and 19?
A 1.0
B 1.6
C 2.0
D 2.6
E 3.0
Question 4
The product of 89 and 91 is closest to
A 810
B 900
C 8000
D 8100
E 18000
Question 5
Set S = {-2, -1, 1, 2}
Set T = {-2, -1, 0, 1, 2}
What is the value of the mean of set S minus the mean
of set T?
A -2
B -4/5
C 0
D 4/5
E 1
Question 6
What is 10,000 divided by 6, when rounded off to the nearest
whole number?
A 1667
B 167
C 1666
D 16.67
E 166.7
Question 7
What is the value of 31/2 + 7/4 + 6/8?
A 6.25
B 6.0
C 5.5
D 4.75
E 4.0
Question 8
If 5/25 is added to 421.467, what is the result?
A 421.469
B 421.487
C 421.667
D 421.967
E 423.467
Question 9
One box of pop tarts costs 1.73 dollars. If purchasing
more than 10 boxes, each box costs 1.53 dollars. How many
dollars are saved by purchasing 54 boxes of pop tarts all
at once rather than one at a time?
A 5.40
B 8.80
C 10.80
D 12.40
E 16.20
Question 10
A class is divided so that one fifth of students take
auto shop and the rest take woodwork. If one student moves
from the woodwork group to the auto shop group, what is
the percentage of students in the class taking auto shop?
A 19
B 20
C 21
D 25
E There is not enough information to solve the problem.
Question 11
What is the first integer larger than the positive square
root of 39?
A 5
B 6
C 7
D 8
E 9
Question 12
If a = 3 and b = 4, what is the value of |a| - |b| + |a
- b| ?
A 8
B 7
C 3
D 1
E 0
Question 13
3a + b = 11. What is the value of 9a + 3b?
A 22
B 24
C 30
D 32
E 33
Question 14
If a is positive, and if a1/2 is greater than a, then
what is one possible value for a?
A 0.0
B 0.5
C 1.0
D 1.5
E 4.0
Question 15
Let x@y be defined for all x,y as 3x + 2y
What is the value of 9@4?
A 30
B 32
C 35
D 38
E 40
Question 16
Let u^v be defined for all u,v as
u2 - v2
What is the value of 5^3?
A 16
B 20
C 25
D 32
E 36
Question 17
How many positive integers less than 62 have 8 as a factor?
A 9
B 8
C 7
D 6
E 2
Question 18
What is 5% of y if y = 6500/5?
A 0.65
B 6.5
C 65
D 500
E 650
Question 19
What is the value of 2*5*2*5*2*5*2*5?
A 100
B 625
C 1000
D 10,000
E 15,000
Question 20
What is the value of 
?
A 1,000,000
B 100,000
C 10,000
D 1,000
E 100
ANSWERS
1. A
The most direct way to solve this is to write out a mathematical
expression that represents the statement.
Let n be the first integer. Then n + (n + 1) + (n + 2) =
4n. Solving for n we get 3n + 3 = 4n, or equivalently, n
= 3 . So the sequence is 3, 4, 5 , and 5 is the correct
answer.
2. E
It all works out when you have everything over a common
denominator.
1/2 = 4/8 and 1/4 = 2/8 , so the final answer is (4 + 2
+ 1)/8 = 7/8
3. E
There are 5 numbers in this sequence, so the average will
be the total of all the sums in the sequence divided by
5. The sum of all the numbers (-8 + -6 + 3 + 7 +19) is 15,
so the average must be 15/5, or 3.
4. D
It's a valuable skill to be able to make quick judgments
about numbers. In this case, it should be clear that 89
and 91 are very close to 90, so a rough approximation is
90*90 = 8100. More generally, the product of 89 and 91 can
be rewritten:
(90 -1)*(90+1) = 902 - 1 = 8100 - 1 = 8099.
5. C
The mean is the sum of the elements of the set divided by
the number of elements in the set. For both sets the sum
of the elements is zero, therefore the mean of both sets
is zero. It follows that there is no difference between
the means.
6. A
10,000/6 = 1666.66667. The nearest whole number requires
rounding up, so the answer is 1667.
7. B
Changing the fractions to decimals, becomes:
3.5 + 1.75 + 0.75 = 6.0. This is a logical way to solve
this problem as the responses were all given in decimals.
8. C
You're right. 5/25 = 0.20. So when this is added to 421.467,
the result is 421.667.
9. C
When purchasing all at once, we save 0.20 dollars per box.
Since we buy 54 boxes, we save (0.20)(54)=10.80 dollars.
10. E
In order to calculate a percentage, you need to know the
total. Without the total, it is impossible to know what
the new percentage is when one student moves into the auto
group. We know that originally it was 20%, but we cannot
figure out the new percentage unless we know how many students
there are in the whole class.
11. C
You just need to interpret the question correctly. The positive
square root of 39 will be slightly larger than 6, because
the square root of 36 is 6. So the next largest integer
is 7. (And you know that the square root of 39 must be less
than the square root of 49 which is 7.)
12. E
Just fill in the values for a and b and carry out the operations.
|3| - |4| + |3 - 4| = 3 - 4 + 1 = 0.
13. E
(9a + 3b) can be rewritten as (3)(3a + b).
3×11 = 33.
14. B
If a number is between 0 and 1, then the square root of
that number is greater than the number itself. The square
root of 0.5 is 0.7071. For all other positive values, the
square root of a is either equal to or less than a.
15. C
9@4 is 9*3 + 4*2 = 27 + 8 = 35.
16. A
Twenty five minus nine gives sixteen. Notice that the difference
of two perfect squares gave a third perfect square. That
because 3-4-5 are the side lengths of a right triangle and
the Pythagorean Theorem gives 32+42=52.
17. C
The first thing to notice is that 8*8 = 64. So the number
has to be less that 8. But 8*7 = 56, which is less than
62. That means that there are 7 positive integers less than
62 with 8 as a factor.
18. C
First you find that y = 1300. Then, you can multiply 1300
by 0.05, or you can multiply it by 1/20. Either way you
get the correct answer: 65.
19. D
Not hard to do on a calculator, or if you take your time
doing it out by hand. But the quickest way is to rewrite
the question to get:
24*54 = 104 = 10,000
20. D
The number inside the radical is 106 = 1,000,000. If you
know that 1000 is the square root of one million you're
done. You might notice that taking the square root of a
number is equivalent to raising it to the power 1/2.
So (106)1/2 = 103 = 1000.
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