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Unit 1
Practice Quiz 1
Answer Key
If n is a negative integer, what is the
ordering of p, t, and r from greatest
to least?
p = n2 – 2.1 ; t = n3 – 2.1 ; r = (n – 2.1)2
1
Substitute: n = –1
p = (–1)2 – 2.1 t = (–1)3 – 2.1 r = (–1 – 2.1)2
p = 1 – 2.1
t = –1 – 2.1 r = (–3.1)2
p = –1.1
t = –3.1
r>p>t
r = 9.61
2
If x, y, and z are three prime
numbers, and 19 < x < y < z < 35,
find x + y – z.
x = 23 , y = 29 , z = 31
x + y – z
23 + 29 – 31
52 – 31
21
3
When 32 is divided by an integer, the
remainder is 4. When 51 is divided by the
same integer, the remainder is 2. What is
the largest integer for which this is true?
Try E. 18
32  18 = 1
R: 14
18 not answer
Try D. 9
32  9 = 3
R: 5
9 not answer
Try C. 7
32  7 = 4
R: 4
7 works for 32
Try C. 7
51  7 = 7
R: 2
7 works for 51
Answer C. 7
4
Two prime numbers whose sum
is 32 are
A. 7, 25
25 is not a prime number
B. 11, 21
21 is not a prime number
C. 13, 19
13 + 19 = 32
D. 17, 15
15 is not a prime number
E.
5, 27
27 is not a prime number
5
If each of the integers 5, 3, and 2 is used
only once in the expression (a – b)  c,
then what is the largest possible value?
(a – b)  c
(3 – 2)  5
(1)  5
5
(5 – 3)  2
(2)  2
4
(5 – 2)  3
(3)  3
9
6 A large school bus holds 40 students. A small
bus holds 25 students. How many small buses
are needed to hold the number of students
accommodated by 5 large buses?
Large Bus
40 students
5 Large Buses
5  40 students
200 students
Small Bus
25 students
How many small buses
are needed for
200 students?
200  25 = 8 buses
7
If 24 is written as the product of three
integers, each of which is greater than 1,
what could be the largest sum of those
three integers?
Product
Sum
2  3  4 = 24
2+3+4 = 9
2  2  6 = 24
2 + 2 + 6 = 10
8
What digit does R represent?
4RS
+ RR7
QPQP
4RS
+ RR7
1 P 1P
Step 1: Q = 1
The number 1 must
carry over from the
previous column.
Rewrite problem
8
What digit does R represent?
1
4RS
+ RR7
1 P 1P
11
45S
+ 557
1 P1 P
Step 2: Carry a 1 from
the units column.
Step 3: R = 5
R + R + 1 = 11
Carry a 1 to the
hundreds column.
9
What is the value of P ?
PQ
 R8
184
92 .
1104
8  PQ = 184
184  8 = PQ
184  8 = 23
So, PQ = 23
P = 2 and Q = 3
10
What is the value of R ?
23
 R8
184
92 .
1104
From the previous question, the
problem now looks like this.
R  23 = 92
92  23 = R
92  23 = 4
So, R = 4
11
P is a two-digit number. Q is a two-digit
number, with P’s digits reversed. What is the
largest possible value of P so that P and Q
fit the given description and also have a
difference of 54?
Try E. 97 P: 97
Q: 79
Difference
97 – 79 = 18
Try D. 96 P: 96
Q: 69
96 – 69 = 27
Try C. 93 P: 93
Q: 39
93 – 39 = 54 YES
NO
NO
12 110 freshmen participated in sports or clubs
or both. 55 are involved in sports and 68
are involved in clubs. How many students
are involved in both sports and clubs?
Sports
Clubs
55
68
Total
= sports + clubs = 55 + 68 = 123
Involved
12 110 freshmen participated in sports or clubs
or both. 55 are involved in sports and 68
are involved in clubs. How many students
are involved in both sports and clubs?
Total
Involved
= 123
Sports
55
Clubs
13
68
Both sports and clubs = 123 – 110 = 13
13 110 freshmen participated in sports or clubs
or both. 55 are involved in sports and 68
are involved in clubs. How many students
are involved in just sports?
Total
Involved
= 123
Sports
55
Clubs
13
68
Just Sports = Sports – Both = 55 – 13 = 42
13 110 freshmen participated in sports or clubs
or both. 55 are involved in sports and 68
are involved in clubs. How many students
are involved in just sports?
Total
Involved
= 123
Sports
42
Clubs
13
55
Just Sports = Sports – Both = 55 – 13 = 42
14
In a hospital parking lot, the rate is $1.50 for
the first 2 hours and $0.75 for each additional
hour or part of an hour. What does it cost to
park a car for 4 hours and 15 minutes?
2 Hours
3 Hours
4 Hours
15 Minutes
Total
$1.50
$0.75
$0.75
$0.75
$3.75
15
A.
B.
C.
D.
E.
If x is an even integer, which of the following
would represent an odd integer?
–x
x2 – 2
x–1
x2
(x + 2)2
x2
A. (4)2 – (4)
16 – 4
12
No
B. (4)2 – 2
16 – 2
14
No
C. (4) – 1 = 3 Yes
16
A.
B.
C.
D.
E.
If a is a positive integer and b is a
negative integer, which of the following
must be positive?
a=2
b = –4
a–b
A.
2
–
(–4)
=
2
+
4
=
6
a+b
B. 2 + (–4) = –2
ab
ab
C. 2  (–4) = –8
a2b
D. 2  (–4) = –0.5
E. (2)2(–4) = 4(–4) = –16
17
If a, b, and c are consecutive integers
and abc = 0, then what is the smallest
possible sum of these integers?
012=0
Sum
0+1+2=3
–1  0  1 = 0
–1 + 0 + 1 = 0
–2  –1  0 = 0
–2 + –1 + 0 = –3
18
How many odd numbers lie between
20
51
an d
?
3
5
20
 6.67
3
Odd Integers
between
Answer: 2
51
 10.2
5
7 and 9
19 If the product of five integers is an even
integer, what is the least number of
integers that must be even?
23579
Answer: 1
20 If N is an odd or even integer, which
of the following will always be an
even integer?
Substitute odd
integer
2(3 + 1)
Substitute even
integer
2(4 + 1)
2(5)
10
2(4)
8
Answer: 2(N + 1)
21
What is the least common multiple of
12 and 16?
Multiples of 12: 12, 24, 36, 48, 60, …
Multiples of 16: 16, 32, 48, 64, …
Least Common Multiple = 48
22
What is the greatest common factor
of 84 and 77?
Factors of 84: 1, 2, 3, 4, 7, 12, 21, 28, 42, 84
Factors of 77: 1, 7, 11, 77
Greatest Common Factor = 7