SAT Math Hard Practice Quiz
Numbers and Operations
1.
A bag contains tomatoes that are either green or red.
The ratio of green tomatoes to red tomatoes in the bag
is 4 to 3. When five green tomatoes and five red tomatoes
are removed, the ratio becomes 3 to 2. How many red
tomatoes were originally in the bag?
(A)
12
(B)
15
(C)
18
(D)
24
(E)
30
2.
If each digit in an integer is greater than the digit to the
left, the integer is said to be “monotonic”. For example,
12 is a monotonic integer since 2
>
1. How many positive
two-digit monotonic integers are there?
(A)
28
(B)
32
(C)
36
(D)
40
(E)
44
a
, 2
a
−
1, 3
a
−
2, 4
a
−
3,
. . .
3.
For a particular number
a
, the first term in the sequence
above is equal to
a
, and each term thereafter is 7 greater
than the previous term. What is the value of the 16
th
term in the sequence?
4.
If
p
is a prime number, how many factors does
p
3
have?
(A)
One
(B)
Two
(C)
Three
(D)
Four
(E)
Five
5.
How many integers between 10 and 500 begin and end in
3 ?
6.
A particular integer
N
is divisible by two different prime
numbers
p
and
q
. Which of the following must be true?
I.
N
is not a prime number.
II.
N
is divisible by
pq
.
III.
N
is an odd integer.
(A)
I only
(B)
II only
(C)
I and II only
(D)
I and III only
(E)
I, II, and III
7.
A perfect square is an integer that is the square of an
integer. Suppose that
m
and
n
are positive integers such
that
mn >
15. If 15
mn
is a perfect square, what is the
least possible value of
mn
?
8.
M
is a set of six consecutive even integers. When the
least three integers of set
M
are summed, the result is
x
.
When the greatest three integers of set
M
are summed,
the result is
y
. Which of the following is true?
(A)
y
=
x
−
18
(B)
y
=
x
+ 18
(C)
y
= 2
x
(D)
y
= 2
x
+ 4
(E)
y
= 2
x
+ 6
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pg. 1