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