Q. If a number is a factor of 36, which of the following numbers is NOT a factor?
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Solution
All options are factors of 36 except for 9, which is a factor but not a multiple of 4.
Correct Answer: D — 9
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Q. If a number is a multiple of 9, which of the following must also be true?
A.
It is a multiple of 3.
B.
It is a multiple of 27.
C.
It is a prime number.
D.
It is an even number.
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Solution
All multiples of 9 are also multiples of 3.
Correct Answer: A — It is a multiple of 3.
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Q. If a number is a multiple of both 4 and 6, which of the following must it also be a multiple of?
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Solution
The least common multiple of 4 and 6 is 12, so any multiple of both must also be a multiple of 12.
Correct Answer: A — 12
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Q. If a number is a multiple of both 7 and 9, which of the following numbers is a possible candidate?
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Solution
63 is a multiple of both 7 (7x9) and 9 (9x7).
Correct Answer: A — 63
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Q. If a number is divisible by both 3 and 5, which of the following must also be true?
A.
It is divisible by 15
B.
It is divisible by 8
C.
It is divisible by 10
D.
It is not divisible by 6
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Solution
A number divisible by both 3 and 5 is also divisible by their LCM, which is 15.
Correct Answer: A — It is divisible by 15
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Q. If a number is divisible by both 8 and 12, which of the following must it also be divisible by?
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Solution
The least common multiple of 8 and 12 is 24, so the number must be divisible by 24.
Correct Answer: B — 24
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Q. If the least common multiple (LCM) of two numbers is 60 and their greatest common divisor (GCD) is 12, what is the product of the two numbers?
A.
720
B.
180
C.
120
D.
60
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Solution
The product of two numbers is equal to the product of their LCM and GCD. Therefore, 60 * 12 = 720.
Correct Answer: A — 720
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Q. If the product of two consecutive integers is 72, which of the following pairs could represent these integers?
A.
8 and 9
B.
6 and 7
C.
5 and 6
D.
9 and 10
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Solution
6 and 7 are consecutive integers whose product is 42, not 72.
Correct Answer: B — 6 and 7
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Q. If the product of two numbers is a multiple of 15, which of the following must be true?
A.
At least one of the numbers is a multiple of 3.
B.
At least one of the numbers is a multiple of 5.
C.
Both numbers are even.
D.
Both numbers are odd.
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Solution
For the product to be a multiple of 15, at least one of the numbers must be a multiple of 5.
Correct Answer: B — At least one of the numbers is a multiple of 5.
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Q. If the sum of two multiples of 7 is 56, which of the following pairs could represent these multiples?
A.
21 and 35
B.
14 and 42
C.
28 and 28
D.
All of the above.
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Solution
All pairs listed are multiples of 7 that sum to 56.
Correct Answer: D — All of the above.
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Q. In a certain number system, the number 12 is represented as 'A' and the number 18 as 'B'. If 'A' is a factor of 'B', which of the following statements is true?
A.
A is greater than B
B.
B is a multiple of A
C.
A and B are equal
D.
A is a multiple of B
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Solution
'B' (18) is a multiple of 'A' (12) since 18 can be expressed as 12 multiplied by 1.5.
Correct Answer: B — B is a multiple of A
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Q. In a certain number, if 12 is added to it, the result is a multiple of 5. What can be inferred about the original number?
A.
It is a multiple of 5.
B.
It is a multiple of 12.
C.
It is one less than a multiple of 5.
D.
It is one more than a multiple of 5.
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Solution
If the original number is x, then x + 12 is a multiple of 5. This implies that x must be one more than a multiple of 5.
Correct Answer: D — It is one more than a multiple of 5.
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Q. In a classroom, the teacher wants to arrange students in rows such that each row has the same number of students. If there are 24 students, which of the following arrangements is NOT possible?
A.
6 rows of 4 students
B.
8 rows of 3 students
C.
12 rows of 2 students
D.
5 rows of 5 students
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Solution
5 rows of 5 students would require 25 students, which is not possible with only 24 students.
Correct Answer: D — 5 rows of 5 students
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Q. In a sequence of numbers where each number is a multiple of 3, which of the following cannot be a member of this sequence?
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Solution
22 is not a multiple of 3, while 9, 15, and 27 are.
Correct Answer: C — 22
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Q. Which of the following is the best definition of a factor?
A.
A number that can divide another number without leaving a remainder.
B.
A number that is a multiple of another number.
C.
A number that is less than another number.
D.
A number that is greater than one.
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Solution
A factor is defined as a number that divides another number without leaving a remainder.
Correct Answer: A — A number that can divide another number without leaving a remainder.
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Q. Which of the following is the greatest common divisor (GCD) of 48 and 180?
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Solution
The GCD of 48 and 180 is 12, as it is the largest number that divides both without a remainder.
Correct Answer: A — 12
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Q. Which of the following numbers is a multiple of both 4 and 6?
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Solution
12 is the smallest number that is a multiple of both 4 and 6.
Correct Answer: A — 12
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Q. Which of the following statements about multiples is true?
A.
The multiples of a number are infinite.
B.
The multiples of a number are always positive.
C.
The first multiple of any number is the number itself.
D.
All of the above.
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Solution
All statements are true regarding multiples.
Correct Answer: D — All of the above.
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Q. Which of the following statements about the number 30 is true?
A.
It is a prime number
B.
It has exactly 4 factors
C.
It is a multiple of 5
D.
It is not a composite number
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Solution
30 is a multiple of 5, as it can be expressed as 5 multiplied by 6.
Correct Answer: C — It is a multiple of 5
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Q. Which of the following statements is logically consistent with the definition of a multiple?
A.
A multiple of a number is always greater than the number itself.
B.
A multiple of a number can be negative.
C.
A multiple of a number is always an integer.
D.
All of the above.
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Solution
All statements are true; multiples can be negative, can be equal to the number, and are always integers.
Correct Answer: D — All of the above.
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