Q. For a number to be divisible by 10, which of the following must be true?
A.
It must end in 0
B.
It must be a two-digit number
C.
It must be a prime number
D.
It must be even
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Solution
A number is divisible by 10 if it ends in 0.
Correct Answer: A — It must end in 0
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Q. If a number is divisible by 12, which of the following must also be true?
A.
It is divisible by 3
B.
It is divisible by 5
C.
It is divisible by 10
D.
It is a prime number
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Solution
A number divisible by 12 is also divisible by both 3 and 4.
Correct Answer: A — It is divisible by 3
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Q. If a number is divisible by 4, which of the following must also be true?
A.
It is even
B.
It is divisible by 8
C.
It is divisible by 2
D.
It is a multiple of 10
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Solution
Any number divisible by 4 is even, as 4 itself is an even number.
Correct Answer: A — It is even
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Q. If a number is divisible by 7, which of the following is NOT necessarily true?
A.
It is odd
B.
It is not a prime number
C.
It can be a multiple of 14
D.
It can be a two-digit number
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Solution
A number can be divisible by 7 and still be even, such as 14.
Correct Answer: A — It is odd
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Q. If a number is divisible by 8, which of the following must also be true?
A.
It is divisible by 2
B.
It is divisible by 4
C.
It is a multiple of 16
D.
It is a prime number
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Solution
Any number divisible by 8 is also divisible by 4, as 8 is a multiple of 4.
Correct Answer: B — It is divisible by 4
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Q. If a number is divisible by both 2 and 3, which of the following must it also be divisible by?
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Solution
A number divisible by both 2 and 3 is also divisible by their least common multiple, which is 6.
Correct Answer: B — 6
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Q. What is the divisibility rule for 9?
A.
The number must be even
B.
The sum of the digits must be divisible by 9
C.
The last digit must be 0
D.
The number must be a multiple of 3
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Solution
A number is divisible by 9 if the sum of its digits is divisible by 9.
Correct Answer: B — The sum of the digits must be divisible by 9
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Q. Which of the following is a correct application of the divisibility rule for 11?
A.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11
B.
The last digit must be 1
C.
The number must be even
D.
The sum of the digits must be 11
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Solution
For a number to be divisible by 11, the difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11.
Correct Answer: A — The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be divisible by 11
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Q. Which of the following is a correct statement about divisibility by 7?
A.
A number must end in 7
B.
Double the last digit and subtract it from the rest
C.
The sum of the digits must be divisible by 7
D.
A number must be a multiple of 14
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Solution
To check for divisibility by 7, you can double the last digit and subtract it from the rest of the number.
Correct Answer: B — Double the last digit and subtract it from the rest
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Q. Which of the following is a valid divisibility rule for 10?
A.
The number must end in 0
B.
The number must be even
C.
The sum of the digits must be 10
D.
The last digit must be 5
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Solution
A number is divisible by 10 if it ends in 0.
Correct Answer: A — The number must end in 0
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Q. Which of the following numbers is divisible by 11?
A.
121
B.
123
C.
124
D.
125
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Solution
121 is divisible by 11, as 121 = 11 x 11.
Correct Answer: A — 121
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Q. Which of the following numbers is divisible by 8?
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Solution
A number is divisible by 8 if the last three digits form a number that is divisible by 8. 64 is divisible by 8.
Correct Answer: A — 64
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Q. Which of the following numbers is NOT divisible by 12?
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Solution
55 is not divisible by 12, as it does not meet the criteria of being divisible by both 3 and 4.
Correct Answer: C — 55
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Q. Which of the following numbers is NOT divisible by 3?
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Solution
A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 22 (2 + 2 = 4) is not divisible by 3.
Correct Answer: C — 22
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Q. Which of the following statements is true regarding divisibility by 5?
A.
A number must end in 0 or 5
B.
A number must be even
C.
A number must be a multiple of 10
D.
A number must be a prime number
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Solution
A number is divisible by 5 if it ends in either 0 or 5.
Correct Answer: A — A number must end in 0 or 5
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