Q. For a number to be divisible by 11, which of the following must be true?
A.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
B.
The number must be even
C.
The number must end in 1
D.
The sum of the digits must be divisible by 11
Solution
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or 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 0 or divisible by 11
Q. What is the rule for determining if a number is divisible by 11?
A.
The sum of the digits must be even
B.
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
C.
It must end in 1
D.
It must be a prime number
Solution
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is divisible by 11.
Correct Answer:
B
— 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
Q. What is the rule for determining if a number is divisible by 7?
A.
The last digit must be 0
B.
Double the last digit and subtract it from the rest of the number
C.
The sum of the digits must be divisible by 7
D.
The number must end in 7
Solution
To check if a number is divisible by 7, you can double the last digit and subtract it from the rest of the number; if the result is divisible by 7, then the original number is as well.
Correct Answer:
B
— Double the last digit and subtract it from the rest of the number
Q. Which of the following is a characteristic of numbers divisible by 7?
A.
They end in 0 or 5
B.
The double of the last digit subtracted from the rest of the number is divisible by 7
C.
They are always even
D.
They are always prime
Solution
A common rule for checking divisibility by 7 is to double the last digit and subtract it from the rest of the number; if the result is divisible by 7, then the original number is also divisible by 7.
Correct Answer:
B
— The double of the last digit subtracted from the rest of the number is divisible by 7
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
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
