Q. Which of the following is a necessary condition for a number to be divisible by 7?
A.
The last digit must be 0
B.
The number must be even
C.
Double the last digit and subtract it from the rest of the number
D.
The sum of the digits must be divisible by 7
Solution
To check for divisibility 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 also divisible by 7.
Correct Answer:
C
— Double the last digit and subtract it from the rest of the number
Q. Which of the following is a rule for determining if a number is divisible by 11?
A.
The sum of the digits is even
B.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or a multiple of 11
C.
It ends in 1
D.
It is a multiple of 10
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 a multiple of 11.
Correct Answer:
B
— The difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or a multiple of 11
Q. Which of the following is a rule for divisibility by 11?
A.
The last digit 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 0 or divisible by 11
C.
The number must end in 1
D.
The number must be a two-digit number
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 0 or 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 0 or divisible by 11
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. 9 is not prime as it can be divided by 3.
Q. Which of the following numbers is NOT divisible by 11?
A.
121
B.
132
C.
143
D.
154
Solution
To check divisibility by 11, subtract the last digit from the rest of the number. For 154, 15 - 4 = 11, which is divisible by 11. The others are divisible.
