State whether the following statement is True or False
If a number exactly divides the sum of two numbers,it must exactly divide the two numbers separately

True

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False

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Solution

The correct option is B False
Finding if a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately or not:
Lets take a number $2$ and sum as $11 + 3 = 14$
As we can see clearly that $2$ divides $14$ but $2$ cannot divide $11$ and $3$
Lets take another number $3$ and sum as $16 + 2 = 18$
As we can see clearly that $3$ divides $18$ but $3$ cannot divide $16$ and $2$
Hence, if a number divides the sum of two numbers, then it will not always divide the numbers separately
Hence, the given statement is False.

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In the following question, state whether the given statement is true (T) or false (F).
If a number exactly divides the sum of three numbers, it must exactly divide the numbers separately.

If a number exactly divides two numbers separately, it must exactly divide their sum.

Question 79

In the following question, state whether the given statement is true (T) or false (F).
If a number divides three numbers exactly, it must divide their sum exactly.

Q. Write (T) for true and (F) for false against each of the following statements:
(i) If a number is divisible by 4, it must be divisible by 8.
(ii) If a number is divisible by 8, it must be divisible by 4.
(iii) If a number divides the sum of two numbers exactly, it must exactly divide the numbers separately.
(iv) If a number is divisible by both 9 and 10, it must be divisible by 90.
(v) A number is divisible by 18 if it is divisible by both 3 and 6.
(vi) If a number is divisible by 3 and 7, it must be divisible by 21.
(vii) The sum of two consecutive odd numbers is always divisible by 4.
(viii) If a number divides two numbers exactly, it must divide their sum exactly.

Q. Which of the following statements are true?

(i) If a number is divisible by 3, it must be divisible by 9.
(ii) If a number is divisible by 9, it must be divisible by 3.
(iii) If a number is divisible by 4, it must be divisible by 8.
(iv) If a number is divisible by 8, it must be divisible by 4.
(v) A number is divisible by 18, if it is divisible by both 3 and 6.
(vi) If a number is divisible by both 9 and 10, it must be divisible by 90.
(vii) If a number exactly divides the sum of two numbers, it must exactly divide the numbers separately.
(viii) If a number divides three numbers exactly, it must divide their sum exactly.
(ix) If two numbers are co-prime, at least one of them must be a prime number
(x) The sum of two consecutive odd numbers is always divisible by 4.

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State whether the following statement is True or FalseIf a number exactly divides the sum of two numbers,it must exactly divide the two numbers separately

State whether the following statement is True or False
If a number exactly divides the sum of two numbers,it must exactly divide the two numbers separately