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.

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Solution

True
Consider the example: 9, 12, 15 are all divisible by 3.
Sum of 9, 12 and 15 = 36
$36 \div 3 = 12$
Therefore the statement is true.

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Question 80

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.

Q. State whether the following statements are true or false in the respective order.
Statement 1: If two numbers are co-primes, at least one of them must be prime.
Statement 2: If a number exactly divides two numbers, then it must also divide the sum of both numbers.
Statement 3: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Statement 1: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.
Statement 2: If a number exactly divides two numbers, then it must also divide the sum of both numbers.

Question 40

State whether the statement given is True or False.

A trinomial has exactly three terms.

Statement 1: If two numbers are co-primes, at least one of them must be prime.

Statement 2: If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately.

Statement 3: If a number exactly divides two numbers, then it must also divide the sum of both numbers.

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Divisibility Tests for 3

Standard VI Mathematics

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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.

True Consider the example: 9, 12, 15 are all divisible by 3. Sum of 9, 12 and 15 = 36 36÷3=12 Therefore the statement is true.

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.

True
Consider the example: 9, 12, 15 are all divisible by 3.
Sum of 9, 12 and 15 = 36
$36 \div 3 = 12$
Therefore the statement is true.