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.

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Solution

False
If a number divides three numbers exactly, it must divide their sum exactly, but vice-versa is not true.
Example:
84 is divisible by 3. Also the sum of 40 + 19 + 25 = 84.
But 40 is not divisible by 3
19 is not divisible by 3
25 is not divisible by 3

Hence the given statement is false.

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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.

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.

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

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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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.

False If a number divides three numbers exactly, it must divide their sum exactly, but vice-versa is not true. Example: 84 is divisible by 3. Also the sum of 40 + 19 + 25 = 84. But 40 is not divisible by 3 19 is not divisible by 3 25 is not divisible by 3 Hence the given statement is false.

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.

False
If a number divides three numbers exactly, it must divide their sum exactly, but vice-versa is not true.
Example:
84 is divisible by 3. Also the sum of 40 + 19 + 25 = 84.
But 40 is not divisible by 3
19 is not divisible by 3
25 is not divisible by 3

Hence the given statement is false.