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

True

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False

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Solution

The correct option is A True
Step 1: Check the divisibility of a number:
The number $8$ divides $16$ and $24$ separately.
Step 1: Check the divisibility of sum of the numbers:
Sum of the numbers $= 16 + 24 = 40$
The number $8$ divides $40$ exactly.
Therefore, the given 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. 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.

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.

If a number exactly divides the sum of two numbers, it must exactly divide the two numbers separately. (True or False)

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

The correct option is A TrueStep 1: Check the divisibility of a number:The number 8 divides 16and 24 separately.Step 1: Check the divisibility of sum of the numbers:Sum of the numbers =16+24=40The number 8 divides 40 exactly.Therefore, the given statement is true.

The correct option is A True
Step 1: Check the divisibility of a number:
The number $8$ divides $16$ and $24$ separately.
Step 1: Check the divisibility of sum of the numbers:
Sum of the numbers $= 16 + 24 = 40$
The number $8$ divides $40$ exactly.
Therefore, the given statement is true.