A three-digit number abc is divisible by 6 if c is an even number and a + b + c is a multiple of 3. Is the given statement true or false?

Solution:

6 is a multiple of 3 and 2.

So if c is even the number therefore it is divisible by 2.

Since a + b + c is a multiple of 3 implies that it is divisible by 3

Hence the three digit number abc is divisible by 6

The statement is true(T).

✦ Try This: A four digit number abcd is divisible by 12 if the number formed by the digits cd is divisible by four and a + b + c + d is a multiple of 3. Is the given statement true or false?

12 is a multiple of 3 and 4

Since the last two digits cd together are divisible by 4 implies that the complete number is divisible abcd is divisible by 4

Since a + b + c + d is a multiple of 3 implies that abcd is divisible by 3.

Since abcd is divisible by 4 and 3 simultaneously means that the number is divisible by 12 because 4 × 3 = 12.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16

NCERT Exemplar Class 8 Maths Chapter 13 Problem 37

A three-digit number abc is divisible by 6 if c is an even number and a + b + c is a multiple of 3. Is the given statement true or false?

Summary:

“A three-digit number abc is divisible by 6 if c is an even number and a + b + c is a multiple of 3” is a True(T) statement.

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