Statement I: All numbers divisible by 6 are also divisible by 2.
Statement II: All numbers divisible by 2 are also divisible by 6.
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.
Both Statement I and Statement II are true.
Both Statement I and Statement II are false.
Answer
Since 6 = 2 × 3, so 2 is a factor of 6. Therefore, every number divisible by 6 is also divisible by 2.
So, statement I is true.
A number divisible by 2 need not be divisible by 6. For example, 4 is divisible by 2 but not by 6.
So, statement II is false.
Hence, option 1 is the correct option.
Statement I: All even numbers are divisible by 4.
Statement II: All numbers divisible by 4 are even.
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.
Both Statement I and Statement II are true.
Both Statement I and Statement II are false.
Answer
An even number need not be divisible by 4. For example, 6 is an even number but it is not divisible by 4.
So, statement I is false.
Since 4 = 2 × 2, so every number divisible by 4 is also divisible by 2 i.e. it is an even number.
So, statement II is true.
Hence, option 2 is the correct option.
Statement I: If 456x78 is divisible by 3, then the value of x can be 0, 3, 6, or 9.
Statement II: If the sum of digits of a number is divisible by 3, then the number is also divisible by 3.
Statement I is true but Statement II is false.
Statement I is false but Statement II is true.
Both Statement I and Statement II are true.
Both Statement I and Statement II are false.
Answer
∵ 456x78 is divisible by 3
⇒ 4 + 5 + 6 + x + 7 + 8 is divisible by 3
⇒ 30 + x is divisible by 3
⇒ 30 + x = 30, 33, 36, 39, ...............
⇒ x = 0, 3, 6, 9, ...............
Since x is a digit, so x = 0, 3, 6 or 9.
So, statement I is true.
According to the divisibility of 3, if the sum of the digits of a number is divisible by 3 then the number is also divisible by 3.
So, statement II is true.
Hence, option 3 is the correct option.