Which of the following are correct for divisibility?
(A) A number is divisible by 6 if it is divisible by 3 or 2.
(B) A number is divisible by 5 if its unit digit is 0 or 5.
(C) A number is divisible by 3 if its unit digit is divisible by 3.
(D) A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) and (D) only
(A) A number is divisible by 6 if it is divisible by 3 or 2. Incorrect. Since \(6=2\times3\), a number must be divisible by both 2 and 3. 9 is divisible by 3 and 8 by 2, but neither is divisible by 6.
(B) A number is divisible by 5 if its unit digit is 0 or 5. Correct. Every multiple of 10 is divisible by 5, so only the last digit decides, and the multiples of 5 below 10 are 0 and 5.
(C) A number is divisible by 3 if its unit digit is divisible by 3. Incorrect. The test for 3 uses the sum of all the digits, not the last digit: 13 ends in 3 but is not divisible by 3, while 12 is.
(D) A number is divisible by 4 if the number formed by its last two digits is divisible by 4. Correct. Every multiple of 100 is divisible by 4, so only the last two digits decide: 1,316 is divisible by 4 because 16 is.