Which of the following statements is/are correct?

(a) A number is divisible by 125, if the last three digits of the number form a number that is divisible by $$5^3$$​.

(b) If a number is divisible by two numbers, then it is divisible by the product of the two numbers.

(c) A number is divisible by 36, if the number is divisible by 4, 6 and 12.

Correct option is B

Solution:

Statement (a):

"A number is divisible by 125 if the last three digits of the number form a number that is divisible by 5³."

• 5³ = 125, so this is a correct mathematical interpretation.
• The divisibility rule for 125 is: A number is divisible by 125 if its last 3 digits form a number divisible by 125.
• Statement (a) is correct

Statement (b):

"If a number is divisible by two numbers, then it is divisible by the product of the two numbers."

• This is not always true.
• Counter example: 90 is divisible by 6 and 10, but not by 60.
• Only true when the two numbers are coprime.
• Statement (b) is incorrect

Statement (c):

"A number is divisible by 36, if it is divisible by 4, 6, and 12."

• For a number to be divisible by 36, it must be divisible by both 4 and 9.
• Being divisible by 4, 6, and 12 doesn't guarantee divisibility by 9.
• Example: 48 is divisible by 4, 6, 12 but not by 36.
• Statement (c) is incorrect

Final Answer: Option 2: (a) only — is correct