Which of the following statement is\are correct regarding a and b. If

1.	Which of the following statement is\are correct regarding a and b. If the number 85ab46 is divisible by 11 and sum of digits a and b is 5?Statement 1: The product of digit is 6Statement 2: The required digit is 85ab46Statement 3: Both the digits are not prime number1. Statement I and II2. Statement I and III3. Only II4. None of these
Answer» Correct Answer - Option 1 : Statement I and II Given: The given digit is 85ab46 and sum of digits a and b is 5 Concept Used: Divisibility by 11 is check by subtracting the sum of digits of odd places to sum of digits of even places If the difference is zero or multiple of 11 then the whole number is divisible by 11 Calculation: It is given that sum of a and b is 5 ∴ a + b = 5 ----(1) Now, according to the concept Sum of odd place digit = 14 + a And Sum of even place digit = 11 + b Now, it is given that the digit is divisible by 11 ∴ 14 + a – 11 – b = 0 ⇒ a – b = -1 ----(2) By equation (1) and (2) ∴ a = 2 and b = 3 Now, consider the statements 1, the product of digits is 6 ∴ a × b = 2 × 3 = 6 So, statement 1 is correct Now, consider the statements 2, the digit is 852346 ∴ Required number = 85ab46 = 852346 So, statement 2 is correct Now, consider the statements 3, both digits are not prime number ∴ Both 2 and 3 are prime number So, statement 3 is incorrect Hence, option (1) is correct

Which of the following statement is\are correct regarding a and b. If the number 85ab46 is divisible by 11 and sum of digits a and b is 5?Statement 1: The product of digit is 6Statement 2: The required digit is 85ab46Statement 3: Both the digits are not prime number1. Statement I and II2. Statement I and III3. Only II4. None of these

Answer» Correct Answer - Option 1 : Statement I and II

Given:

The given digit is 85ab46 and sum of digits a and b is 5

Concept Used:

Divisibility by 11 is check by subtracting the sum of digits of odd places to sum of digits of even places

If the difference is zero or multiple of 11 then the whole number is divisible by 11

Calculation:

It is given that sum of a and b is 5

∴ a + b = 5 ----(1)

Now, according to the concept

Sum of odd place digit = 14 + a

And Sum of even place digit = 11 + b

Now, it is given that the digit is divisible by 11

∴ 14 + a – 11 – b = 0

⇒ a – b = -1 ----(2)

By equation (1) and (2)

∴ a = 2 and b = 3

Now, consider the statements 1, the product of digits is 6

∴ a × b = 2 × 3 = 6

So, statement 1 is correct

Now, consider the statements 2, the digit is 852346

∴ Required number = 85ab46 = 852346

So, statement 2 is correct

Now, consider the statements 3, both digits are not prime number

∴ Both 2 and 3 are prime number

So, statement 3 is incorrect

Hence, option (1) is correct