Question

Bello all stars!
It is know that 2 + a and 24 - b are divisible by 11. Prove that a + b is also divisible by 11.

Answer 1

➤ Answer

➤ Given

• 2 + a and 24 - b are divisible by 11.

➤ To Proof

• a + b is divisible by 11.

➤ Step By Step Explanation

• Step 1.

To watch the equations carefully.

• Step 2.

Let's assume that a and b are smallest number which can be added or subtracted to 2 and 24 respectively so that they can be divisible by 11.

[ Note - we are taking smallest values to make our calculations easy ]

➠ 2 + a = 11 ( which is divisible by 11 )

➠ a = 11 - 2 => a = 9

➠ 24 - b = 22 ( which is divisible by 11 )

➠ -b = 22 - 24 => b = 2

• Step 3.

Let's substitute the values of a and b and add them.

9 + 2 = 11

By adding a and b we conclude that the result is 11 which is divisible by 11.

➵ Hence proved.

_____________________

Answer 2

Solution!!

We can make our assumptions to solve this or we can try and do it using simple math. So, it is known that 2 + a and 24 - b are divisible by 11. We have to prove that a + b is also divisible by 11. We'll be getting more than one values of a and b while assuming. So, let's find out a suitable value of a and b whose sum is divisible by 11.

Make the two equations.

→ (2 + a) ÷ 11 = 1

→ (24 - b) ÷ 11 = 1

→ 2 + a = 11

→ 24 - b = 11

→ a = 11 - 2

→ 24 - 11 = b

→ a = 9

→ b = 13

Now,

→ a + b = 9 + 13 = 22

22 is divisible by 11 which means that a + b is also divisible by 11.

Hence, proved.