Answer :

Given: (2 + a) and (35 – b) are divisible by 11, such that, a and b are integers.

To Prove: (a + b) is divisible by 11.


Proof: If (2 + a) and (35 – b) are divisible by 11, then their sum and difference will also be divisible by 11.


Let us take difference of these two numbers.


We can write as,


Difference = (2 + a) – (35 – b) = Divisible by 11


2 + a – 35 + b = Divisible by 11


a + b – 33 = Divisible by 11


Note that, here -33 is absolutely divisible by 11.


a + b must also be divisible by 11, as a + b – 33 is divisible by 11.


Hence, proved.


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