Number System
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Q.

Two prime numbers $A, B(A < B)$ are called twin primes if they differ by 2 (e.g. 11,13,or 41,43....).

If A and B are twin primes with $B > 23$, then which of the following numbers would always divide $A+B$?

 A.

12

 B.

8

 C.

24

 D.

None of these

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Solution:
Option(A) is correct

Any prime number greater than 3 will be in the form of $6x+1$ or $6x-1$.

Thus, both prime number are twins:

Let first be $6x-1$
and 2nd be $6x+1$
$\text{Sum} = 12x$

Thus it is always divisible by 12.


(1) Comment(s)


Krish
 ()

prime numbers near to 23 are 29 and 31 and both differ by 2

so,29+31=60 which is divisible by 12