jullysabat wrote:

nitya34 wrote:

10/12 it is

10/12=5/6=(1/2) + (1/3)

Was it a guess ??? or how do we approach to this kind of problem...

prab wrote:

are there any theories for these kinds of problems? haven't came across any yet, i think hit and trial is the best one!

Which of the following could be the sum of the reciprocals of two different prime numbers?A. 7/13

B. 10/12

C. 11/30

D. 23/50

E. 19/77

Let

x and

y be two different primes, then their sum will be

\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}. So, the denominator of the reduced fraction must be the product of two different primes: only B,

\frac{10}{12}=\frac{5}{6}=\frac{5}{2*3}, and E,

\frac{19}{77}=\frac{19}{7*11}, have such denominators and nominator must be the sum of the primes in denominator, thus only B is left:

\frac{10}{12}=\frac{5}{6}=\frac{2+3}{2*3}.

Answer: B.

Hope it's clear.

Thank u so much.. for this explanation...