anwarma wrote:Which of the following could be the sum of the reciprocals of two different prime numbers?
(A) 7/13
(B) 10/21
(C) 11/30
(D) 23/50
(E) 19/77
ANS is B
Can someone help me with this?
If p and q are two different primes, the sum of their reciprocals is:
1/p + 1/q = (p+q)/pq
So, in lowest terms, the sum of these reciprocals can be written as (p+q)/pq. In particular, in lowest terms, the denominator is the product of two different primes, and the numerator is the sum of those same two primes. All of the answer choices are in lowest terms, and only E and B have a suitable denominator. Only B has the correct sum in the numerator: 10/21 = (3+7)/3*7.
