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Reciprocal problem

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Source: — Problem Solving |
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by leovonp » Thu Jun 12, 2008 6:55 am
The reciprocal of a prime number is going to be 1/(prime number).
From this you should start looking for a denominator that equals the multiplication of two primes. (b) and (d) fit the profile as b is 3 x 7
and d is 7 x 11.

Working out (b) you will have to see if 1/3 + 1/7 sum up to 10/21. 1/3 equals 7/21 and 1/7 equals 3/21. Bingo.
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Re: Reciprocal problem

by Ian Stewart » Thu Jun 12, 2008 7:55 am
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.
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