GeminiHeat wrote:
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 \(x\) be one of the prime numbers
Let \(y\) be the other prime number
So, the sum of their reciprocals \(= \frac{1}{x}+\frac{1}{y} = \frac{y}{xy}+\frac{x}{xy}=\frac{x+y}{xy} \)
So, we're looking for an answer choice such that the denominator can be written as the product of two primes, and the numerator can be written as the sum of two primes.
Notice that the fraction in answer choice B (\(\frac{10}{12}\)) isn't expressed in simplest terms.
When we simplify \(\frac{10}{12}\), we get \(\frac{5}{6}\), which can be expressed as: \(\frac{2+3}{(2)(3)}\)
So, if the two prime numbers are \(2\) and \(3\), the sum of the reciprocals \(= \frac{5}{6}\)
Answer: B
_________________
Brent Hanneson - founder of Greenlight Test Prep