Fractions/Ratios/Decimals, Number Properties

swerve wrote: ↑

Thu Apr 09, 2020 1:20 pm

Which of the following could be the sum of the reciprocals of two different prime numbers?

A. \(\dfrac{7}{13}\)
B. \(\dfrac{10}{12}\)
C. \(\dfrac{11}{30}\)
D. \(\dfrac{23}{50}\)
E. \(\dfrac{19}{77}\)

The OA is B

Source: GMAT Paper Tests

Let p and q be the two prime numbers

So the sum of their reciprocals = 1/p + 1/q = q/pq + p/pq = (q + p)/pq
This means we are looking for an answer choice in which the numerator can be expressed as the SUM of two prime numbers, and the denominator can be expressed as the PRODUCT of those same two prime numbers.

Check the answer choices....

B) 10/12 = 5/6 = (2 + 3)/(2)(3) perfect!!!

Answer: B

Cheers,
Brent

swerve wrote: ↑

Thu Apr 09, 2020 1:20 pm

Which of the following could be the sum of the reciprocals of two different prime numbers?

A. \(\dfrac{7}{13}\)
B. \(\dfrac{10}{12}\)
C. \(\dfrac{11}{30}\)
D. \(\dfrac{23}{50}\)
E. \(\dfrac{19}{77}\)

The OA is B

Source: GMAT Paper Tests

Since 1/2 + 1/3 = 3/6 + 2/6 = 5/6 = 10/12, the correct answer is B.

Answer: B