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Fractions/Ratios/Decimals, Number Properties

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by swerve » Thu Apr 09, 2020 1:20 pm

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B

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Difficulty—

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
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Re: Fractions/Ratios/Decimals, Number Properties

by Brent@GMATPrepNow » Fri Apr 10, 2020 4:30 am
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
Brent Hanneson - Creator of GMATPrepNow.com
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Re: Fractions/Ratios/Decimals, Number Properties

by Scott@TargetTestPrep » Sun Apr 19, 2020 4:48 am
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

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