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Which of the following could be the sum of the reciprocals

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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
[Reveal] Spoiler: OA
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Re: sum of reciprocals. [#permalink]

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New post 31 Mar 2009, 22:07
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New post 02 Jan 2011, 22:23
nitya34 wrote:
10/12 it is
10/12=5/6=(1/2) + (1/3) :)


Was it a guess ??? or how do we approach to this kind of problem...
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New post 03 Jan 2011, 01:41
are there any theories for these kinds of problems? haven't came across any yet, i think hit and trial is the best one!
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New post 03 Jan 2011, 02:53
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jullysabat wrote:
nitya34 wrote:
10/12 it is
10/12=5/6=(1/2) + (1/3) :)


Was it a guess ??? or how do we approach to this kind of problem...

prab wrote:
are there any theories for these kinds of problems? haven't came across any yet, i think hit and trial is the best one!


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 \(x\) and \(y\) be two different primes, then their sum will be \(\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\). So, the denominator of the reduced fraction must be the product of two different primes: only B, \(\frac{10}{12}=\frac{5}{6}=\frac{5}{2*3}\), and E, \(\frac{19}{77}=\frac{19}{7*11}\), have such denominators and nominator must be the sum of the primes in denominator, thus only B is left: \(\frac{10}{12}=\frac{5}{6}=\frac{2+3}{2*3}\).

Answer: B.

Hope it's clear.
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Re: sum of reciprocals. [#permalink]

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New post 03 Jan 2011, 11:00
Bunuel wrote:
jullysabat wrote:
nitya34 wrote:
10/12 it is
10/12=5/6=(1/2) + (1/3) :)


Was it a guess ??? or how do we approach to this kind of problem...

prab wrote:
are there any theories for these kinds of problems? haven't came across any yet, i think hit and trial is the best one!


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 \(x\) and \(y\) be two different primes, then their sum will be \(\frac{1}{x}+\frac{1}{y}=\frac{x+y}{xy}\). So, the denominator of the reduced fraction must be the product of two different primes: only B, \(\frac{10}{12}=\frac{5}{6}=\frac{5}{2*3}\), and E, \(\frac{19}{77}=\frac{19}{7*11}\), have such denominators and nominator must be the sum of the primes in denominator, thus only B is left: \(\frac{10}{12}=\frac{5}{6}=\frac{2+3}{2*3}\).

Answer: B.

Hope it's clear.


Hey Bunnel,

Thank u so much.. for this explanation...
very very simple and robust way of explaning things...
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New post 11 Jun 2013, 09:22
Hi Bunuel

Why not the ans would be 11/30? Pls explain

If we take 2 prime number as 5 and 6 then by equation it is 5+6/5*6=11/30 ans.....

Apart from this PS question I have a query..that is currently I am doing practice from GMAT club. Is it enough or I must follow some other source ?

Needless to say +Kudos to your simplistic approach for every question.

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Re: Which of the following could be the sum of the reciprocals [#permalink]

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New post 11 Jun 2013, 09:28
[quote="prasannajeet"]Hi Bunuel

Why not the ans would be 11/30? Pls explain

If we take 2 prime number as 5 and 6 then by equation it is 5+6/5*6=11/30 ans.....



Because 6 is not a prime)
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New post 11 Jun 2013, 09:29
Expert's post
prasannajeet wrote:
Hi Bunuel

Why not the ans would be 11/30? Pls explain

If we take 2 prime number as 5 and 6 then by equation it is 5+6/5*6=11/30 ans.....

Apart from this PS question I have a query..that is currently I am doing practice from GMAT club. Is it enough or I must follow some other source ?

Needless to say +Kudos to your simplistic approach for every question.

Rgds
Prasannajeet


6=2*3 is not a prime number.
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New post 11 Jun 2013, 09:38
Expert's post
prasannajeet wrote:

Apart from this PS question I have a query..that is currently I am doing practice from GMAT club. Is it enough or I must follow some other source ?


I think that we have more than enough questions and theory topics on the site. Though you can check Best GMAT Books:
best-gmat-math-prep-books-reviews-recommendations-77291.html
books-to-read-improve-verbal-score-and-enjoy-a-good-read-76079.html

Hope it helps.
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New post 11 Jun 2013, 10:53
Hi Sivtozar & Bunuel

Thank you . I made a felony not a mistake to identify the prime number.
Also thanx for the thread.

Rgds
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New post 10 Nov 2015, 00:58
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milind1979 wrote:
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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


This question has to be solved by taking on option at a time.
However, we do not need to check all the options here as some can be eliminated by checking the given condition.

We have to find the sum of reciprocals of two different prime numbers.
This means that the denominator will be the multiplication of the two different prime numbers.

Checking the options for this.

Option A = 13*1. Does not satisfy the condition of two prime numbers
Option B = 10/12 = 5/6, Here 6 = 2*3. This is what we need.
To cross check, see that 1/2 + 1/3 = 5/6 = 10/12 Our answer.

Let us check for the others too
Option C: 30 = 5*6 or 3*10. Does not satisfy the condition of two prime numbers
Option D: 50 = 25*2 or 50*1. Does not satisfy the condition of two prime numbers
Option E: 77 = 7*11. This satisfies our condition.
Checking for the numerator: 1/11 + 1/7 = 18/77
But option has 19/77. Hence not the correct answer.

Correct answer: Option B
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New post 10 Nov 2015, 23:57
num=sum of prime numbers

denom=product of those numbers

A. 7/13, no such primes exist

B. 10/12=5/6, the numbers are 3 and 2

C. 11/30, no such primes

D. 23/50, no such primes

E. 19/77, no such primes

B
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Re: Which of the following could be the sum of the reciprocals [#permalink]

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New post 27 Feb 2016, 11:27
what a brain tease...
to have an odd number in the numerator, it must be that one of the prime numbers is 2.
2*3=6.
2+2=5
5/6 *2 = 10/12

B.

we can also rewrite:
a+b/ab
where ab must be either the result of 2 prime numbers multiplied, or we must have a factor as well: abx - where x is the factor.
A. 7/13 - ab=13 - can't have such option.
B. 10/12 = ab=2*3*2 => so 2 primes multiplied by a factor of 2. numerator must also be the sum of 2 prime numbers multiplied by 2.
C. 11/30 = ab=5*3*2 => so either ab is multiplied by 5, 3, or by 2. in this case, a+b as well needs to be multiplied by the same factor. but 11 is not a multiple of 5, 3, or 2. so out.
D. 23/50 = 5x2x5 -> 23 is not a factor of 5 or 2. so out.
E. 19/77 = 7x11 => so 2 primes. a+b must be equal to 18. so definitely not what we need.

only B works.
Re: Which of the following could be the sum of the reciprocals   [#permalink] 27 Feb 2016, 11:27
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