Which of the following could be the sum of the reciprocals : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 07 Dec 2016, 11:43

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Which of the following could be the sum of the reciprocals

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Sep 2008
Posts: 103
Followers: 1

Kudos [?]: 82 [4] , given: 1

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

### Show Tags

31 Mar 2009, 20:29
4
KUDOS
18
This post was
BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

50% (02:09) correct 50% (01:21) wrong based on 508 sessions

### HideShow timer Statistics

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
[Reveal] Spoiler: OA
Director
Joined: 04 Jan 2008
Posts: 912
Followers: 68

Kudos [?]: 561 [0], given: 17

### Show Tags

31 Mar 2009, 21:07
1
This post was
BOOKMARKED
10/12 it is
10/12=5/6=(1/2) + (1/3)
_________________

http://gmatclub.com/forum/math-polygons-87336.html
http://gmatclub.com/forum/competition-for-the-best-gmat-error-log-template-86232.html

Manager
Joined: 02 Oct 2010
Posts: 158
Followers: 2

Kudos [?]: 39 [0], given: 29

### Show Tags

02 Jan 2011, 21:23
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...
Senior Manager
Joined: 13 Aug 2010
Posts: 314
Followers: 1

Kudos [?]: 21 [0], given: 1

### Show Tags

03 Jan 2011, 00:41
are there any theories for these kinds of problems? haven't came across any yet, i think hit and trial is the best one!
Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90022 [8] , given: 10402

### Show Tags

03 Jan 2011, 01:53
8
KUDOS
Expert's post
6
This post was
BOOKMARKED
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: $$\frac{10}{12}=\frac{5}{6}=\frac{2+3}{2*3}$$.

Hope it's clear.
_________________
Manager
Joined: 02 Oct 2010
Posts: 158
Followers: 2

Kudos [?]: 39 [0], given: 29

### Show Tags

03 Jan 2011, 10:00
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: $$\frac{10}{12}=\frac{5}{6}=\frac{2+3}{2*3}$$.

Hope it's clear.

Hey Bunnel,

Thank u so much.. for this explanation...
very very simple and robust way of explaning things...
Manager
Joined: 26 Feb 2012
Posts: 116
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)
Followers: 0

Kudos [?]: 19 [0], given: 56

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

### Show Tags

11 Jun 2013, 08:22
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.

Rgds
Prasannajeet
Intern
Joined: 14 Feb 2013
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

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

### Show Tags

11 Jun 2013, 08:28
[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)
Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90022 [0], given: 10402

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

### Show Tags

11 Jun 2013, 08:29
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 35912
Followers: 6851

Kudos [?]: 90022 [0], given: 10402

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

### Show Tags

11 Jun 2013, 08:38
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

Hope it helps.
_________________
Manager
Joined: 26 Feb 2012
Posts: 116
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)
Followers: 0

Kudos [?]: 19 [0], given: 56

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

### Show Tags

11 Jun 2013, 09:53
Hi Sivtozar & Bunuel

Thank you . I made a felony not a mistake to identify the prime number.

Rgds
Prasannajeet
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12886
Followers: 561

Kudos [?]: 158 [0], given: 0

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

### Show Tags

09 Jul 2014, 08:19
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 12886
Followers: 561

Kudos [?]: 158 [0], given: 0

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

### Show Tags

08 Nov 2015, 23:15
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Senior Manager
Joined: 20 Aug 2015
Posts: 398
Location: India
GMAT 1: 760 Q50 V44
Followers: 23

Kudos [?]: 202 [0], given: 10

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

### Show Tags

09 Nov 2015, 23:58
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.

_________________

Reach out to us at bondwithus@gmatify.com

Director
Joined: 23 Jan 2013
Posts: 568
Schools: Cambridge'16
Followers: 1

Kudos [?]: 41 [0], given: 40

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

### Show Tags

10 Nov 2015, 22:57
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
SVP
Joined: 17 Jul 2014
Posts: 2084
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
WE: General Management (Transportation)
Followers: 18

Kudos [?]: 248 [0], given: 124

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

### Show Tags

27 Feb 2016, 10:27
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.
Manager
Joined: 29 Aug 2008
Posts: 114
Followers: 2

Kudos [?]: 32 [0], given: 279

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

### Show Tags

19 Oct 2016, 02:49
Missed reducing the fraction and got it wrong even after the correct approach.

Good question.
Re: Which of the following could be the sum of the reciprocals   [#permalink] 19 Oct 2016, 02:49
Similar topics Replies Last post
Similar
Topics:
1 If the reciprocal of n is less than -2, which of the following positio 6 04 Apr 2016, 00:03
4 In which of the following pairs are the two numbers reciprocals of one 5 11 Jan 2015, 11:29
7 In which of the following pairs are the two numbers reciproc 8 26 Dec 2013, 07:56
3 Of the following sums, which is the greatest? 6 28 Sep 2013, 15:32
25 If x is positive, which of the following could be the 15 01 Nov 2010, 16:28
Display posts from previous: Sort by