GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 18 Oct 2019, 19:11

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
Joined: 02 Sep 2008
Posts: 97
Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

New post 31 Mar 2009, 21:29
9
1
26
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

53% (01:35) correct 47% (01:53) wrong based on 529 sessions

HideShow timer Statistics

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
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

New post 03 Jan 2011, 02:53
11
6
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.
_________________
General Discussion
Director
Director
User avatar
Joined: 04 Jan 2008
Posts: 648
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

New post 31 Mar 2009, 22:07
1
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
Manager
avatar
Joined: 02 Oct 2010
Posts: 84
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

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...
Manager
Manager
avatar
Joined: 13 Aug 2010
Posts: 123
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

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!
Manager
Manager
avatar
Joined: 02 Oct 2010
Posts: 84
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

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...
Manager
Manager
avatar
Joined: 26 Feb 2012
Posts: 88
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

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.

Rgds
Prasannajeet
Intern
Intern
avatar
Joined: 14 Feb 2013
Posts: 1
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

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)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

New post 11 Jun 2013, 09:29
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
User avatar
V
Joined: 02 Sep 2009
Posts: 58453
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

New post 11 Jun 2013, 09:38
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
books-to-read-improve-verbal-score-and-enjoy-a-good-read-76079.html

Hope it helps.
_________________
Manager
Manager
avatar
Joined: 26 Feb 2012
Posts: 88
Location: India
Concentration: General Management, Finance
WE: Engineering (Telecommunications)
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

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
Prasannajeet
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 386
Location: India
GMAT 1: 760 Q50 V44
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

New post 10 Nov 2015, 00:58
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.

Correct answer: Option B
Director
Director
User avatar
G
Joined: 23 Jan 2013
Posts: 525
Schools: Cambridge'16
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

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
Board of Directors
User avatar
P
Joined: 17 Jul 2014
Posts: 2509
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
GMAT ToolKit User Reviews Badge
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

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.
Manager
Manager
avatar
Joined: 29 Aug 2008
Posts: 106
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

New post 19 Oct 2016, 03:49
Missed reducing the fraction and got it wrong even after the correct approach.

Good question.
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 728
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

New post 26 Sep 2017, 02:03
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


Here we have to find the number which is sum of reciprocals of two prime numbers say x ,y
So, 1/x + 1/y = (x+y)/xy, which means denominator must be multiple of two prime numbers.

In the given options we can see that only option B fulfills this. 10/12 = 5/6 = 5/3*2

Now 1/3+1/2 = 5/6


Answer B
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Manager
Manager
User avatar
G
Status: wake up with a purpose
Joined: 24 Feb 2017
Posts: 118
Concentration: Accounting, Entrepreneurship
GMAT ToolKit User Premium Member
Re: Which of the following could be the sum of the reciprocals of two  [#permalink]

Show Tags

New post 07 Apr 2019, 04:28
try to reduce the answer choices to prime. Look every choices has prime numbers except (B).
If answer choice (B) were 5/6, you would pick choice (B) easily.

Posted from my mobile device
_________________
If people are NOT laughing at your GOALS, your goals are SMALL.
GMAT Club Bot
Re: Which of the following could be the sum of the reciprocals of two   [#permalink] 07 Apr 2019, 04:28
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne