Can the positive integer n be written as the sum of two : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 22 Feb 2017, 13:33

### 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

# Can the positive integer n be written as the sum of two

Author Message
TAGS:

### Hide Tags

Intern
Joined: 01 Jan 2012
Posts: 44
Location: United States
Concentration: Marketing, Technology
GMAT 1: Q42 V32
GMAT 2: 0 Q50 V35
GPA: 3.6
Followers: 1

Kudos [?]: 118 [1] , given: 5

Can the positive integer n be written as the sum of two [#permalink]

### Show Tags

29 Jan 2012, 10:56
1
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

60% (02:33) correct 40% (00:55) wrong based on 282 sessions

### HideShow timer Statistics

Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

When I am checking the case using both conditions so can i rephrase problem statement as "Can every odd integer which is greater than 3 can be written as sum of two positive integers " OR
"Can any odd integer which is greater than 3 can be written as sum of two positive integers"
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 37083
Followers: 7243

Kudos [?]: 96332 [1] , given: 10737

### Show Tags

29 Jan 2012, 11:40
1
KUDOS
Expert's post
3
This post was
BOOKMARKED
monikaleoster wrote:
90. Can the positive integer n be written as the sum of two different positive prime numbers?
(1) n is greater than 3.
(2) n is odd.

When I am checking the case using both conditions so can i rephrase problem statement as "Can every odd integer which is greater than 3 can be written as sum of two positive integers " OR
"Can any odd integer which is greater than 3 can be written as sum of two positive integers"

Note that n is some particular, fixed number. If we take two statements together the question becomes: can odd integer n, which is greater than 3, be written as the sum of two different prime numbers?

Now, if EVERY odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would be sufficient as we get definite YES answer to the question (because if it can be done for EVERY odd integer greater than 3 then it can be done for some particular n, from this group, too). Also, if NEITHER odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would still be sufficient, though at this time we'd get definite NO answer to the question (because if it cannot be done for ANY odd integer greater than 3 then it can not be done for some particular n, from this group, too).

Next, if we can find two values of odd integer n greater than 3 and one of them can be written as the sum of two different prime numbers and another cannot, then taken together statements would NOT be sufficient.

For this question the answer is E:
If n=5=odd>3, then the answer would be YES, 5=2+3=prime+prime;
If n=11=odd>3, then the answer would be NO, (11=odd and in order it to be the sum of two different primes one must be 2=even=prime, in this case another number would be 9, since 9 is not a prime, you cannot write 11 as the sum of two different primes).

So, we have two values of odd integer n greater than 3: one of them can be written as the sum of two different prime numbers and another cannot, hence taken together statements are not sufficient.

Hope it's clear.
_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 630
Followers: 82

Kudos [?]: 1136 [1] , given: 136

Re: Can the positive integer n be written as the sum of two [#permalink]

### Show Tags

14 Mar 2013, 21:50
1
KUDOS
monikaleoster wrote:
Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

Nothing new to add after Bunuel's explanation. But just to point down what I observed for F.S 2;we know that n is odd. Again we have been asked if n is a sum of 2 different primes. Now we know that only odd+even = odd. Thus out of the two given prime numbers, we can have only 2 as the even prime. So now the statement basically states that if we subtract 2 from n, do we end up with a prime greater than 2.

or Is n-2 = a prime greater than 2. Take any odd integer for n. For n=13, we get a YES. For n=17, we get a NO. Insufficient.
_________________
Director
Joined: 14 Dec 2012
Posts: 842
Location: India
Concentration: General Management, Operations
GMAT 1: 700 Q50 V34
GPA: 3.6
Followers: 60

Kudos [?]: 1310 [1] , given: 197

Re: Can the positive integer n be written as the sum of two... [#permalink]

### Show Tags

12 Aug 2013, 02:24
1
KUDOS
Stiv wrote:
Can the positive integer n be written as the sum of two different positive prime numbers?
1) n is greater than 3.
2) n is odd.

1) n is greater than 3.
let n = 8 =5+3 ==>yes
let n = 11 no
not sufficient
2) n is odd
let n= 11 no
let n=5 =2+3..yes
not suffiecient.

combining also with same examples..not sufficient.

hence E
_________________

When you want to succeed as bad as you want to breathe ...then you will be successfull....

GIVE VALUE TO OFFICIAL QUESTIONS...

learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment

Intern
Joined: 01 Jan 2012
Posts: 44
Location: United States
Concentration: Marketing, Technology
GMAT 1: Q42 V32
GMAT 2: 0 Q50 V35
GPA: 3.6
Followers: 1

Kudos [?]: 118 [0], given: 5

Re: Can the positive integer n be written as the sum of two [#permalink]

### Show Tags

30 Jan 2012, 09:55
Thanks for wonderful Explanation..
Manager
Joined: 12 Dec 2012
Posts: 230
GMAT 1: 540 Q36 V28
GMAT 2: 550 Q39 V27
GMAT 3: 620 Q42 V33
GPA: 2.82
WE: Human Resources (Health Care)
Followers: 4

Kudos [?]: 79 [0], given: 181

### Show Tags

14 Mar 2013, 17:24
Bunuel wrote:
monikaleoster wrote:
90. Can the positive integer n be written as the sum of two different positive prime numbers?
(1) n is greater than 3.
(2) n is odd.

When I am checking the case using both conditions so can i rephrase problem statement as "Can every odd integer which is greater than 3 can be written as sum of two positive integers " OR
"Can any odd integer which is greater than 3 can be written as sum of two positive integers"

Note that n is some particular, fixed number. If we take two statements together the question becomes: can odd integer n, which is greater than 3, be written as the sum of two different prime numbers?

Now, if EVERY odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would be sufficient as we get definite YES answer to the question (because if it can be done for EVERY odd integer greater than 3 then it can be done for some particular n, from this group, too). Also, if NEITHER odd integer greater than 3 can be written as the sum of two different prime numbers, then taken together statements would still be sufficient, though at this time we'd get definite NO answer to the question (because if it cannot be done for ANY odd integer greater than 3 then it can not be done for some particular n, from this group, too).

Next, if we can find two values of odd integer n greater than 3 and one of them can be written as the sum of two different prime numbers and another cannot, then taken together statements would NOT be sufficient.

For this question the answer is E:
If n=5=odd>3, then the answer would be YES, 5=2+3=prime+prime;
If n=11=odd>3, then the answer would be NO, (11=odd and in order it to be the sum of two different primes one must be 2=even=prime, in this case another number would be 9, since 9 is not a prime, you cannot write 11 as the sum of two different primes).

So, we have two values of odd integer n greater than 3: one of them can be written as the sum of two different prime numbers and another cannot, hence taken together statements are not sufficient.

Hope it's clear.

solved it correctly but could not find a clear takeaway for this problem
_________________

My RC Recipe
http://gmatclub.com/forum/the-rc-recipe-149577.html

My Problem Takeaway Template
http://gmatclub.com/forum/the-simplest-problem-takeaway-template-150646.html

Manager
Joined: 14 Aug 2005
Posts: 86
Followers: 0

Kudos [?]: 12 [0], given: 2

Re: Can the positive integer n be written as the sum of two [#permalink]

### Show Tags

16 Mar 2013, 13:08
vinaymimani wrote:
monikaleoster wrote:
Can the positive integer n be written as the sum of two different positive prime numbers?

(1) n is greater than 3.
(2) n is odd.

Nothing new to add after Bunuel's explanation. But just to point down what I observed for F.S 2;we know that n is odd. Again we have been asked if n is a sum of 2 different primes. Now we know that only odd+even = odd. Thus out of the two given prime numbers, we can have only 2 as the even prime. So now the statement basically states that if we subtract 2 from n, do we end up with a prime greater than 2.

or Is n-2 = a prime greater than 2. Take any odd integer for n. For n=13, we get a YES. For n=17, we get a NO. Insufficient.

Good explanation!

I almost read n to be one of the numbers and did a mental calculation to arrive at C. But, now i am clear!
_________________

One Last Shot

Manager
Joined: 16 Feb 2012
Posts: 237
Concentration: Finance, Economics
Followers: 7

Kudos [?]: 293 [0], given: 121

Can the positive integer n be written as the sum of two... [#permalink]

### Show Tags

12 Aug 2013, 02:20
Can the positive integer n be written as the sum of two different positive prime numbers?
1) n is greater than 3.
2) n is odd.
_________________

Kudos if you like the post!

Failing to plan is planning to fail.

Math Expert
Joined: 02 Sep 2009
Posts: 37083
Followers: 7243

Kudos [?]: 96332 [0], given: 10737

Re: Can the positive integer n be written as the sum of two... [#permalink]

### Show Tags

12 Aug 2013, 02:28
Stiv wrote:
Can the positive integer n be written as the sum of two different positive prime numbers?
1) n is greater than 3.
2) n is odd.

Merging similar topics.

All OG13 questions are here: the-official-guide-quantitative-question-directory-143450.html
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13919
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: Can the positive integer n be written as the sum of two [#permalink]

### Show Tags

02 Sep 2015, 01:07
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.
_________________
Intern
Joined: 12 Dec 2015
Posts: 20
Followers: 0

Kudos [?]: 1 [0], given: 28

Re: Can the positive integer n be written as the sum of two [#permalink]

### Show Tags

16 Mar 2016, 11:11
Hi Guys, I am not a native speaker and I am confused by the question - should I read it as "Is the positive integer n represents the sum of two different positive prime numbers?"

Thanks!
Math Expert
Joined: 02 Sep 2009
Posts: 37083
Followers: 7243

Kudos [?]: 96332 [0], given: 10737

Re: Can the positive integer n be written as the sum of two [#permalink]

### Show Tags

16 Mar 2016, 11:15
AlexIV wrote:
Hi Guys, I am not a native speaker and I am confused by the question - should I read it as "Is the positive integer n represents the sum of two different positive prime numbers?"

Thanks!

No. It means is it possible to write positive integer n as the sum of two different positive prime numbers.
_________________
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 1926
Followers: 59

Kudos [?]: 421 [0], given: 476

Re: Can the positive integer n be written as the sum of two [#permalink]

### Show Tags

20 Dec 2016, 18:52
Nice Official Question.
Here is what i did int his one ->

Taking N=7 => 2+5
and N=27 -> We cannot write 27 as a sum if two primes

Hence Insufficient

Hence E
Takeaways =>
If sum of two primes is even -> 2 is not one of them
If sum of two primes is odd => 2 is one of them

_________________

Give me a hell yeah ...!!!!!

Re: Can the positive integer n be written as the sum of two   [#permalink] 20 Dec 2016, 18:52
Similar topics Replies Last post
Similar
Topics:
20 Can the positive integer n be written as the sum of two diff 15 12 Feb 2014, 01:14
1 If n is a positive integer, can it be written as difference 3 12 Jan 2014, 08:57
30 The sum of two positive integers, m and n, is a multiple of 9 13 Jun 2013, 04:57
8 Can the positive integer n be written as the sum of two different posi 8 17 Jun 2011, 12:07
2 The positive integer 4 can NOT be written as the sum of two 8 17 Jun 2010, 07:59
Display posts from previous: Sort by