It is currently 28 Jun 2017, 05:36

### 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 CANNOT be the sum of two prime numbers?

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

### Hide Tags

Manager
Joined: 10 Feb 2011
Posts: 114
Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

17 Feb 2011, 15:10
21
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

62% (02:03) correct 38% (01:06) wrong based on 405 sessions

### HideShow timer Statistics

Which of the following CANNOT be the sum of two prime numbers?

(A) 19
(B) 45
(C) 68
(D) 79
(E) 88
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 39744
Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

17 Feb 2011, 15:44
5
KUDOS
Expert's post
9
This post was
BOOKMARKED
banksy wrote:
187. Which of the following CANNOT be the sum of two prime numbers?
(A) 19
(B) 45
(C) 68
(D) 79
(E) 88

Any prime number more than 3 can be expressed as $$p=6n+1$$ or $$p=6n+5$$ ($$p=6n-1$$), where n is an integer >0 (check this: http://gmatclub.com/forum/primality-check-108425.html).

So the sum of two primes more than 3 can yield the following remainders upon division by 6:
0 - if two primes are of a type $$p=6n+1$$ and $$p=6n+5$$;
2 - if both primes are of a type $$p=6n+1$$;
4 - if both primes are of a type $$p=6n+5$$;

Now, we are looking for the choice which is not a prime+2, or prime+3 or has a remainder other than 0, 2, or 4 upon division by 6.

(A) 19 --> 19-2=17=prime;
(B) 45 --> 45-2=43=prime;
(C) 68 --> yields a remainder of 2 upon division by 6 so theoretically can be the sum of two primes (and it is 61+7=68);
(D) 79 --> 79-2 is not a prime, 79-3 is not a prime and also 79 yields a remainder of 1 upon division by 6, so it can not be the sum of two primes;
(E) 88 --> 71+17=88.

Of course the above can be done much easier by just subtracting the primes starting from 2 from the answer choices and seeing whether the result is also a prime.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16021
Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

11 Feb 2015, 12:44
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.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7449
Location: Pune, India
Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

11 Feb 2015, 22:09
6
KUDOS
Expert's post
6
This post was
BOOKMARKED
banksy wrote:
187. Which of the following CANNOT be the sum of two prime numbers?
(A) 19
(B) 45
(C) 68
(D) 79
(E) 88

We know that other than 2, all prime numbers are odd. When you add two odd numbers, you get an even sum. To get an odd sum, one number must be even and then other odd. So to get 19, 45 and 79, one prime must be 2.
Now we just need to subtract 2 out of each of these three options to see whether we get another prime. 79 - 2 = 77 which is not prime. So 79 CANNOT be the sum of two prime numbers.
Note that there is a conjecture that every even number greater than 2 can be written as sum of two prime numbers. So we don't even need to check for the even sum options.
For more on this, check: http://www.veritasprep.com/blog/2014/08 ... t-part-iv/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Current Student
Joined: 29 Jul 2014
Posts: 17
Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

04 Sep 2015, 17:56
Bunuel wrote:
banksy wrote:
187. Which of the following CANNOT be the sum of two prime numbers?
(A) 19
(B) 45
(C) 68
(D) 79
(E) 88

Any prime number more than 3 can be expressed as $$p=6n+1$$ or$$p=6n+5$$ ($$p=6n-1$$), where n is an integer >0 (check this: primality-check-108425.html).

So the sum of two primes more than 3 can yield the following remainders upon division by 6:
0 - if two primes are of a type $$p=6n+1$$ and $$p=6n+5$$;
2 - if both primes are of a type $$p=6n+1$$;
4 - if both primes are of a type $$p=6n+5$$;

Now, we are looking for the choice which is not a prime+2, or prime+3 or has a remainder other than 0, 2, or 4 upon division by 6.

(A) 19 --> 19-2=17=prime;
(B) 45 --> 45-2=43=prime;
(C) 68 --> yields a remainder of 2 upon division by 6 so theoretically can be the sum of two primes (and it is 61+7=68);
(D) 79 --> 79-2 is not a prime, 79-3 is not a prime and also 79 yields a remainder of 1 upon division by 6, so it can not be the sum of two primes;
(E) 88 --> 71+17=88.

Of course the above can be done much easier by just subtracting the primes starting from 2 from the answer choices and seeing whether the result is also a prime.

Awesome explanation based on the crucial theory that any prime number >3 can be expressed in 6n+1 or 6n-1 format. I did not know this hence ended up taking an alternative logic. Where can I find more of such theorems on number theory.
Math Expert
Joined: 02 Sep 2009
Posts: 39744
Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

05 Sep 2015, 04:04
Expert's post
1
This post was
BOOKMARKED
diptimba wrote:
Bunuel wrote:
banksy wrote:
187. Which of the following CANNOT be the sum of two prime numbers?
(A) 19
(B) 45
(C) 68
(D) 79
(E) 88

Any prime number more than 3 can be expressed as $$p=6n+1$$ or$$p=6n+5$$ ($$p=6n-1$$), where n is an integer >0 (check this: primality-check-108425.html).

So the sum of two primes more than 3 can yield the following remainders upon division by 6:
0 - if two primes are of a type $$p=6n+1$$ and $$p=6n+5$$;
2 - if both primes are of a type $$p=6n+1$$;
4 - if both primes are of a type $$p=6n+5$$;

Now, we are looking for the choice which is not a prime+2, or prime+3 or has a remainder other than 0, 2, or 4 upon division by 6.

(A) 19 --> 19-2=17=prime;
(B) 45 --> 45-2=43=prime;
(C) 68 --> yields a remainder of 2 upon division by 6 so theoretically can be the sum of two primes (and it is 61+7=68);
(D) 79 --> 79-2 is not a prime, 79-3 is not a prime and also 79 yields a remainder of 1 upon division by 6, so it can not be the sum of two primes;
(E) 88 --> 71+17=88.

Of course the above can be done much easier by just subtracting the primes starting from 2 from the answer choices and seeing whether the result is also a prime.

Awesome explanation based on the crucial theory that any prime number >3 can be expressed in 6n+1 or 6n-1 format. I did not know this hence ended up taking an alternative logic. Where can I find more of such theorems on number theory.

Theory on Number Properties: math-number-theory-88376.html
Tips on Number Properties: number-properties-tips-and-hints-174996.html

All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38
All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

_________________
Manager
Joined: 09 Jun 2015
Posts: 101
Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

16 Apr 2016, 02:14
banksy wrote:
Which of the following CANNOT be the sum of two prime numbers?

(A) 19
(B) 45
(C) 68
(D) 79
(E) 88

Sum of two prime numbers are odd only when one of the numbers is 2
A)2+17 possible
B)2+43 possible
D)2+77 is not possible
Hence D is the answer.
BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2185
Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

17 Jan 2017, 06:58
This is a great Question.
Essentially this is testing our knowledge on Even/odd numbers.
If sum of 2 primes is even => 2 must not be either of them.
If sum of 2 primes is odd => 2 must be one of them.

Hence as 79 =2+77 =>79 can never be written as sum of 2 prime numbers.

Hence D

_________________

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

Director
Joined: 02 Sep 2016
Posts: 532
Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

04 May 2017, 07:05
prime nos. >3 can be written in the form: 6n+1 or 6n-1

Sum of two prime nos.= 6n+1+6n+1= 2(6n+1)

C and E can be eliminated on this basis.

Al the prime nos. are odd except 2.
Odd +Odd= Even
Odd + 2= Odd

The remaining three options are odd.
So subtract 2 from every choice.
D is the number that is always a multiple of some no.

D it is.
_________________

Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.

Senior Manager
Joined: 12 Nov 2016
Posts: 376
Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

19 Jun 2017, 12:44
Bunuel wrote:
banksy wrote:
187. Which of the following CANNOT be the sum of two prime numbers?
(A) 19
(B) 45
(C) 68
(D) 79
(E) 88

Any prime number more than 3 can be expressed as $$p=6n+1$$ or$$p=6n+5$$ ($$p=6n-1$$), where n is an integer >0 (check this: http://gmatclub.com/forum/primality-check-108425.html).

So the sum of two primes more than 3 can yield the following remainders upon division by 6:
0 - if two primes are of a type $$p=6n+1$$ and $$p=6n+5$$;
2 - if both primes are of a type $$p=6n+1$$;
4 - if both primes are of a type $$p=6n+5$$;

Now, we are looking for the choice which is not a prime+2, or prime+3 or has a remainder other than 0, 2, or 4 upon division by 6.

(A) 19 --> 19-2=17=prime;
(B) 45 --> 45-2=43=prime;
(C) 68 --> yields a remainder of 2 upon division by 6 so theoretically can be the sum of two primes (and it is 61+7=68);
(D) 79 --> 79-2 is not a prime, 79-3 is not a prime and also 79 yields a remainder of 1 upon division by 6, so it can not be the sum of two primes;
(E) 88 --> 71+17=88.

Of course the above can be done much easier by just subtracting the primes starting from 2 from the answer choices and seeing whether the result is also a prime.

Bunuel when you say

p=6n+1p=6n+1 orp=6n+5p=6n+5 (p=6n−1p=6n−1),

do you mean

p=6n+1p=6n+1 "or" p=6n+5p=6n+5 (p=6n−1p=6n−1), ?
Math Expert
Joined: 02 Sep 2009
Posts: 39744
Which of the following CANNOT be the sum of two prime numbers? [#permalink]

### Show Tags

19 Jun 2017, 12:49
1
KUDOS
Expert's post
Nunuboy1994 wrote:
Bunuel wrote:
banksy wrote:
187. Which of the following CANNOT be the sum of two prime numbers?
(A) 19
(B) 45
(C) 68
(D) 79
(E) 88

Any prime number more than 3 can be expressed as $$p=6n+1$$ or$$p=6n+5$$ ($$p=6n-1$$), where n is an integer >0 (check this: http://gmatclub.com/forum/primality-check-108425.html).

So the sum of two primes more than 3 can yield the following remainders upon division by 6:
0 - if two primes are of a type $$p=6n+1$$ and $$p=6n+5$$;
2 - if both primes are of a type $$p=6n+1$$;
4 - if both primes are of a type $$p=6n+5$$;

Now, we are looking for the choice which is not a prime+2, or prime+3 or has a remainder other than 0, 2, or 4 upon division by 6.

(A) 19 --> 19-2=17=prime;
(B) 45 --> 45-2=43=prime;
(C) 68 --> yields a remainder of 2 upon division by 6 so theoretically can be the sum of two primes (and it is 61+7=68);
(D) 79 --> 79-2 is not a prime, 79-3 is not a prime and also 79 yields a remainder of 1 upon division by 6, so it can not be the sum of two primes;
(E) 88 --> 71+17=88.

Of course the above can be done much easier by just subtracting the primes starting from 2 from the answer choices and seeing whether the result is also a prime.

Bunuel when you say

p=6n+1p=6n+1 orp=6n+5p=6n+5 (p=6n−1p=6n−1),

do you mean

p=6n+1p=6n+1 "or" p=6n+5p=6n+5 (p=6n−1p=6n−1), ?

You mean space was omitted?

It's $$p=6n+1$$ or $$p=6n+5$$ ($$p=6n-1$$)...
_________________
Which of the following CANNOT be the sum of two prime numbers?   [#permalink] 19 Jun 2017, 12:49
Similar topics Replies Last post
Similar
Topics:
1 If x is a prime number, which of the following cannot be an integer? 7 16 Jan 2017, 04:27
1 Which of the following cannot be the sum of 3 different prime numbers? 1 11 Apr 2016, 08:37
2 If a and b are prime numbers, which of the following CANNOT be the val 4 20 Jun 2017, 18:58
17 Which of the following cannot be the sum of two or more cons 10 03 Apr 2016, 08:47
8 If x and y are prime numbers, which of the following CANNOT 9 14 Jun 2017, 06:21
Display posts from previous: Sort by

# Which of the following CANNOT be the sum of two prime numbers?

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

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.