Find all School-related info fast with the new School-Specific MBA Forum

It is currently 01 Sep 2015, 13:29
GMAT Club Tests

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 10 Feb 2011
Posts: 115
Followers: 1

Kudos [?]: 96 [0], given: 10

Which of the following CANNOT be the sum of two prime numbers? [#permalink] New post 17 Feb 2011, 14:10
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

69% (01:58) correct 31% (01:01) wrong based on 71 sessions
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
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50038 [0], given: 7519

Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink] New post 17 Feb 2011, 14:44
Expert's post
1
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: 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.

Answer: D.

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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

GMAT Club Premium Membership - big benefits and savings

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6162
Followers: 344

Kudos [?]: 70 [0], given: 0

Premium Member
Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink] New post 11 Feb 2015, 11:44
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5863
Location: Pune, India
Followers: 1481

Kudos [?]: 7972 [0], given: 190

Re: Which of the following CANNOT be the sum of two prime numbers? [#permalink] New post 11 Feb 2015, 21:09
Expert's post
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

Re: Which of the following CANNOT be the sum of two prime numbers?   [#permalink] 11 Feb 2015, 21:09
    Similar topics Author Replies Last post
Similar
Topics:
If a and b are prime numbers, which of the following CANNOT be the sum sunita123 0 05 Jul 2015, 14:32
38 Experts publish their posts in the topic Which of the following numbers is prime? honchos 11 01 Mar 2014, 22:56
11 Experts publish their posts in the topic Which of the following cannot be the sum of two or more cons TheNona 7 25 Mar 2013, 09:00
9 Experts publish their posts in the topic Which of the following numbers is not prime ? abhi47 12 03 May 2012, 00:14
3 Experts publish their posts in the topic If x and y are prime numbers, which of the following CANNOT fiendex 6 06 Feb 2012, 03:14
Display posts from previous: Sort by

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

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.