December 11, 2018 December 11, 2018 09:00 PM EST 10:00 PM EST Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST. December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 10 Feb 2011
Posts: 108

Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
17 Feb 2011, 14:10
Question Stats:
62% (01:36) correct 38% (01:34) wrong based on 645 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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 51101

Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
17 Feb 2011, 14:44
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 \(p=6n+5\) (\(p=6n1\)), where n is an integer >0 (check this: http://gmatclub.com/forum/primalitycheck108425.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 > 192=17=prime; (B) 45 > 452=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 > 792 is not a prime, 793 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 the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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? Extrahard Quant Tests with Brilliant Analytics




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8659
Location: Pune, India

Re: Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
11 Feb 2015, 21:09
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 ... tpartiv/
_________________
[b]Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



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, 16:56
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\(p=6n+5\) (\(p=6n1\)), where n is an integer >0 (check this: primalitycheck108425.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 > 192=17=prime; (B) 45 > 452=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 > 792 is not a prime, 793 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. Awesome explanation based on the crucial theory that any prime number >3 can be expressed in 6n+1 or 6n1 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: 51101

Re: Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
05 Sep 2015, 03:04
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\(p=6n+5\) (\(p=6n1\)), where n is an integer >0 (check this: primalitycheck108425.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 > 192=17=prime; (B) 45 > 452=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 > 792 is not a prime, 793 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. Awesome explanation based on the crucial theory that any prime number >3 can be expressed in 6n+1 or 6n1 format. I did not know this hence ended up taking an alternative logic. Where can I find more of such theorems on number theory.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 09 Jun 2015
Posts: 93

Re: Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
16 Apr 2016, 01:14
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.



Current Student
Joined: 12 Aug 2015
Posts: 2629

Re: Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
17 Jan 2017, 05:58
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
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



Director
Joined: 02 Sep 2016
Posts: 682

Re: Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
04 May 2017, 06:05
prime nos. >3 can be written in the form: 6n+1 or 6n1 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.



Director
Joined: 12 Nov 2016
Posts: 734
Location: United States
GPA: 2.66

Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
19 Jun 2017, 11:44
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\(p=6n+5\) (\(p=6n1\)), where n is an integer >0 (check this: http://gmatclub.com/forum/primalitycheck108425.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 > 192=17=prime; (B) 45 > 452=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 > 792 is not a prime, 793 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. 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: 51101

Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
19 Jun 2017, 11:49
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\(p=6n+5\) (\(p=6n1\)), where n is an integer >0 (check this: http://gmatclub.com/forum/primalitycheck108425.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 > 192=17=prime; (B) 45 > 452=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 > 792 is not a prime, 793 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. 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 \(p=6n+5\) (\(p=6n1\))...
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  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? Extrahard Quant Tests with Brilliant Analytics



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4278
Location: United States (CA)

Re: Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
22 Jul 2018, 17:06
banksy wrote: Which of the following CANNOT be the sum of two prime numbers?
(A) 19 (B) 45 (C) 68 (D) 79 (E) 88 Recall that odd + odd = even and odd + even = odd. Also recall that 2 is the only even prime number. If the sum of two distinct prime numbers is odd, then one of them must be 2 since the other one will be odd, and the sum of 2 and an odd number is odd. So let’s check the answer choices that are odd numbers first. A) 19 19 = 2 + 17 Since 17 is prime, A is not the correct choice. B) 45 45 = 2 + 43 Since 43 is prime, B is not the correct choice either. D) 79 79 = 2 + 77 Since 77 is not a prime, D is the correct choice. Answer: D
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



VP
Joined: 09 Mar 2016
Posts: 1213

Re: Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
23 Jul 2018, 05:25
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 \(p=6n+5\) (\(p=6n1\)), where n is an integer >0 (check this: http://gmatclub.com/forum/primalitycheck108425.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 > 192=17=prime; (B) 45 > 452=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 > 792 is not a prime, 793 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. Bunuel what is the reason you subtract 2 (A) 19 > 192=17=prime; (B) 45 > 452=43=prime;



Manager
Joined: 16 May 2017
Posts: 57
Location: India
WE: General Management (Retail Banking)

Re: Which of the following CANNOT be the sum of two prime numbers?
[#permalink]
Show Tags
05 Aug 2018, 08:09
banksy wrote: Which of the following CANNOT be the sum of two prime numbers?
(A) 19 (B) 45 (C) 68 (D) 79 (E) 88 A prime number always ends with 1 2,3,5,7,9. So if we add any 2 prime numbers we cannot obtain a last digit 9. So Ans: D
_________________
"The harder you work the luckier you get"




Re: Which of the following CANNOT be the sum of two prime numbers? &nbs
[#permalink]
05 Aug 2018, 08:09






