February 20, 2019 February 20, 2019 08:00 PM EST 09:00 PM EST Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST February 21, 2019 February 21, 2019 10:00 PM PST 11:00 PM PST Kick off your 2019 GMAT prep with a free 7day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.
Author 
Message 
TAGS:

Hide Tags

Senior Manager
Status: Up again.
Joined: 31 Oct 2010
Posts: 489
Concentration: Strategy, Operations
GMAT 1: 710 Q48 V40 GMAT 2: 740 Q49 V42

Two different primes may be said to"rhyme" around an integer
[#permalink]
Show Tags
03 Jan 2011, 09:58
Question Stats:
34% (02:47) correct 66% (02:06) wrong based on 486 sessions
HideShow timer Statistics
Two different primes may be said to"rhyme" around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? A. 12 B. 15 C. 17 D. 18 E. 20 Source: MGMAT Heaven knows what I'll do if I encounter such a question on GMAT!! It is solvable no doubt but very time consuming.. Please do post the time you take to solve this question.. I took 1.4 minutes to grasp the question, then left it as I thought it would eat away the valuable remaining time on the test.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
My GMAT debrief: http://gmatclub.com/forum/from620to710mygmatjourney114437.html




Math Expert
Joined: 02 Sep 2009
Posts: 52971

Two different primes may be said to"rhyme" around an integer
[#permalink]
Show Tags
03 Jan 2011, 12:30
gmatpapa wrote: Two different primes may be said to"rhyme" around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? 1. 12 2. 15 3. 17 4. 18 5. 20 Source: MGMAT Heaven knows what I'll do if I encounter such a question on GMAT!! It is solvable no doubt but very time consuming.. Please do post the time you take to solve this question.. I took 1.4 minutes to grasp the question, then left it as I thought it would eat away the valuable remaining time on the test. As per definition two different primes \(p_1\) and \(p_2\) are "rhyming primes" if \(np_1=p_2n\), for some integer \(n\) > \(2n=p_1+p_2\). So twice the number \(n\) must equal to the sum of two different primes, one less than \(n\) and another more than \(n\). Let's test each option: A. 12 > 2*12=24 > 24=5+19=7+17=11+13: 6 rhyming primes (start from the least prime and see whether we can get the sum of 24 by adding another prime more than 12 to it); B. 15 > 2*15=30 > 30=7+23=11+19=13+17: 6 rhyming primes; C. 17 > 2*17=34 > 34=3+31=5+29=11+23: 6 rhyming primes; D. 18 > 2*18=36 > 36=5+31=7+29=13+23=17+19: 8 rhyming primes; E. 20 > 2*20=40 > 40=3+37=11+29=17+23: 6 rhyming primes. Answer: D.
_________________
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




Board of Directors
Joined: 01 Sep 2010
Posts: 3349

Two different primes may be said to “rhyme” around an integer if they
[#permalink]
Show Tags
11 Mar 2012, 12:45




Manager
Joined: 13 Aug 2010
Posts: 150

Re: rhyming primes
[#permalink]
Show Tags
04 Jan 2011, 01:23
great explanation Bunel, thanks a lot..... and a nice question



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8883
Location: Pune, India

Re: rhyming primes
[#permalink]
Show Tags
04 Jan 2011, 18:32
gmatpapa wrote: Two different primes may be said to"rhyme" around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? 1. 12 2. 15 3. 17 4. 18 5. 20 Source: MGMAT Heaven knows what I'll do if I encounter such a question on GMAT!! It is solvable no doubt but very time consuming.. Please do post the time you take to solve this question.. I took 1.4 minutes to grasp the question, then left it as I thought it would eat away the valuable remaining time on the test. Alternative solution: Since we are concerned with integers between 1 and 20, write down the primes till 40. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (you should be very comfortable with the first few primes... ) 2, 3, 5, 7, 11, 12, 13, 17, 19, 23, 29, 31, 37  Three pairs (11,13), (7,17), (5, 19) 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 37  Three pairs (13, 17), (11, 19), (7, 23) 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37  Three pairs (11, 23), (5, 29), (3, 31) 2, 3, 5, 7, 11, 13, 17, 18, 19, 23, 29, 31, 37  Four pairs (17, 19), (13, 23), (7, 29), (5, 31) 2, 3, 5, 7, 11, 13, 17, 19, 20, 23, 29, 31, 37  definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore. Answer (D). It doesn't take too much time to look for equidistant pairs...
_________________
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 >



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Two different primes may be said to “rhyme” around an integer if they
[#permalink]
Show Tags
11 Mar 2012, 13:12



Board of Directors
Joined: 01 Sep 2010
Posts: 3349

Re: Two different primes may be said to “rhyme” around an integer if they
[#permalink]
Show Tags
11 Mar 2012, 14:35



Math Expert
Joined: 02 Sep 2009
Posts: 52971

Re: Two different primes may be said to “rhyme” around an integer if they
[#permalink]
Show Tags
11 Mar 2012, 23:01
carcass wrote: Thanks Bunuel.
This is the first time I see something like that in a question. Intersting is your formula because I don't understand why if we had 20 numbers we worked with 40.
Can you give me some links to investigate a little further this concept ??'
Thnaks again for explanation. There is no special concept behind it. We have that: \(2n=p_1+p_2\), for some integer \(n\). Answer choices give different values of \(n\) and we should find out which \(n\) has the greatest number of distinct rhyming primes around it. When plugging values from answer choices for \(n\) in \(2n=p_1+p_2\), you'll have \(2n\) to wok with since there is \(2n\) in the formula. Hope it's clear.
_________________
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



Intern
Joined: 22 Apr 2013
Posts: 1

Re: rhyming primes
[#permalink]
Show Tags
20 May 2013, 22:43
VeritasPrepKarishma wrote: gmatpapa wrote: Two different primes may be said to"rhyme" around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? 1. 12 2. 15 3. 17 4. 18 5. 20 Source: MGMAT Heaven knows what I'll do if I encounter such a question on GMAT!! It is solvable no doubt but very time consuming.. Please do post the time you take to solve this question.. I took 1.4 minutes to grasp the question, then left it as I thought it would eat away the valuable remaining time on the test. Alternative solution: Since we are concerned with integers between 1 and 20, write down the primes till 40. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (you should be very comfortable with the first few primes... ) 2, 3, 5, 7, 11, 12, 13, 17, 19, 23, 29, 31, 37  Three pairs (11,13), (7,17), (5, 19) 2, 3, 5, 7, 11, 13, 15, 17, 19, 23, 29, 31, 37  Three pairs (13, 17), (11, 19), (7, 23) 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37  Three pairs (11, 23), (5, 29), (3, 31) 2, 3, 5, 7, 11, 13, 17, 18, 19, 23, 29, 31, 37  Four pairs (17, 19), (13, 23), (7, 29), (5, 31) 2, 3, 5, 7, 11, 13, 17, 19, 20, 23, 29, 31, 37  definitely cannot be more than 4 since there are only 4 primes more than 20. So must be less than 4 pairs. Ignore. Answer (D). It doesn't take too much time to look for equidistant pairs... why are we considering till 40?? I did not get it



Senior Manager
Joined: 16 Dec 2011
Posts: 303

Re: rhyming primes
[#permalink]
Show Tags
21 May 2013, 01:14
royal wrote: why are we considering till 40?? I did not get it As the highest integer, for which rhyming pair to be found, is 20, we need to consider equal range below the number 20 and above the number 20. In fact, we need to consider the range (2,38) as the lowest prime is 2.



Intern
Joined: 12 Aug 2014
Posts: 10
Location: United States
Concentration: Strategy, General Management
GMAT 1: 710 Q50 V35 GMAT 2: 720 Q49 V40
WE: Other (Consulting)

Re: Two different primes may be said to"rhyme" around an integer
[#permalink]
Show Tags
21 Dec 2014, 05:29
Bunuel and Karishma,
17 has four set of rhyming primes. You both haven't considered (3,31) as a possible answer.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8883
Location: Pune, India

Re: Two different primes may be said to"rhyme" around an integer
[#permalink]
Show Tags
21 Dec 2014, 20:29
anon1111 wrote: Bunuel and Karishma,
17 has four set of rhyming primes. You both haven't considered (3,31) as a possible answer. Both Bunuel and I have considered 3 and 31 as rhyming primes for 17 in our solutions above. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37  Three pairs (11, 23), (5, 29), (3, 31)
_________________
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 >



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 415
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: Two different primes may be said to"rhyme" around an integer
[#permalink]
Show Tags
30 Dec 2014, 11:07
Hello,
I wanted to share how I ended up with the correct answer. It is probably a lucky choice, but just in case I wanted to share.
So, I didn't see the connection with the mean (even though statistics is my biggest strength). What I did was to first find the primes up to 20, just to see if there is a pattern that makes sense.
So, I lined them up, smaller to larger, and tried to find a number that is between 1 and 20. For me this meant 1<x<20, so I wanted a number that is one of these: 2,3,4....,19.
Then, I realised that there is no upper limmit to the primes  so there is no reason why they should stop at 19. What I realised then, is that the number that has most primes should be the highest possible in the range we are given: one of 2,3,4,....,19. So, 19 being the highest value, it is logical that this one would have the most primes around it. I rejected 20, because of the range, so I chose 18 (D), because it was the second highest.
Does it make any sense?



CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2788
Location: India
GMAT: INSIGHT
WE: Education (Education)

Re: Two different primes may be said to “rhyme” around an integer if they
[#permalink]
Show Tags
22 Oct 2015, 05:55
carcass wrote: Two different primes may be said to “rhyme” around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it? (A) 12 (B) 15 (C) 17 (D) 18 (E) 20 How to deal with ??? Just solve it by checking every option Answer : Option D
Attachments
File comment: www.GMATinsight.com
sol2.jpg [ 102.15 KiB  Viewed 5294 times ]
_________________
Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha email: info@GMATinsight.com I Call us : +919999687183 / 9891333772 Online OneonOne Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html
ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13553
Location: United States (CA)

Re: Two different primes may be said to “rhyme” around an integer if they
[#permalink]
Show Tags
07 Mar 2018, 19:37
Hi All, This question requires a bit of a tactical approach combined with "brute force." The answers to this question provide 5 possible values that COULD have the GREATEST number of rhyming primes, so we just have to figure out which one it is. We can't afford to stare at the problem though; to be efficient, we have to get in and throw some punches. We're told to look for prime numbers that are equidistant from a number, but we're limited to numbers from 1 to 20, inclusive. Let's list out the primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37 (nothing above 40 is required, since there wouldn't be a matching rhyme prime on the other "side" of the number) Logically, the correct answer will probably be one of the bigger integers, since those values allow for a greater number of primes that are "lower." We can quickly check them all though. A: 12  5&19, 7&17, 11&13 B: 15  7&23, 11&19, 13&17 C: 17  3&31, 5&29, 11&23 D: 18  5&31, 7&29, 13&23, 17&19 E: 20  3&37, 11&29, 17&23 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



CEO
Joined: 11 Sep 2015
Posts: 3432
Location: Canada

Re: Two different primes may be said to “rhyme” around an integer if they
[#permalink]
Show Tags
19 Apr 2018, 14:48
gmatpapa wrote: Two different primes may be said to"rhyme" around an integer if they are the same distance from the integer on the number line. For instance, 3 and 7 rhyme around 5. What integer between 1 and 20, inclusive, has the greatest number of distinct rhyming primes around it?
A. 12 B. 15 C. 17 D. 18 E. 20
If two numbers are rhyming primes, then the integer they rhyme around will be the AVERAGE of the two primes. For example, 3 and 7 rhyme around 5. Notice that the AVERAGE of 3 and 7 is 5. Likewise, 5 and 23 rhyme around 14, and the AVERAGE of 5 and 23 is 14. Now onto the solution... List several primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,....Now check the answer choices: A)12 For 12 to be the integer that two primes rhyme around, we need 2 primes that have an AVERAGE of 12. In other words, we need 2 primes that ADD to 24. Now check the list of primes to find pairs that satisfy this condition. We get: 5 & 19, 7 & 17, 11 & 13 Total of 3 pairs. B)15 So, we need 2 distinct primes that ADD to 30. We get: 7 & 23, 11 & 19, 13 & 17 Total of 3 pairs. C)17 So, we need 2 distinct primes that ADD to 34. We get: 3 & 31, 5 & 29, 11 & 23 Total of 3 pairs. D)18 So, we need 2 distinct primes that ADD to 36. We get: 5 & 31, 7 & 29, 13 & 23, 17 & 19 Total of 4 pairs. E)20 So, we need 2 distinct primes that ADD to 40. We get: 3 & 37, 11 & 29, 17 & 23 Total of 3 pairs. Answer: D Cheers, Brent
_________________
Test confidently with gmatprepnow.com




Re: Two different primes may be said to “rhyme” around an integer if they
[#permalink]
19 Apr 2018, 14:48






