Last visit was: 21 Jul 2024, 03:44 It is currently 21 Jul 2024, 03:44
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
User avatar
Senior Manager
Senior Manager
Joined: 31 Oct 2010
Status:Up again.
Posts: 415
Own Kudos [?]: 2274 [92]
Given Kudos: 75
Concentration: Strategy, Operations
GMAT 1: 740 Q49 V42
GMAT 2: 710 Q48 V40
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94439
Own Kudos [?]: 642670 [34]
Given Kudos: 86716
Send PM
Tutor
Joined: 16 Oct 2010
Posts: 15125
Own Kudos [?]: 66752 [13]
Given Kudos: 436
Location: Pune, India
Send PM
General Discussion
User avatar
Manager
Manager
Joined: 13 Aug 2010
Posts: 86
Own Kudos [?]: 121 [1]
Given Kudos: 1
Send PM
Re: rhyming primes [#permalink]
1
Kudos
great explanation Bunel, thanks a lot..... and a nice question
Board of Directors
Joined: 01 Sep 2010
Posts: 4558
Own Kudos [?]: 33617 [11]
Given Kudos: 4565
Send PM
Two different primes may be said to “rhyme” around an integer if they [#permalink]
4
Kudos
7
Bookmarks
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
Math Expert
Joined: 02 Sep 2009
Posts: 94439
Own Kudos [?]: 642670 [8]
Given Kudos: 86716
Send PM
Two different primes may be said to “rhyme” around an integer if they [#permalink]
6
Kudos
2
Bookmarks
Expert Reply
Board of Directors
Joined: 01 Sep 2010
Posts: 4558
Own Kudos [?]: 33617 [0]
Given Kudos: 4565
Send PM
Re: Two different primes may be said to “rhyme” around an integer if they [#permalink]
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.
Math Expert
Joined: 02 Sep 2009
Posts: 94439
Own Kudos [?]: 642670 [2]
Given Kudos: 86716
Send PM
Re: Two different primes may be said to “rhyme” around an integer if they [#permalink]
2
Kudos
Expert Reply
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.
avatar
Intern
Intern
Joined: 22 Apr 2013
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 0
Send PM
Re: rhyming primes [#permalink]
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 :(
User avatar
Manager
Manager
Joined: 16 Dec 2011
Posts: 236
Own Kudos [?]: 796 [0]
Given Kudos: 70
Re: rhyming primes [#permalink]
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.
avatar
Intern
Intern
Joined: 12 Aug 2014
Posts: 10
Own Kudos [?]: 20 [0]
Given Kudos: 27
Location: United States
Concentration: Strategy, General Management
GMAT 1: 710 Q50 V35
GMAT 2: 720 Q49 V40
WE:Other (Consulting)
Send PM
Re: Two different primes may be said to"rhyme" around an integer [#permalink]
Bunuel and Karishma,

17 has four set of rhyming primes. You both haven't considered (3,31) as a possible answer.
Tutor
Joined: 16 Oct 2010
Posts: 15125
Own Kudos [?]: 66752 [1]
Given Kudos: 436
Location: Pune, India
Send PM
Re: Two different primes may be said to"rhyme" around an integer [#permalink]
1
Kudos
Expert Reply
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)
User avatar
Senior Manager
Senior Manager
Joined: 07 Apr 2014
Status:Math is psycho-logical
Posts: 335
Own Kudos [?]: 393 [0]
Given Kudos: 169
Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
Re: Two different primes may be said to"rhyme" around an integer [#permalink]
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?
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 6020
Own Kudos [?]: 13812 [5]
Given Kudos: 125
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Re: Two different primes may be said to “rhyme” around an integer if they [#permalink]
5
Kudos
Expert Reply
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
sol2.jpg [ 102.15 KiB | Viewed 18247 times ]

GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11790 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: Two different primes may be said to “rhyme” around an integer if they [#permalink]
Expert Reply
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
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30844 [2]
Given Kudos: 799
Location: Canada
Send PM
Re: Two different primes may be said to “rhyme” around an integer if they [#permalink]
1
Kudos
1
Bookmarks
Expert Reply
Top Contributor
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
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19175
Own Kudos [?]: 22685 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: Two different primes may be said to “rhyme” around an integer if they [#permalink]
Expert Reply
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

Source: MGMAT



We are looking for pairs of prime numbers that are equidistant from a given integer. The approach we will use is to consider each prime number less than that integer and then pair that number with its equidistant match on the other side of the integer. If both numbers are prime, then we have a rhyme.

For example, for choice A, which is 12, we will consider the prime numbers less than 12. Since 11 is 1 less than 12, then 13 is its match because it is 1 more than 12. The pair (11, 13) is a rhyme because both numbers are prime. For the next prime, we skip 9 (not prime) and use 7. Since 7 is 5 less than 12, we see that 17 is 5 greater than 12, and the pair is (7, 17), which is a rhyme. The next pair is (5, 19), which is a rhyme. The final consideration is the pair (3, 21), but this is not a rhyme because 21 is not prime. Thus, for choice A, the integer 12 has 6 distinct rhyming primes.

Let’s use the same approach for the remaining answer choices B through E.

B. 15

(13, 17) ... Yes; (11, 19) ... Yes; (9, 21) ... No; (7, 23) ... Yes; (5, 25) ... No; 3, 27) ... No

We see that 15 has 6 distinct rhyming primes around it.

C. 17

(15, 19) ... No; (13, 21)… No; (11, 23) ... Yes; (9, 25) ... No; (7, 27) ... No; (5, 29) ... Yes; (3, 3)... Yes

We see that 17 has 6 distinct rhyming primes around it.

D. 18

(17, 19)… Yes; (15, 21) ... No; (13, 23) ... Yes; (11, 25) ... No; (9, 27) ... No; (7, 29) ... Yes; (5, 31) ... Yes;
(3, 33) ... No

We see that 18 has 8 distinct rhyming primes around it.

E. 20


(19, 21) ... No; (17, 23) ... Yes; (15, 25) ... No; (13, 27) ... No; (11, 29) ... Yes; (9, 31) ... No; (7, 33) ... No; (5, 35) ... No; (3, 37) ... Yes

We see that 20 has 6 distinct rhyming primes around it.

Answer: D
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34039
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: Two different primes may be said to rhyme around an integer if they [#permalink]
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 Club Bot
Re: Two different primes may be said to rhyme around an integer if they [#permalink]
Moderator:
Math Expert
94439 posts