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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Two different primes may be said to"rhyme" around an integer [#permalink]
03 Jan 2011, 09:58

1

This post received KUDOS

6

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

55% (medium)

Question Stats:

31% (02:22) correct
69% (01:34) wrong based on 95 sessions

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.

Re: rhyming primes [#permalink]
03 Jan 2011, 12:30

5

This post received KUDOS

Expert's post

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 n-p_1=p_2-n, 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*15=30 --> 34=7+23=11+19=13+17: 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.

Re: rhyming primes [#permalink]
04 Jan 2011, 18:32

2

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

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, 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...

Re: rhyming primes [#permalink]
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, 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...

Re: rhyming primes [#permalink]
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.

Re: Two different primes may be said to"rhyme" around an integer [#permalink]
04 Jul 2014, 10:00

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.