BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

Two different primes may be said to"rhyme" around

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 7187
Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members
by BTGmoderatorDC » Tue May 28, 2019 1:28 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

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

OA D

Source: Manhattan Prep
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Tue May 28, 2019 5:42 am
BTGmoderatorDC 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

OA D

Source: Manhattan Prep
If two numbers are rhyming primes, then the integer the 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
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8151
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

by Scott@TargetTestPrep » Wed May 29, 2019 5:48 pm
BTGmoderatorDC 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

OA D

Source: Manhattan Prep
Since a pair of distinct numbers equidistant from an integer must have the same parity (i.e., both odd or both even). Therefore, we don't need to check if the pair are even numbers. We also don't need to check if 1 is one of the two numbers of the pair since 1 is not a prime. With these facts in mind, let's check each given answer choice.

A. 12

11, 13 ... Yes; 9, 15 ... No; 7, 17 ... Yes; 5, 19 ... Yes; 3, 21 ... No

We see that 12 has 6 distinct rhyming primes around it.

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, 21vNo; 11, 23 ... Yes; 9, 25 v No; 7, 27 v No; 5, 29 ... Yes; 3, 3v Yes

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

D. 18

17, 19vYes; 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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1