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

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
Vote for Target Test Prep, Newsweek Readers’ Choice Awards 2026
NEWSWEEK READERS’ CHOICE 2026

BIG NEWS! Target Test Prep has been nominated, and they’d love your vote!

TTP has worked incredibly hard to build the best test prep experience possible, and winning Newsweek’s 2026 Readers’ Choice Award for Best Test Prep would mean a lot to them. If TTP has helped you, they’d be incredibly grateful for your vote. You can vote once each day through September 9.

Vote for TTP
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Prime number

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members
Thanked: 48 times
by vinay1983 » Sun Sep 29, 2013 11:33 pm
If P is a prime number, then which of the following COULD be the sum of the factors of P?

1. 2P-1 2. P+1 3. P^2-1

A. 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1 only
E. 1,2 and 3
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 391
Joined: Sat Mar 02, 2013 5:13 amFollowed by: 4 members
Thanked: 50 times

by rakeshd347 » Sun Sep 29, 2013 11:42 pm
vinay1983 wrote:If P is a prime number, then which of the following COULD be the sum of the factors of P?

1. 2P-1 2. P+1 3. P^2-1

A. 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1 only
E. 1,2 and 3
I think answer should be E.
Prime number only have 2 factors itself and 1. But as we have 2 as a prime number then we could have 1and 3 true as well.
2 has 2 factors 2 and 1. sum of the factors is 3. and hence all the 3 conditions are met. As it is a COULD be true questions so we can have answer E. If it were must be true then the answer will be A
Last edited by rakeshd347 on Sun Sep 29, 2013 11:45 pm, edited 1 time in total.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 358
Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members
Location: Jeddah, Saudi Arabia
Thanked: 42 times
GMAT Score:730

by faraz_jeddah » Sun Sep 29, 2013 11:44 pm
vinay1983 wrote:If P is a prime number, then which of the following COULD be the sum of the factors of P?

1. 2P-1 2. P+1 3. P^2-1

A. 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1 only
E. 1,2 and 3
I will go with E

P + 1 is obvious

If P = 2 then sum of factors is 1+2 = 3
P^2 - 1 = 2^2 - 1 = 4 - 1 = 3

same goes for 2P - 1
A good question also deserves a Thanks.

Messenger Boy: The Thesselonian you're fighting... he's the biggest man i've ever seen. I wouldn't want to fight him.
Achilles: That's why no-one will remember your name.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 283
Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members
Location: Bangalore, India
Thanked: 97 times
GMAT Score:750

by ganeshrkamath » Mon Sep 30, 2013 12:22 am
vinay1983 wrote:If P is a prime number, then which of the following COULD be the sum of the factors of P?

1. 2P-1 2. P+1 3. P^2-1

A. 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1 only
E. 1,2 and 3
Take the prime number 2.
Sum of its factors = 1+2 = 3
2(2) - 1 = 3
2 + 1 = 3
2^2 - 1 = 3
Choose E

In general,
Sum of factors of a number = (a^(n+1) - 1)/(a-1) * (b^(m+1) - 1)/(b-1) * ...
where a,b,.. are the prime factors of the number.
and n,m,.. are their respective powers.

Example: 6 = 2*3
Sum of factors of 6 = (2^(1+1)-1)/(2-1) * (3^(1+1)-1)/(3-1)
= (3/1) * (8/2) = 12

Cheers
Every job is a self-portrait of the person who did it. Autograph your work with excellence.

Kelley School of Business (Class of 2016)
GMAT Score: 750 V40 Q51 AWA 5 IR 8
https://www.beatthegmat.com/first-attemp ... tml#688494
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

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 » Mon Sep 30, 2013 5:58 am
vinay1983 wrote:If P is a prime number, then which of the following COULD be the sum of the factors of P?

1. 2P-1 2. P+1 3. P^2-1

A. 2 only
B. 2 and 3 only
C. 1 and 3 only
D. 1 only
E. 1,2 and 3
Picking numbers is a great way to go here.
Another option is to recognize that, if P is a prime number, then 1 and P are its ONLY factors.
So, the sum of the factors of P MUST EQUAL P + 1

Statement I: 2P - 1
Is it possible for the sum of the factors to be 2P - 1?
To find out, we'll set this equal to P + 1 to get . . .
2P - 1 = P + 1
Solve, to get P = 2
So, when P = 2, the sum of the factors is 2P - 1 (as well as P + 1)
Statement I can be true

Statement II: P + 1
P + 1 = P + 1, so statement II MUST be true

Statement III: P² - 1
Set this equal to P + 1 to get . . .
P² - 1 = P + 1
Rearrange: P² - P - 2 = 0
Factor: (P - 2)(P + 1) = 0
Solve, to get P = 2 or P = -1 [-1 is not prime, so we won't consider it]
So, when P = 2, the sum of the factors is P² - 1 (as well as P + 1)
Statement III can be true

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Legendary Member
Posts: 643
Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members
Thanked: 48 times

by vinay1983 » Mon Sep 30, 2013 6:10 am
So if i am right we are supposed to calculate/arrive at whether the statements "could be true" and not necessarily "must be true"
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

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 » Mon Sep 30, 2013 6:11 am
vinay1983 wrote:So if i am right we are supposed to calculate/arrive at whether the statements "could be true" and not necessarily "must be true"
That's right.

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

by Brent@GMATPrepNow » Mon Sep 30, 2013 6:24 am
Notice that, if we set each answer choice equal to P + 1 (as I did in my solution above), we can handle much trickier statements.
For example, COULD P² - 4P - 13 be the sum of the factors of P?
What about P² - 7P - 15?

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
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Mon Sep 30, 2013 11:16 pm
Hi vinay1983,

What is the source for this question? I only ask because it doesn't follow the typical GMAT style for Roman Numeral questions (which would ask "what MUST be true?"), it can be beaten by using the easiest number possible (the number 2, without testing the thoroughness of your knowledge) and doesn't have any of the "frequency shortcuts" that are typical of Roman Numeral questions. Roman Numeral questions on the GMAT are usually a bit more "involved" than this question.

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1