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 →

Prime number

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Fri Aug 23, 2013 6:23 am
vinay1983 wrote:If X is a positive integer, is X!+(x+1) a prime number?

1. X is less than 10
2. X is even
Both statements are satisfies by x=2.
Here, x! + (x+1) = 2! + 3 = 5, which is prime.

Both statements are satisfied by x=8.
Here, x! + x+1 = 8! + 9 = (8*7*6*5*4*3*2*1) + (3*3) = 3(8*7*6*5*4*2*1 + 3).
In this case, x! + (x+1) has a factor of 3 and thus is NOT prime.

Thus, the two statements combined are INSUFFICIENT.

The correct answer is E.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
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 » Fri Aug 23, 2013 6:34 am
vinay1983 wrote:If X is a positive integer, is X!+(x+1) a prime number?

1. X is less than 10
2. X is even

Target question: Is x! + (x+1) a prime number?

Statement 1: X is less than 10
To make things easy on ourselves, we'll try small values of x
x = 1: we get 1! + (1+1) = 3, which is prime
x = 3: we get 3! + (3+1) = 10, which is not prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: X is even
Start with small values of x
Try x = 2: we get 2! + (2+1) = 5, which is prime
Try x = 4: we get 4! + (4+1) = 29, which is prime
Try x = 6: we get 6! + (6+1) = 727, which is prime??? TOO HARD - SKIP IT
Try x = 8: we get 8! + (8+1) = 8! + 9. DO NOT EVALUATE! Since 8! and 9 are both divisible by 3, (8!+9) must be divisible by 3, which means it is not prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When x = 2, x!+(x+1) is a prime number.
When x = 8, x!+(x+1) is not prime .
So, the combined statements are NOT SUFFICIENT

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 » Fri Aug 23, 2013 6:38 am
Brent@GMATPrepNow wrote:
vinay1983 wrote:If X is a positive integer, is X!+(x+1) a prime number?

1. X is less than 10
2. X is even

Target question: Is x! + (x+1) a prime number?

Statement 1: X is less than 10
To make things easy on ourselves, we'll try small values of x
x = 1: we get 1! + (1+1) = 3, which is prime
x = 3: we get 3! + (3+1) = 10, which is not prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: X is even
Start with small values of x
Try x = 2: we get 2! + (2+1) = 5, which is prime
Try x = 4: we get 4! + (4+1) = 29, which is prime
Try x = 6: we get 6! + (6+1) = 727, which is prime??? TOO HARD - SKIP IT
Try x = 8: we get 8! + (8+1) = 8! + 9. DO NOT EVALUATE! Since 8! and 9 are both divisible by 3, (8!+9) must be divisible by 3, which means it is not prime
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
When x = 2, x!+(x+1) is a prime number.
When x = 8, x!+(x+1) is not prime .
So, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent
So does this mean that if a sequence of numbers have 3 in them, then that sequence is divisible/multiple by/of 3?
Can this be generalized?
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 » Fri Aug 23, 2013 6:42 am
vinay1983 wrote:
So does this mean that if a sequence of numbers have 3 in them, then that sequence is divisible/multiple by/of 3?
Can this be generalized?
You bet.
We can say that n! is divisible by n, n-1, n-2, n-3, . . . 3, 2 and (of course) 1
For example, 11! is divisible by 11, 10, 9, 8, . . . 3, 2 and 1

Aside: 11! is also divisible by numbers other than those mentioned.

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1