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 →

tricky integer properties question: If p and q are ...

Expert replies
Post new topic Post Reply
Previous Topic Next Topic

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 Apr 24, 2017 6:17 am
If p and q are different prime numbers, and n = pq - 2q, then which of the following cannot be true?

A) n is odd
B) n + 3 is a prime number
C) n is a prime number
D) nq is a prime number
E) n(p - 2) is a prime number

Answer: D

Source: www.gmatprepnow.com
Difficulty level: 650 - 700
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 2663
Joined: Wed Jan 14, 2015 8:25 amFollowed by: 128 members
Location: Boston, MA
Thanked: 1153 times
GMAT Score:770

by DavidG@VeritasPrep » Mon Apr 24, 2017 7:40 am
Brent@GMATPrepNow wrote:If p and q are different prime numbers, and n = pq - 2q, then which of the following cannot be true?

A) n is odd
B) n + 3 is a prime number
C) n is a prime number
D) nq is a prime number
E) n(p - 2) is a prime number

Answer: D

Source: www.gmatprepnow.com
Difficulty level: 650 - 700
You could always do a little simple number-picking here. Say p =3 and q =2. In that case, n = 3*2 - 2*2 = 6-4 = 2.

A) 2 is not ODD; hang on to it.
B) 2 + 3 = 5; 5 is prime; we want the option that cannot be true, so this is out
C) 2 is prime. Nope.
D) nq = 2*2 =4. Not prime. Hold on to it.
E) 2(3 - 2) = 2. 2 is prime, so this is out.

We're left with A or D. Try new numbers. Say p =3 and q = 5. In that case n= 3*5 - 2*5 = 5; Now n is ODD, so A could true. If A is out, we're left with D
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Fri Apr 28, 2017 12:15 am
n = pq - 2q

n = q * (p - 2)

From here,

n * q = (q * (p - 2)) * q

or

nq = q² * (p - 2)

Since q is prime, we have nq = (some square > 1) * (some other integer) = not prime.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1