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 →

Five Consecutive positive integers

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 438
Joined: Mon Feb 12, 2007 9:44 am
Thanked: 26 times
by chidcguy » Sat Jun 21, 2008 5:20 pm
Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4?

(1) The third of the five integers is a prime number.

(2) The second of the five integers is the square of an integer.
Please do not post answer along with the Question you post/ask

Let people discuss the Questions with out seeing answers.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members
Location: Toronto
Thanked: 1710 times
GMAT Score:800

Re: Five Consecutive positive integers

by Stuart@KaplanGMAT » Sat Jun 21, 2008 5:51 pm
chidcguy wrote:Five consecutive positive integers are chosen at random. If the average of the five integers is odd, what is the remainder when the largest of the five integers is divided by 4?

(1) The third of the five integers is a prime number.

(2) The second of the five integers is the square of an integer.
Since the average is odd, we know that middle term is odd. Accordingly, the last term is also odd.

So, the possible remainders when we divide an odd number by 4 are 1 and 3.

(1) The third integer is prime.

Primes are pretty random, unless two is an option (and in this case it's not), so we should suspect that we don't have enough info.

We can try numbers to be sure:

{1, 2, 3, 4, 5}... 5/4 has a remainder of 1.
{3, 4, 5, 6, 7)... 7/4 has a remainder of 3.

Insufficient!

(2) The second term is a perfect square.

Well, we know that the second term is even. Every even perfect square can be written as (2^2)(x^2), where x is an integer. Since term 2 has (2^2) as factor, term 2 is a multiple of 4.

If term 2 is a multiple of 4, that means that term 5 is going to be (a multiple of 4) + (3). Therefore term 5 divided by 4 will always have a remainder of 3: sufficient.

(2) is suff and (1) isn't: choose (B).
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 438
Joined: Mon Feb 12, 2007 9:44 am
Thanked: 26 times

by chidcguy » Sat Jun 21, 2008 7:00 pm
Since the average is odd, we know that middle term is odd.

Can you explain this?
Please do not post answer along with the Question you post/ask

Let people discuss the Questions with out seeing answers.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 167
Joined: Tue Apr 22, 2008 12:48 am
Thanked: 15 times

by durgesh79 » Sat Jun 21, 2008 7:32 pm
chidcguy wrote:Since the average is odd, we know that middle term is odd.

Can you explain this?
For 5 consecutive integers, middles term (third) is the average ....

consider c-2,c-1,c,c+1,c+2, Average = 5c/5 = c
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 438
Joined: Mon Feb 12, 2007 9:44 am
Thanked: 26 times

by chidcguy » Sat Jun 21, 2008 8:01 pm
Thanks dude. Dummy me! I guess some times my brain just comes to a grinding halt. Jeez.
Please do not post answer along with the Question you post/ask

Let people discuss the Questions with out seeing answers.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1