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
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.

Nice DS problem

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Master | Next Rank: 500 Posts
Posts: 194
Joined: Mon Oct 15, 2012 7:14 pmFollowed by: 6 members
Location: India
Thanked: 47 times
by The Iceman » Thu Dec 06, 2012 1:36 am
Let p(x) = x^2 + 40. Then for any two positive integers i and j where i > j, is p(i) + p(j) a composite number?

(I) p(i) - p(j) is not a composite number

(II) p(2i) + p(2j) is a composite number
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 145
Joined: Tue Jan 31, 2012 6:50 amFollowed by: 2 members
Location: New Delhi
Thanked: 16 times
GMAT Score:760

by nisagl750 » Thu Dec 06, 2012 5:05 am
The Iceman wrote:Let p(x) = x^2 + 40. Then for any two positive integers i and j where i > j, is p(i) + p(j) a composite number?

(I) p(i) - p(j) is not a composite number

(II) p(2i) + p(2j) is a composite number
Statement1:
Lets take different values of i & j
i=3, j=2
p(i)-p(j) = 5 which is a Prime number (Not composite)
p(i)+p(j) = 93 Composite

i=5, j=2
p(i)-p(j) = 61 which is a Prime number (Not composite)
p(i)+p(j) = 109 which is a Prime number (Not composite)
Insufficient

Statement2:
Lets take different values of i & j
i=3, j=2
p(2i)+p(2j) = 132 which is composite
p(i)+p(j) = 93 Composite

i=5, j=2
p(2i)+p(2j) = 196 which is composite
p(i)+p(j) = 109 which is a Prime number (Not composite)
Insufficient

Statements 1 & 2 Together:
Take same examples
i=3, j=2 & i=5, j=2

Insufficent

Ans E
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 194
Joined: Mon Oct 15, 2012 7:14 pmFollowed by: 6 members
Location: India
Thanked: 47 times

by The Iceman » Thu Dec 06, 2012 8:49 am
nisagl750 wrote:
i=5, j=2
p(i)-p(j) = 61 which is a Prime number (Not composite)
p(i)+p(j) = 109 which is a Prime number (Not composite)
Insufficient

Calculation mistake highlighted in red. Please try again.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 145
Joined: Tue Jan 31, 2012 6:50 amFollowed by: 2 members
Location: New Delhi
Thanked: 16 times
GMAT Score:760

by nisagl750 » Thu Dec 06, 2012 9:09 am
The Iceman wrote:
Calculation mistake highlighted in red. Please try again.
I have corrected. Hope It makes sense now.....

Statement1:
Lets take different values of i & j
i=3, j=2
p(i)-p(j) = 5 which is a Prime number (Not composite)
p(i)+p(j) = 93 Composite

i=4, j=3
p(i)-p(j) = 7 which is a Prime number (Not composite)
p(i)+p(j) = 105 which is composite

i=6, i=5
p(i)-p(j) = 11 which is a Prime number (Not composite)
p(i)+p(j) = 141 which is composite

sufficient

Statement2:
Lets take different values of i & j
i=3, j=2
p(2i)+p(2j) = 132 which is composite
p(i)+p(j) = 93 Composite

i=5, j=2
p(2i)+p(2j) = 196 which is composite
p(i)+p(j) = 109 which is a Prime number (Not composite)
Insufficient

Statements 1 & 2 Together:
Take same examples
i=3, j=2 & i=5, j=2

Insufficent

Ans A
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 194
Joined: Mon Oct 15, 2012 7:14 pmFollowed by: 6 members
Location: India
Thanked: 47 times

by The Iceman » Thu Dec 06, 2012 10:04 am
nisagl750 wrote: i=5, j=2
p(2i)+p(2j) = 196 which is composite
p(i)+p(j) = 109 which is a Prime number (Not composite)
Insufficient

Statements 1 & 2 Together:
Take same examples
i=3, j=2 & i=5, j=2

Insufficent

Ans A
Bingo!

Statement I can be validated using a generic process.

p(i) - p(j) is not a composite number
=>i^2-j^2 is a prime as i ,j are positive integers and i >j, ( i^2-j^2) can't be 1
=>(i+j)(i-j)= prime
so i-j=1
let p be the prime so i=(p+1)/2 and j=(p-1)/2
clearly p is not 2, hence p is odd
p(i) + p(j)=80 +(p^2+1)/2
for p =3, p(i) + p(j)=85, which is not a prime

Also p^2=6k+1 ( for p>3 )

=>p(i) + p(j)=80 +(p^2+1)/2= 80+(6k+2)/2 = 81+3k = 3(27+k), which is not a prime => can be answered using I
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1