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

Redeem

Nice DS problem

This topic has 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 pm
Location: India
Thanked: 47 times
Followed by:6 members

Nice DS problem

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
Source: — Data Sufficiency |
User avatar
Master | Next Rank: 500 Posts
Posts: 145
Joined: Tue Jan 31, 2012 6:50 am
Location: New Delhi
Thanked: 16 times
Followed by:2 members
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
User avatar
Master | Next Rank: 500 Posts
Posts: 194
Joined: Mon Oct 15, 2012 7:14 pm
Location: India
Thanked: 47 times
Followed by:6 members

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
User avatar
Master | Next Rank: 500 Posts
Posts: 145
Joined: Tue Jan 31, 2012 6:50 am
Location: New Delhi
Thanked: 16 times
Followed by:2 members
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
User avatar
Master | Next Rank: 500 Posts
Posts: 194
Joined: Mon Oct 15, 2012 7:14 pm
Location: India
Thanked: 47 times
Followed by:6 members

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
Post new topic Post Reply
• Page 1 of 1