GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
If q, r, and s are consecutive even integers and q < r < s, which of t
[#permalink]
04 Jun 2021, 22:57
04 Jun 2021, 22:57
Expert Reply
00:00
Question Stats:
62% (02:25) correct
37% (02:14) wrong based on 8 sessions
Hide Show timer Statistics
If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of \(s^2 – r^2 – q^2\)?
(A) -20
(B) 0
(C) 8
(D) 12
(E) 16
(A) -20
(B) 0
(C) 8
(D) 12
(E) 16
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
Re: If q, r, and s are consecutive even integers and q < r < s, which of t
[#permalink]
05 Jun 2021, 11:29
05 Jun 2021, 11:29
1
GeminiHeat wrote:
If q, r, and s are consecutive even integers and q < r < s, which of the following CANNOT be the value of \(s^2 – r^2 – q^2\)?
(A) -20
(B) 0
(C) 8
(D) 12
(E) 16
(A) -20
(B) 0
(C) 8
(D) 12
(E) 16
Let the consecutive even integers in increasing order be (x-2), x and (x+2)
S0, \(s^2 – r^2 – q^2 = (x+2)^2 - x^2 - (x-2)^2\)
\(= x^2 + 4 + 4x - x^2 - x^2 - 4 + 4x\)
\(= 8x - x^2\)
\(= x(8-x)\)
When \(x = -2\), \(s^2 – r^2 – q^2 = -20\)
When \(x = 0\), \(s^2 – r^2 – q^2 = 0\)
When \(x = 2\), \(s^2 – r^2 – q^2 = 12\)
When \(x = 4\), \(s^2 – r^2 – q^2 = 16\)
Hence, option C
gmatclubot
Re: If q, r, and s are consecutive even integers and q < r < s, which of t [#permalink]
05 Jun 2021, 11:29
Moderators:
