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.
If x #y = (x + y)(x - y) for all real numbers, then which of the follo
[#permalink]
09 Mar 2022, 04:00
09 Mar 2022, 04:00
Expert Reply
1
Bookmarks
00:00
Question Stats:
78% (01:10) correct
21% (01:14) wrong based on 19 sessions
Hide Show timer Statistics
If x #y = (x + y)(x - y) for all real numbers, then which of the following must be true?
I. x #y = y #x
II. x #0 = 0 #x = x^2
III. x #-y = x #y
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
I. x #y = y #x
II. x #0 = 0 #x = x^2
III. x #-y = x #y
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
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 x #y = (x + y)(x - y) for all real numbers, then which of the follo
[#permalink]
25 Mar 2022, 05:51
25 Mar 2022, 05:51
1
Carcass wrote:
If x #y = (x + y)(x - y) for all real numbers, then which of the following must be true?
I. x #y = y #x
II. x #0 = 0 #x = x^2
III. x #-y = x #y
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
I. x #y = y #x
II. x #0 = 0 #x = x^2
III. x #-y = x #y
(A) I only
(B) II only
(C) III only
(D) II and III
(E) I, II, and III
I. x # y = y # x
x # y = (x + y)(x - y) = \(x^2 - y^2\)
y # x = (y + x)(y - x) = \(y^2 - x^2\)
Not true always
II. x # 0 = 0 # x = \(x^2\)
x # 0 = (x + 0)(x - 0) = \(x^2\)
0 # x = (0 + x)(0 - x) = \(-x^2\)
III. x # -y = x # y
x # -y = [x + (-y)][x - (-y)] = [x - y][x + y] = \(x^2 - y^2\)
x # y = (x - y)(x + y) = \(x^2 - y^2\)
Hence, option C
gmatclubot
Re: If x #y = (x + y)(x - y) for all real numbers, then which of the follo [#permalink]
25 Mar 2022, 05:51
Moderators:
