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.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If x + y = 7 and (x + 1)(y 1) = 6, what are the possible values of x
[#permalink]
07 Jul 2022, 07:20
07 Jul 2022, 07:20
1
00:00
Question Stats:
50% (02:31) correct
50% (02:12) wrong based on 10 sessions
Hide Show timer Statistics
If x + y = 7 and (x + 1)(y – 1) = 6, what are the possible values of xy?
Indicate all such numbers.
(A) -10
(B) -6
(C) 0
(D) 6
(E) 8
(F) 10
Indicate all such numbers.
(A) -10
(B) -6
(C) 0
(D) 6
(E) 8
(F) 10
If x + y = 7 and (x + 1)(y 1) = 6, what are the possible values of x
[#permalink]
24 Jul 2022, 22:38
24 Jul 2022, 22:38
1
Bookmarks
GreenlightTestPrep wrote:
If x + y = 7 and (x + 1)(y – 1) = 6, what are the possible values of xy?
Indicate all such numbers.
(A) -10
(B) -6
(C) 0
(D) 6
(E) 8
(F) 10
(G) 12
Indicate all such numbers.
(A) -10
(B) -6
(C) 0
(D) 6
(E) 8
(F) 10
(G) 12
Sir, explanation please
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
If x + y = 7 and (x + 1)(y 1) = 6, what are the possible values of x
[#permalink]
25 Jul 2022, 07:56
25 Jul 2022, 07:56
1
GreenlightTestPrep wrote:
If x + y = 7 and (x + 1)(y – 1) = 6, what are the possible values of xy?
Indicate all such numbers.
(A) -10
(B) -6
(C) 0
(D) 6
(E) 8
(F) 10
Indicate all such numbers.
(A) -10
(B) -6
(C) 0
(D) 6
(E) 8
(F) 10
Take x + y = 7, and solve for x to get: x = 7 - y
Take (x + 1)(y – 1) = 6, and substitute the x-value from the above equation to get: (7 - y + 1)(y – 1) = 6
Simplify: (8 - y)(y – 1) = 6
Use FOIL to expand: 8y - 8 - y² + y = 6
Multiply both sides of the equation by -1 to get: -8y + 8 + y² - y = -6
Simplify and set equal to zero: y² - 9y + 14 = 0
Factor: (y - 2)(y - 7) = 0
This means either y = 2 or y = 7.
case i: If y = 2, we can substitute this value into the first equation to get x + 2 = 7, which means x = 5. In this case, xy = (5)(2) = 10
case ii: If y = 7, we can substitute this value into the first equation to get x + 7 = 7, which means x = 0. In this case, xy = (0)(7) = 0
Answer: C.F
