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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
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07 Jul 2022, 07:20
07 Jul 2022, 07:20
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Question Stats:
50% (02:31) correct
50% (02:12) wrong based on 10 sessions
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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
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24 Jul 2022, 22:38
24 Jul 2022, 22:38
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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
