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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1053
GPA: 3.39
If (Z-3)^2 = 12,then 2z(z-6)=
[#permalink]
08 Feb 2020, 05:59
08 Feb 2020, 05:59
Expert Reply
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Question Stats:
100% (01:58) correct
0% (00:00) wrong based on 5 sessions
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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If (Z-3)^2 = 12,then 2z(z-6)=
[#permalink]
08 Feb 2020, 06:39
08 Feb 2020, 06:39
1
GeminiHeat wrote:
If \((z-3)^2 = 12\),then \(2z(z-6)=\)
A. 6
B. 9
C. 10
D. 15
E. 27
A. 6
B. 9
C. 10
D. 15
E. 27
There are two possible approaches here:
1) Solve the original equation for z, and then plug that value into \(2z(z-6)\)
2) Take the original equation, \((z-3)^2 = 12\), and manipulate it so that it looks like \(2z(z-6)\)
Let's go with approach #2
Given: \((z-3)^2 = 12\)
Expand and simplify the left side: \(z^2-6z+9=12\)
Multiply both sides of the equation by 2 to get: \(2z^2-12z+18=24\)
Subtract 18 from both sides to get: \(2z^2-12z=6\)
Back to the left side: \(2z(z-6)=6\)
Answer: A
Cheers,
Brent
GRE Instructor
Joined: 19 Jan 2020
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Re: If (Z-3)^2 = 12,then 2z(z-6)=
[#permalink]
09 Feb 2020, 07:50
09 Feb 2020, 07:50
1
GeminiHeat wrote:
If \((z-3)^2 = 12\),then \(2z(z-6)=\)
A. 6
B. 9
C. 10
D. 15
E. 27
A. 6
B. 9
C. 10
D. 15
E. 27
Method 1
\((z-3)^2 = 12\)
\(=> z^2 - 6x + 9 = 12\)
\(=> z^2 - 6x = 3\)
\(=> z(z - 6) = 3\)
\(=> 2z(z - 6) = 2 * 3 = 6\)
Answer A
Method 2:
Let us approximate (or use a calculator!):
\((z-3)^2 = 12\)
\(=> z - 3 = \sqrt{12} = \sqrt{(3 * 4)} = 2 * \sqrt{3} = 2 * 1.7 = 3.4\)
\(=> z = 6.4\)
\(=> 2z(z - 6) = 2 * 6.4 * (6.4 - 6) = 12.8 * 0.4 =~ 13 * 0.4 = 5.2\)
=> Best Option is A (= 6)
