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Math Expert V
Joined: 02 Sep 2009
Posts: 58320
If z is not equal to zero, and z = 6zs - 9s^2, then z equals:  [#permalink]

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4
4 00:00

Difficulty:   5% (low)

Question Stats: 88% (01:47) correct 12% (01:50) wrong based on 174 sessions

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Tough and Tricky questions: Algebra.

If z is not equal to zero, and $$z = \sqrt{6zs - 9s^2}$$, then z equals:

A. s
B. 3s
C. 4s
D. -3s
E. -4s

Kudos for a correct solution.

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Re: If z is not equal to zero, and z = 6zs - 9s^2, then z equals:  [#permalink]

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$$z = \sqrt{6zs - 9s^2}$$

Squaring both sides

$$z^2 = 6zs - 9s^2$$

$$z^2 - 6zs + 9s^2 = 0$$

The LHS is a perfect square of (z - 3s)

$$(z - 3s)^2 = 0$$

z = 3s

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Intern  Joined: 12 May 2013
Posts: 48
Re: If z is not equal to zero, and z = 6zs - 9s^2, then z equals:  [#permalink]

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2
This is how i got the answer.

squaring on both the sides gives Z^2 = 6ZS -9S^2
= Z^2-6ZS+9S^2
= Z(Z-3S) -3S(Z-3S)
= (Z-3S) (Z-3S)
= Z = 3S

i will go with B Originally posted by adymehta29 on 06 Nov 2014, 10:59.
Last edited by adymehta29 on 06 Nov 2014, 14:52, edited 1 time in total.
Verbal Forum Moderator B
Joined: 10 Oct 2012
Posts: 591
Re: If z is not equal to zero, and z = 6zs - 9s^2, then z equals:  [#permalink]

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2
Bunuel wrote:

Tough and Tricky questions: Algebra.

If z is not equal to zero, and $$z = \sqrt{6zs - 9s^2}$$, then z equals:

A. s
B. 3s
C. 4s
D. -3s
E. -4s

Kudos for a correct solution.

One can easily eliminate A,D and E, as because for any of the values of z for these options, the expression under the root would equal a negative integer. Thus, we are left with only B or C. Easily start with any one, plug-in the value of z(say z=4s), this gives the expression under the root as $$5s^2$$, which is obviously not correct.

B.
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Re: If z is not equal to zero, and z = 6zs - 9s^2, then z equals:  [#permalink]

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1
This is how i got the answer.

squaring on both the sides gives Z^2 = 6ZS -9Z^2
= Z^2-6ZS+9Z^2
= Z(Z-3S) -3S(Z-3S)
= (Z-3S) (Z-3S)
= Z = 3S

i will go with B Agree with your answer. I just think you had some typo (Z mixed with S) in there that might confuse people. Current Student D
Joined: 12 Aug 2015
Posts: 2572
Schools: Boston U '20 (M)
GRE 1: Q169 V154 Re: If z is not equal to zero, and z = 6zs - 9s^2, then z equals:  [#permalink]

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Bunuel wrote:

Tough and Tricky questions: Algebra.

If z is not equal to zero, and $$z = \sqrt{6zs - 9s^2}$$, then z equals:

A. s
B. 3s
C. 4s
D. -3s
E. -4s

Kudos for a correct solution.

Here z^2 = 6zs -9s^2
now using the quadratic formula => z = 6s /2 = 3s
hence B
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Re: If z is not equal to zero, and z = 6zs - 9s^2, then z equals:  [#permalink]

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One can easily eliminate D and E as value of z can not be negative because of Square root.
By plugging, z = 3s, 3s = \sqrt{6*3s*s - 9s^2}
then, squaring on both side: 9s^2 = 18s^2 - 9s^2,
we get both sides equal.
Non-Human User Joined: 09 Sep 2013
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Re: If z in not equal to zero, and z=sqrt(6zs-9s^2) , then z  [#permalink]

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_________________ Re: If z in not equal to zero, and z=sqrt(6zs-9s^2) , then z   [#permalink] 30 Aug 2019, 02:41
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