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

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

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06 Nov 2014, 08:58
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Question Stats:

81% (01:16) correct 19% (00:51) wrong based on 101 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.
[Reveal] Spoiler: OA

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Manager
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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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06 Nov 2014, 10:59
2
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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

Last edited by adymehta29 on 06 Nov 2014, 14:52, edited 1 time in total.

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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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06 Nov 2014, 11:23
1
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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.

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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06 Nov 2014, 12:09
1
KUDOS
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.

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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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10 Nov 2014, 00:21
4
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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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Re: If z is not equal to zero, and z = 6zs - 9s^2, then z equals: [#permalink]

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08 Mar 2016, 08:12
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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21 Jul 2016, 09:23
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.

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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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29 Sep 2017, 00:13
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Re: If z is not equal to zero, and z = 6zs - 9s^2, then z equals:   [#permalink] 29 Sep 2017, 00:13
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