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# If 2xy + z = 9, what is the value of the positive integer z?

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If 2xy + z = 9, what is the value of the positive integer z? [#permalink]

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13 Oct 2009, 06:38
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If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z^2 = 0

(2) x + y – 3z = -5

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-2xy-z-9-what-is-the-value-of-the-positive-integer-z-158228.html
[Reveal] Spoiler: OA

Last edited by hogann on 13 Oct 2009, 11:42, edited 1 time in total.

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Re: Tuesday Q2 - Value of Z [#permalink]

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13 Oct 2009, 07:07
hogann wrote:
If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z2 = 0

(2) x + y – 3z = -5

not entirely sure of this but A seems sufficient

1. xyz -z2 = 0 then z(xy-2) =0 since z is +ve so xy -2 =0 so xy = 2 and we get value of z. so A suff
2. using the equation given in question and option we are left with 6xy +x+y =22. So B is insuff

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Re: Tuesday Q2 - Value of Z [#permalink]

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13 Oct 2009, 07:55
is it z*2 or z^2.....in both cases value of z can be known...A - SI sufficient
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Re: Tuesday Q2 - Value of Z [#permalink]

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13 Oct 2009, 09:39
asterixmatrix wrote:
not entirely sure of this but A seems sufficient

1. xyz -z2 = 0 then z(xy-2) =0 since z is +ve so xy -2 =0 so xy = 2 and we get value of z. so A suff
2. using the equation given in question and option we are left with 6xy +x+y =22. So B is insuff

I think with 1 you have xy - 2 = 0 => xy = 2 => 2z - 2z = 0

This does not give you the value of Z i'm sorry ! Z can be 1 or 4324236543253465,4 !

if we consider z² this is the same:

xyz - z² = 0 => z (xy - z) = 0 => xy = z => z² - z² = 0

I would choose E!

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Re: Tuesday Q2 - Value of Z [#permalink]

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14 Oct 2009, 01:43
I have serious doubts that correct answer would be A...

2z - 2z = 0 does not give the value of Z i'm sorry !!

Z=4 it works
Z=Pi it works too

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Re: Tuesday Q2 - Value of Z [#permalink]

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14 Oct 2009, 03:27
hi,,,
pl dont substitute the value of xy in the eq from which u have derived the value xy.. it will ofcourse be 0..
substitute it in main eq 2xy + z = 9....ie..2*2+z=9....z=5... sufficient
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Re: Tuesday Q2 - Value of Z [#permalink]

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14 Oct 2009, 05:14
hogann wrote:
If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z^2 = 0

(2) x + y – 3z = -5

Had a problem with exponents this morning!

Reorganising question stem:
2xy+z=9 => xy=(9-z)/2

Using Equation 1)
xyz-z^2 =0
Substitute in the question stem we get
\frac{z(9-z)}{2} - z^2=0
z(9-z) - 2z^2=0
9z-z^2-2z^2=0
9z-3z^2=0
3z(3-z)=0

Z=0 or Z=3 but we know from quesiton z is positive. Hence A is suff.

Using Equation 2) We cannot solve for Z. We can only get it down to two variables.

Hence ANS = A

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Re: Tuesday Q2 - Value of Z [#permalink]

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14 Oct 2009, 07:04
Oohhhhhhhhhhhhhh yes!! I did not see that... (

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Re: Tuesday Q2 - Value of Z [#permalink]

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15 Oct 2013, 07:31
yangsta8 wrote:
hogann wrote:
If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z^2 = 0

(2) x + y – 3z = -5

Had a problem with exponents this morning!

Reorganising question stem:
2xy+z=9 => xy=(9-z)/2

Using Equation 1)
xyz-z^2 =0
Substitute in the question stem we get
\frac{z(9-z)}{2} - z^2=0
z(9-z) - 2z^2=0
9z-z^2-2z^2=0
9z-3z^2=0
3z(3-z)=0

Z=0 or Z=3 but we know from quesiton z is positive. Hence A is suff.

Using Equation 2) We cannot solve for Z. We can only get it down to two variables.

Hence ANS = A

Good job buddy, I didn't see that one coming either.
Guys, always remember that when you are given something like in this case z is a positive integer, then they usually if not always say it for some reason
Just to keep in mind

Cheers
J

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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink]

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15 Oct 2013, 07:50
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If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz - z^2 = 0 --> $$z(xy-z)=0$$ --> $$z=0$$ or $$z=xy$$. Since given that z is a positive integer, then discard $$z=0$$ and we are left with $$z=xy$$. From $$2xy + z = 9$$ we get that $$2z + z = 9$$ --> $$z=3$$. Sufficient.

(2) x + y - 3z = -5. We cannot solve for z. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-2xy-z-9-what-is-the-value-of-the-positive-integer-z-158228.html
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Re: If 2xy + z = 9, what is the value of the positive integer z?   [#permalink] 15 Oct 2013, 07:50
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