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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] New post   19 Aug 2013, 09:36
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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
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Bunuel
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink] New post   19 Aug 2013, 09:43
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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.

Answer: A.
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink] New post   14 Nov 2015, 23:20
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stoy4o wrote:
If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz – z^2 = 0

(2) x + y – 3z = -5


Hi,

1) statement one gives us xyz – z^2 = 0
or z(xy-z)=0..
so either z=0 or xy=z or xy=z=0..
here it is given that z is a positive integer, so z cannot be 0..
xy =z

substitute in main Q, we get value of z as 3.. suff

2) x + y – 3z = -5..
three variables and two equations... in suff

ans A
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink] New post   15 Nov 2015, 03:40
1) z(xy-z)=0
z≠0 as z is +ve, xy=z
2xy+z=9
Or 3z=9
Or z= 3….sufficient.

2)….not sufficient

ANS: A
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If 2xy + z = 9, what is the value of the positive integer z? [#permalink] New post   20 May 2018, 12:06
Bunuel

i have a doubt.

using the equation given in the question and st2,

x +y - 3(9-2xy) = -5
x +y -27 +6xy =-5
x +y +6xy = 22

here if x=3, y =1, it satisfies the equation.

so 2xy +z = 9
so z = 9 - 6 = 3

so why st2 is wrong?
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink] New post   20 May 2018, 12:12
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nightvision wrote:
Bunuel

i have a doubt.

using the equation given in the question and st2,

x +y - 3(9-2xy) = -5
x +y -27 +6xy =-5
x +y +6xy = 22

here if x=3, y =1, it satisfies the equation.

so 2xy +z = 9
so z = 9 - 6 = 3

so why st2 is wrong?


Infinitely many pairs of (x, y) satisfy x + y + 6xy = 22. For any value of x, there will exist y for which x + y + 6xy = 22. For example, x = 0, y = 22; x = 1, y = 3; ...
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink] New post   16 Feb 2021, 08:23
Statement 1
xyz - z^2 = 0

=> xyz = z^2
=> xy = z

Substitute this in the equation given in the question to solve for z

2xy + z = 9
=> 2z + z = 9
=> z = 3

So statement 1 is sufficient

Since this is an equation in 3 variables, you need 3 equations to solve it. Sometimes you get lucky and get some relationship (such as statement 1) which you can use to solve the equation. But statement 2 offers no such simplifying relationship. Hence, statement 2 is insufficient

Remember the 12TEN mnemonic for answering DS questions!

Option A

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Arun Krishnan
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Stiv wrote:
If 2xy + z = 9, what is the value of the positive integer z?

(1) xyz - z^2 = 0

(2) x + y - 3z = -5
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink] New post   24 Dec 2023, 11:33
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Re: If 2xy + z = 9, what is the value of the positive integer z? [#permalink]
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