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19 Aug 2013, 09:36
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Difficulty:
35%
(medium)
Question Stats:
74% (01:46) correct
26%
(02:09)
wrong
based on 393
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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
(1) xyz - z^2 = 0
(2) x + y - 3z = -5
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.
(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.
14 Nov 2015, 23:20
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stoy4o
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
