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Difficulty:
45%
(medium)
Question Stats:
67% (01:43) correct
33%
(02:05)
wrong
based on 986
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The operation Θ is defined by x Θ y = 1/x + 1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true?
I. \(z \theta (-z) = 0\)
II. \(z \theta \frac{z}{(z-1)}= 1\)
III. \(\frac{2}{z} \theta \frac{2}{z}= z\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
I. \(z \theta (-z) = 0\)
II. \(z \theta \frac{z}{(z-1)}= 1\)
III. \(\frac{2}{z} \theta \frac{2}{z}= z\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
rskanumuri
GMAT 1: 750 Q50 V41
Posts: 33
08 Sep 2013, 04:19
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Can anyone verify the question? I think that first option should be z Θ (-z) =0 for this to be true!..
So either D or E! cheers~!!~
So either D or E! cheers~!!~
08 Sep 2013, 06:48
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rskanumuri
Edited the question.
The operation Θ is defined by x Θ y = 1/x + 1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true?
I. \(\hspace{10} z \hspace{2} \theta \hspace{2} (-z) = 0\)
II. \(\hspace{10} z \hspace{2} \theta \hspace{2} \frac{z}{(z-1)}= 1\)
III. \(\hspace{10} \frac{2}{z} \hspace{2} \theta \hspace{2} \frac{2}{z}= z\)
A. I only
B. I and II only
C. I and III only
D. II and III only
E. I, II, and III
I. \(\hspace{10} z \hspace{2} \theta \hspace{2} (-z) =\frac{1}{z}-\frac{1}{z}=0\) --> true.
II. \(\hspace{10} z \hspace{2} \theta \hspace{2} \frac{z}{(z-1)}=\frac{1}{z}+\frac{z-1}{z}=1\) --> true.
III. \(\hspace{10} \frac{2}{z} \hspace{2} \theta \hspace{2} \frac{2}{z}= \frac{z}{2}+\frac{z}{2}=z\) --> true.
Answer: E.
