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# Consider three real numbers, x, y, and z

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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1183
Location: India
GPA: 3.82
Consider three real numbers, x, y, and z  [#permalink]

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10 Sep 2017, 09:20
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82% (00:49) correct 18% (00:37) wrong based on 44 sessions

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Consider three real numbers, $$x$$, $$y$$, and $$z$$. Is $$z$$ the smallest of these numbers?

A. $$x$$ is greater than at least one of $$y$$ and $$z$$

B. $$y$$ is greater than at least one of $$x$$ and $$z$$
Intern
Joined: 13 Jul 2017
Posts: 1
Re: Consider three real numbers, x, y, and z  [#permalink]

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10 Sep 2017, 11:30
1
Consider three real numbers, x, y, and z. Is z the smallest of these numbers?

A. x is greater than at least one of y and z

B. y is greater than at least one of x and z

Statement 1: x is greater than at least one of y and z
So, x> y or x >z but it is not clear y>z or z>y, -> Insufficient.

Statement 2: y is greater than at least one of x and z.
So y>x or y>z but it is not clear x>z or z>x. -> insufficient.

1+2 we can consider x>z and y>z -> Sufficient.

If I am wrong kindly correct me.
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1183
Location: India
GPA: 3.82
Re: Consider three real numbers, x, y, and z  [#permalink]

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12 Sep 2017, 08:16
niks18 wrote:
Consider three real numbers, $$x$$, $$y$$, and $$z$$. Is $$z$$ the smallest of these numbers?

A. $$x$$ is greater than at least one of $$y$$ and $$z$$

B. $$y$$ is greater than at least one of $$x$$ and $$z$$

OE

Statement A: implies $$x>y$$ or $$x>z$$ or $$x>y$$ and $$z$$. Hence Insufficient

Statement B: implies $$y>x$$ or $$y>z$$ or $$y>x$$ and $$z$$. Hence Insufficient

Combining both statements, we can get $$y>x >z$$ or $$x>y>z$$. In either case $$z$$ is the smallest.

Option C
Re: Consider three real numbers, x, y, and z &nbs [#permalink] 12 Sep 2017, 08:16
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