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Permutations and Combinations

If w < x < ...

Question

If $w < x < z$ and $w < y < z$ , which of the following statements must be true?
I. $w < z$
II. $x < y$
III. $y < z$

A

I only

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B

II only

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C

III only

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D

I and III only

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E

I, II, and III

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Solution

The correct option is D I and III only
Since $w < x$ and $x < z$
By transitive property $w < z$
Since $w < y$ and $y < z$
By transitive property $w < z$
From both the inequations it is true that $w < z$
Also, we know that $y < z$
$w < z$ an $y < z$
We cannot talk about relation between $x, y$ because it is impossible to get it from the given data
Option D is correct

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