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If x, y, and z are positive numbers, is x < y < z ?

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If x, y, and z are positive numbers, is x < y < z ?

(1) xy < yz
(2) xz < yz

[Reveal] Spoiler:
1 and 2 are insuff by themselves; but when evaluating C, we have:

x < z
x < y

If we subtract the 2 inequalities, we get 0 < z - y ; or --> y<z
Since we now know how y and z also relate to each other, isn't this info sufficient to answer the question?

Got this from Hacks Challenge Algebra; DS; answer given is E

Please help :)

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