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If 0 <X <1 and 1 <Y <2, will X> 1/2? 1) XY =

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mihai9 Junior | Next Rank: 30 Posts Default Avatar
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If 0 <X <1 and 1 <Y <2, will X> 1/2? 1) XY =

Post Wed Nov 08, 2017 10:44 pm
If 0 1/2?

1) XY = 1
2) (X-32)(X+1)(X-32)(X+1) = 0If 0 1/2?

1) XY = 1
2) (X-32)(X+1)(X-32)(X+1) = 0

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Post Thu Nov 09, 2017 5:35 pm
I think we should reformat the question first, for those attempting it:

Quote:
If 0 < x < 1 < y < 2, is x > 0.5 ?

S1:: xy = 1

S2:: (x - 32)² * (x + 1)² = 0

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Post Thu Nov 09, 2017 5:46 pm
... and here's my solution!

S1::

Since xy = 1, we know that x = 1/y.

Suppose x ≤ 1/2. Then we'd have something like x = 1/2, 1/3, 1/4, 1/5, ..., whatever. But since x = 1/y, those give us y = 2, 3, 4, 5. ..., all of which are too big! So as x shrinks below 1/2, y grows beyond 2, contradicting the stem. That means we can't have x ≤ 1/2, because it would force y ≥ 2. So x must be > 1/2, and S1 is sufficient.

S2::

We've got two solutions: x = 32 and x = -1. Both of these contradict the stem, so this statement is broken and can't be properly evaluated.

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