why do these statements contradict?

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why do these statements contradict?

by abcdefg » Thu Jul 16, 2009 9:01 am
If r > 0 and s > 0, is r/s < s/r?

1) r/3s = 1/4
2. s = r + 4

The OA is D. . What I don't get is why these 2 statements contradict each other. For example, I cross multiply statement #1 and get 4r = 3s. Therefore r = (3/4)s. So I choose a random number s = 4, then r = 3.

But plugging s = 4 and r = 3 into the second equation, it doesn't match. If r = 3 then s = 7 in the second equation.

How can both statements be sufficient yet contradict each other? Thanks.
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Re: why do these statements contradict?

by Ian Stewart » Thu Jul 16, 2009 10:37 am
abcdefg wrote:If r > 0 and s > 0, is r/s < s/r?

1) r/3s = 1/4
2. s = r + 4

The OA is D. . What I don't get is why these 2 statements contradict each other. For example, I cross multiply statement #1 and get 4r = 3s. Therefore r = (3/4)s. So I choose a random number s = 4, then r = 3.

But plugging s = 4 and r = 3 into the second equation, it doesn't match. If r = 3 then s = 7 in the second equation.

How can both statements be sufficient yet contradict each other? Thanks.
They don't contradict each other. All you've proved with your numerical example is that s is not 4, and r is not 3. If you know both statements are true, you have the two equations:

4r = 3s
r + 4 = s

This is two equations in two unknowns. You can solve using substitution, or by subtracting equations. Either way, you'll find that r = 12 and s = 16. Of course, we don't need both statements here, but they aren't contradictory.
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