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Number Properties

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by carllecat » Tue Nov 17, 2009 8:39 am
If 0 < R < 1 < S < 2, which of the following must be less than 1?

I. R/S
II. RS
III. S-R

A) I only
B) II only
C) III only
D) I and II
E) I , II and III

Answer to be posted later.
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by carllecat » Tue Nov 17, 2009 8:52 am
A) I only.

Why isn't II also good.
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by palvarez » Tue Nov 17, 2009 10:23 am
carllecat wrote:A) I only.

Why isn't II also good.
0 < R < 1
1 < S < 2

0 < RS < 2
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by carllecat » Tue Nov 17, 2009 10:34 am
palvarez wrote:
carllecat wrote:A) I only.

Why isn't II also good.
0 < R < 1
1 < S < 2

0 < RS < 2
I got owned on that one...
Thanks,
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by manochsa » Tue Nov 17, 2009 10:35 am
Note that R is a proper fraction while S is an improper fraction bw 1 and 2. "Less than 1" means a proper fraction. So which of the following is a proper fraction?

Test some upper and lower limit numbers -- its obvious that a small R and a small S should give you something less than 1 (e.g., 1/4 x 5/4 = 5/16). Good, no question there.

But what about a large R and a large S? 3/4 x 7/4 = 21/16. This is not less than 1.
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by carllecat » Tue Nov 17, 2009 11:13 am
manochsa wrote:Note that R is a proper fraction while S is an improper fraction bw 1 and 2. "Less than 1" means a proper fraction. So which of the following is a proper fraction?

Test some upper and lower limit numbers -- its obvious that a small R and a small S should give you something less than 1 (e.g., 1/4 x 5/4 = 5/16). Good, no question there.

But what about a large R and a large S? 3/4 x 7/4 = 21/16. This is not less than 1.
It makes a lot of sense now and an easy trap for some people like me.

Thanks again.
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