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Absolute values!


 
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Cybermusings
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PostPosted: Wed May 16, 2007 2:17 am    Post subject: Absolute values! Reply with quote
2. Is ¦x - y¦>¦x - z¦?
(1) ¦y¦>¦z¦
(2) x < 0
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bww
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PostPosted: Wed May 16, 2007 5:15 am    Post subject: Reply with quote
Quote:
2. Is ¦x - y¦>¦x - z¦?
(1) ¦y¦>¦z¦
(2) x < 0


(1) alone is not sufficient. This tells us that the absolute value of Y is greater than that of Z. Yet plugging in both positive and negative values for Y and Z in the question produces different inequalities (i.e. let x=5, y=+3/-3, and z=+2/-2).

(2) alone is not sufficient either. Now we can let x=-5, but without (1) we have nothing to work with.

Putting the two statements together, along with the examples we have used, is not sufficient. Let x=-5. We can have |-5-3|>|-5-2| but also |-5-(-3)|<|-5-(-2)|.

I think the answer is E.
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