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27 Oct 2013, 15:46
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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55% (02:17) correct
45%
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based on 179
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Updated on: 03 May 2020, 00:22
Originally posted by Reinfrank2011 on 27 Oct 2013, 16:36.
Last edited by Reinfrank2011 on 03 May 2020, 00:22, edited 3 times in total.
Last edited by Reinfrank2011 on 03 May 2020, 00:22, edited 3 times in total.
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Is |ab| > -ab?
--> Is |ab| + ab > 0 ?
Notice that this is true only when the product ab is positive. (If ab is negative, |ab| + ab = 0, which is not greater than 0. If ab is equal to zero, |ab| + ab = 0, which is not greater than 0.)
Thus, what we really want to know...
Is ab > 0 ?
1) a > 1/b
If a = 2 and b = 1, the answer is YES.
If a = 2 and b = -1, the answer is NO. --> Insufficient.
2) a + b > 0
This can be shown to be insufficient in the same manner
If a = 2 and b = 1, the answer is YES.
If a = 2 and b = -1, the answer is NO. --> Insufficient.
Thus, even combined the statements are insufficient. Answer E.
--> Is |ab| + ab > 0 ?
Notice that this is true only when the product ab is positive. (If ab is negative, |ab| + ab = 0, which is not greater than 0. If ab is equal to zero, |ab| + ab = 0, which is not greater than 0.)
Thus, what we really want to know...
Is ab > 0 ?
1) a > 1/b
If a = 2 and b = 1, the answer is YES.
If a = 2 and b = -1, the answer is NO. --> Insufficient.
2) a + b > 0
This can be shown to be insufficient in the same manner
If a = 2 and b = 1, the answer is YES.
If a = 2 and b = -1, the answer is NO. --> Insufficient.
Thus, even combined the statements are insufficient. Answer E.
31 Oct 2013, 10:29
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TheKraken
SleeB
Is |ab| > -ab?
1) a > 1/b
2) a + b > 0
but if b < 0 then that inequality won't hold as the inequality sign will flip
1) a > 1/b
2) a + b > 0
but if b < 0 then that inequality won't hold as the inequality sign will flip
The sign flip is only upon multiplying and dividing by a negative number.
That's the point. Do you know whether b is negative or positive? Do you know whether you should flip the sign of the inequality when multiplying by b?
Never multiply or reduce inequality by an unknown (a variable) unless you are sure of its sign.
So you CANNOT multiply a>1/b by b since you don't know the sign of b: if b>0, then you'll have ab>1 but if b<0, then you'll have ab<1 (flip the sign when multiplying by negative value).
Hope it's clear.
As always thanks for the poke 
. 
