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20 Dec 2006, 15:21
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
63% (01:51) correct
37%
(01:47)
wrong
based on 978
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If a and b are integers, and a not= b, is |a|b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer
(1) |a^b| > 0
(2) |a|^b is a non-zero integer
15 Sep 2010, 09:39
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ravitejapandiri
Absolute value of of an expression is alway non-negative: \(|some \ expression|\geq{0}\). Please check Walker's post on Absolute Value at: https://gmatclub.com/forum/math-absolut ... 86462.html
As for the question:
If a and b are integers, and a does not equal to b, is |a|*b > 0?
\(|a|*b>0\) is true when \(a\) does not equal to zero and \(b>0\).
(1) \(|a^b| > 0\).
- This implies that \(a\) does not equal to zero (the first condition satisfied), but we don't know about \(b\)
\(b\) can be any value, positive or negative or 0.
Not sufficient.
(2) \(|a|^b\) is a non-zero integer.
- This again implies that \(a\) does not equal to zero (the first condition satisfied), but we don't know about \(b\).
For example, \(a\) can be 1 and in this case, \(b\) can be any integer, positive or negative or 0.
Not sufficient.
(1)+(2) If \(a=1\) and \(b=2\), then \(|a|*b>0\), but if \(a=1\) and \(b=-2\), then \(|a|*b<0\). Not sufficient.
Answer: E.
Similar question: https://gmatclub.com/forum/the-power-of ... 01661.html
Hope it helps.
20 Dec 2006, 15:37
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(E) for me.
|a|*b > 0 ?
<=> b > 0 ?
From (1)
|a^b| > 0
o If b=-1 and a=1, 1 > 0 and b < 0
o If b=1 and a=-1, 1 > 0 and b > 0
INSUFF.
From (2)
|a|^b is a non zero integer implies that b must be positive or equal to 0 in order to not create a real number such as 2^-1.
So, we remains with the cases of b = 0 and b > 0.
INSUFF.
Both (1) and (2)
It brings nothing more.
INSUFF.
|a|*b > 0 ?
<=> b > 0 ?
From (1)
|a^b| > 0
o If b=-1 and a=1, 1 > 0 and b < 0
o If b=1 and a=-1, 1 > 0 and b > 0
INSUFF.
From (2)
|a|^b is a non zero integer implies that b must be positive or equal to 0 in order to not create a real number such as 2^-1.
So, we remains with the cases of b = 0 and b > 0.
INSUFF.
Both (1) and (2)
It brings nothing more.
INSUFF.
