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a ≠ b, is |a| b > 0?

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a ≠ b, is |a| b > 0?

by sanju09 » Sat Aug 14, 2010 4:48 am
If a and b are integers, and a ≠ b, is |a| b > 0?

(1) |a^b| > 0
(2) |a|^b is a non-zero integer.

[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]
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by reply2spg » Sat Aug 14, 2010 5:17 am
I think the answer is B to this.
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by kvcpk » Sat Aug 14, 2010 5:24 am
sanju09 wrote:If a and b are integers, and a ≠ b, is |a| b > 0?

(1) |a^b| > 0
(2) |a|^b is a non-zero integer.

[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]
(1) |a^b| > 0
let a=1, b=2
1^2>0 and 1*2 = 2>0..YES
Let a=1,b=-2
1^-2>0 and 1*-2<0..NO
INSUFF

(2) |a|^b is a non-zero integer.
a=1,b=2
1^2=1 and 1*2 =2>0..YES
Let a=1,b=-2
1^-2>0 and 1*-2<0..NO
INSUFF

Combining:

Still same example as above, can be used to prove INSUFF

pick E.
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by crackinggmat » Sat Aug 14, 2010 8:43 pm
E is my answer
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by thirst4edu » Mon Aug 16, 2010 7:21 am
sanju09 wrote:If a and b are integers, and a ≠ b, is |a| b > 0?

(1) |a^b| > 0
(2) |a|^b is a non-zero integer.

[spoiler]Source: Picked from some source unknown to www.avenuesabroad.org[/spoiler]
B should be the answer, according to me..

|a|b > 0 is basicaly asking, is b positive?

1) |a^b| > 0
Tells us nothing about b is positive or negative. Either way we can still have above expression true.

2) |a|^b is a non-zero integer.
Here 'a' could be positive or negative we dont care, if 'b' is positive we get the integer answer, if number is negative we get non-integer answer, so according to statement 2, 'b' should be positive to get |a|^b a non-zero integer.

So Answer is B.
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by uwhusky » Mon Aug 16, 2010 11:12 pm
Agree with B. The question asks whether b is positive, and |a|^b is a non-zero integer can only result with b being positive.
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by kvcpk » Tue Aug 17, 2010 2:21 am
uwhusky wrote:Agree with B. The question asks whether b is positive, and |a|^b is a non-zero integer can only result with b being positive.
Hi Uwhusky,

try with a=1, b=-2

See my post above, I believe answer is E.

Am I missing something?
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by thirst4edu » Tue Aug 17, 2010 6:13 am
kvcpk wrote:
uwhusky wrote:Agree with B. The question asks whether b is positive, and |a|^b is a non-zero integer can only result with b being positive.
Hi Uwhusky,

try with a=1, b=-2

See my post above, I believe answer is E.

Am I missing something?

For a second you got me, but I know what you are missing. :) Let me explain
Lets start with given info -
1) a and b both are integers
2) Question is - is b positive? or if you are not comfortable re-stating the question we can keep as it is |a|b > 0?.

Now since, we already established about stmt 1, jumping straight to stmt 2
stmt 2) |a|^b is a non-zero integer.

Focus on "a non-zero integer", this is means that |a|^b is a fraction.
To get above expression as fraction, two things are necessary -
a) 'a' is a fraction - which is not the case, we are given that a is an integer.
b) 'b' is negative, and 'a' is NOT 1 or 0. Here, only 'b' as a negative exponent can make above expression fraction, and also 'a' must not be 1 or 0.

Hence, the value for 'a' you picked (a=1) is not eligible for test.

Which means a > 1 and b < 0 to be able to make |a|^b non-zero integer.

This is a very good mistake to learn at the time of practice rather than do it in exam!

Hope this helps!
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by kvcpk » Tue Aug 17, 2010 6:38 am
thirst4edu wrote: Focus on "a non-zero integer", this is means that |a|^b is a fraction.
Unfortunately, I still dont get you.

Why does a "non-zero integer" mean a fraction?

1 is a non-zero integer.
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by thirst4edu » Tue Aug 17, 2010 6:52 am
kvcpk wrote:
thirst4edu wrote: Focus on "a non-zero integer", this is means that |a|^b is a fraction.
Unfortunately, I still dont get you.

Why does a "non-zero integer" mean a fraction?

1 is a non-zero integer.
Ouch !! what a classic mistake! You got me.. I never realized I shouldn't read it as "non-integer"!!
You are abosultely right , answer should be E, now I get it.. Oh boy!

Thank you!
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by kvcpk » Tue Aug 17, 2010 6:55 am
thirst4edu wrote:
kvcpk wrote:
thirst4edu wrote: Focus on "a non-zero integer", this is means that |a|^b is a fraction.
Unfortunately, I still dont get you.

Why does a "non-zero integer" mean a fraction?

1 is a non-zero integer.
Ouch !! what a classic mistake! You got me.. I never realized I shouldn't read it as "non-integer"!!
You are abosultely right , answer should be E, now I get it.. Oh boy!

Thank you!
Kool.. I thought I was missing something after seeing Uwhusky also getting B.

Now feeling better :)
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by thirst4edu » Tue Aug 17, 2010 6:57 am
kvcpk wrote:
thirst4edu wrote:
kvcpk wrote:
thirst4edu wrote: Focus on "a non-zero integer", this is means that |a|^b is a fraction.
Unfortunately, I still dont get you.

Why does a "non-zero integer" mean a fraction?

1 is a non-zero integer.
Ouch !! what a classic mistake! You got me.. I never realized I shouldn't read it as "non-integer"!!
You are abosultely right , answer should be E, now I get it.. Oh boy!

Thank you!
Kool.. I thought I was missing something after seeing Uwhusky also getting B.

Now feeling better :)
Yeah, this mistake definitely goes into my flash cards. :) Thanks a lot!
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by uwhusky » Tue Aug 17, 2010 8:21 am
|a|^b is a non-zero integer.

I think you're mistaking what this means. It is saying that |a|^b is an integer that isn't 0, not a fraction. Hence b cannot be a negative value.

It isn't saying that |a|^b is a non integer.
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