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If a>0, b>0, c>0, Is a(bc)=0 1) bc=cb 2) b/c=c/b [#permalink]
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06 Jun 2008, 11:19
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If a>0, b>0, c>0, Is a(bc)=0
1) bc=cb 2) b/c=c/b
I don't have an OA, but want to verify my answer. Thanks. Soomodh



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Re: Is a(bc)=0 [#permalink]
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06 Jun 2008, 11:39
I think each one is suff. (D)
(1) gives b=c. So suff. for any a. (2) gives b=c or b=c, but, taken together with the condition b>0, c>0, it gives b=c. Suff.



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Re: Is a(bc)=0 [#permalink]
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06 Jun 2008, 11:42
Greenoak, thanks thats what I got (I initially got wrong coz I didn't realize greater than zero condition). S



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Re: Is a(bc)=0 [#permalink]
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06 Jun 2008, 12:52
Hi guys, I got D.
1) b  c = c  b
or 2B = 2C, B = C. any value of a * (b  c) will be 0 .suff
2) b/c = c/b = c^2 = b^2 or c = b , again same analysis. suff.
if my logic is incorrect, please let me know.



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Re: Is a(bc)=0 [#permalink]
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06 Jun 2008, 15:28
ca_gold careful with c2= b2 , so c= b statement, this is only true if c and b are positive, if ve then not. Soomodh



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Re: Is a(bc)=0 [#permalink]
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06 Jun 2008, 16:32
It's D.
Statement (1) is straight forward.
Lets look at statement (2) \(\frac {b} {c} = \frac {c} {b}\)
or \(b^2=c^2\) or \(b^2c^2=0\) or \((b+c)(bc)=0\)
which gives us either\(b=c\), or \(b=c\) Since we know from the question stem that \(b>0, c>0\), we can ignore \(b=c\) Therefore, statement (2) is also sufficient.



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Re: Is a(bc)=0 [#permalink]
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06 Jun 2008, 18:51
soomodh wrote: ca_gold careful with c2= b2 , so c= b statement, this is only true if c and b are positive, if ve then not. Soomodh hi soomodh, good call, thanks for the that!










