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If a > 0, b > 0 and c > 0, is a(b  c) = 0? [#permalink]
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Updated on: 30 Jun 2013, 08:03
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If a > 0, b > 0 and c > 0, is a(b  c) = 0? (1) b  c = c  b (2) b/c = c/b
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http://gmatclub.com/forum/countdownbeginshasended8548340.html#p649902
Originally posted by tejal777 on 21 Aug 2009, 19:24.
Last edited by Bunuel on 30 Jun 2013, 08:03, edited 2 times in total.
Edited the question and added the OA.



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Re: if a>0, b>0, c>0, is a(bc)=0? [#permalink]
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21 Aug 2009, 19:45
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Answer is D. a>0, b>0, c>0 for 1), bc=cb ==>> 2b=2c ==>>b=c therefore a(bc)=0, suff for 2), b/c=c/b ==>> b^2=c^2 because b>0, c>0, ==>>b=c therefore a(bc)=0, suff
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Re: if a>0, b>0, c>0, is a(bc)=0? [#permalink]
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25 Aug 2009, 10:32
[quote="tejal777"]if a>0, b>0, c>0, is a(bc)=0?
I. bc = cb II. b/c = c/b
A(BC) = 0 and as a>0 thus it is POSSIBLE ONLY WHEN B = C
from 1
bcc+b = 0 thus 2b = 2c thus b=c...suff
from 2
b/c = c/b all +ve thus b^2 = c^2 thus b=c....suff
D



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Re: if a>0, b>0, c>0, is a(bc)=0? I. bc = cb II. b/c [#permalink]
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30 Jun 2013, 07:33
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For statement 2 we get \(b^2=c^2\) then \(b^2  C^2 = 0\) >> \((bc) (b+c) = 0\) Why is this manipulation incorrect?
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Re: if a>0, b>0, c>0, is a(bc)=0? I. bc = cb II. b/c [#permalink]
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30 Jun 2013, 07:37
fozzzy wrote: For statement 2
we get \(b^2=c^2\) then \(b^2  C^2 = 0\) >> \((bc) (b+c) = 0\)
Why is this manipulation incorrect? That is not incorrect. You get \((bc) (b+c) = 0\) so one (or both) terms equal zero. However we know that both b and c are positive, so (b+c) is positive as well, so bc=0 Hence \(a(bc)=0\) => sufficient
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Re: if a>0, b>0, c>0, is a(bc)=0? I. bc = cb II. b/c [#permalink]
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30 Jun 2013, 07:52
Zarrolou wrote: That is not incorrect.
You get \((bc) (b+c) = 0\) so one (or both) terms equal zero. However we know that both b and c are positive, so (b+c) is positive as well, so bc=0 Hence \(a(bc)=0\) => sufficient
So basically B+C is just redundant information once we solve till that point? Hence that case is ignored and we focus on the second case?
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Re: if a>0, b>0, c>0, is a(bc)=0? I. bc = cb II. b/c [#permalink]
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30 Jun 2013, 07:56
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fozzzy wrote: Zarrolou wrote: That is not incorrect.
You get \((bc) (b+c) = 0\) so one (or both) terms equal zero. However we know that both b and c are positive, so (b+c) is positive as well, so bc=0 Hence \(a(bc)=0\) => sufficient
So basically B+C is just redundant information once we solve till that point? Hence that case is ignored and we focus on the second case? I do not know what you mean by "redundant information", but yes: we know that \(b+c\) cannot be zero, so the other term (\(bc\)) must be zero. All we get from \(b^2c^2=0\) in this problem is that \(bc=0\)
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Re: If a > 0, b > 0 and c > 0, is a(b  c) = 0? [#permalink]
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30 Jun 2013, 08:09



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Re: If a > 0, b > 0 and c > 0, is a(b  c) = 0? [#permalink]
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30 Nov 2016, 21:15
Whoo!!! another super tricky question which can take you off the hooks during exam. The simplest way to look at this question is we have 3 conditions a>0, b>0 and c>0 so thy are positive numbers but can be integers or fraction. (always proceed with this thought process  even if irrelevant here, it helps in the long run). Question asks if a(bc)=0 now we know a>0 thus a not equal to 0 hence bc=0 or B=C Statement 1 Bc=0 B=c Sufficient Statement 2 c^2=B^2 C=B since they are both greater than 0 hence c=b Suffcienet Answer is D. +kudos I need to unlock the exams



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Re: If a > 0, b > 0 and c > 0, is a(b  c) = 0? [#permalink]
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06 Feb 2017, 07:26
Bunuel wrote: If a > 0, b > 0 and c > 0, is a(b  c) = 0?
Is \(a(b  c) = 0\)? > is \(a=0\) or \(bc=0\)? Since given that \(a > 0\), then the questions basically asks whether \(bc=0\).
(1) b  c = c  b > \(2b2c=0\) > \(bc=0\). Sufficient. (2) b/c = c/b > \(b^2=c^2\) > \((bc)(b+c)=0\) > \(b+c=0\) or \(bc=0\) but since \(b\) and \(c\) are positive, then \(b+c>0\). Therefore \(bc=0\). Sufficient.
Answer: D. Nice Explanation Bunuel. Thanks for sharing your approach.
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If a > 0, b > 0 and c > 0, is a(b  c) = 0? [#permalink]
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26 Mar 2018, 02:08
tejal777 wrote: If a > 0, b > 0 and c > 0, is a(b  c) = 0?
(1) b  c = c  b (2) b/c = c/b
This is a yes/ no question. After simplifying the equation we get, if b=c then bc = 0. so the question depends on two equation. 1. Whether a is 0. or 2. b=c. option 1 says b = c . sufficient. option 2 says b^2=c^c. no as b>0 and c>0, b=c. sufficient.
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If a > 0, b > 0 and c > 0, is a(b  c) = 0?
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