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M11-26

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M11-26  [#permalink]

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New post 16 Sep 2014, 00:45
1
12
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

34% (01:16) correct 66% (01:06) wrong based on 93 sessions

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Re M11-26  [#permalink]

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New post 16 Sep 2014, 00:45
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1
Official Solution:


Inequality \(a^7*b^2*c^3 \gt 0\) to be true \(a\) and \(c\) must be either both positive or both negative AND \(b\) must not be zero (in order \(a^7*b^2*c^3\) not to equal zero).

(1) \(bc \lt 0\). Hence, \(b \ne 0\). Don't know about \(a\) and \(c\). Not sufficient.

(2) \(ac \gt 0\). Hence, \(a\) and \(c\) are either both positive or both negative. Don't know about \(b\): if \(b=0\), then the expression will be equal 0. Not sufficient.

(1)+(2) Sufficient.


Answer: C
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Re: M11-26  [#permalink]

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New post 24 Oct 2014, 02:08
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anubhavmax wrote:
Bunuel - Could you please look into why (2) alone is not sufficient ?

We have ac > 0.

\(a^7*b^2*c^3 = a^4 * b^2 * a^3 * c^3 = a^4 * b^2 * (ac)^3\). All 3 are positive, so the whole expression is positive. B should be the answer I feel.



Hi anubhav...

How about of b=0 then the expression a^7*b^2*c*3=0
So you need information that terms are not zero..B tells you a and c have same sign but not whether b =0 or not


hope it helps
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Re: M11-26  [#permalink]

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Re: M11-26  [#permalink]

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New post 24 Oct 2014, 00:32
Bunuel - Could you please look into why (2) alone is not sufficient ?

We have ac > 0.

\(a^7*b^2*c^3 = a^4 * b^2 * a^3 * c^3 = a^4 * b^2 * (ac)^3\). All 3 are positive, so the whole expression is positive. B should be the answer I feel.
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Re: M11-26  [#permalink]

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New post 24 Oct 2014, 02:42
Oh right... thanks a lot. Simply overlooked the zero case. :(
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Re: M11-26  [#permalink]

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New post 10 Dec 2014, 20:20
bc<0
ac>0

here we have:
either b is negative, then a and c are positive, in this case a^7*b^2*c*3<0
or b is positive, and a and c are negative, in this case a^7*b^2*c*3>0
from where did we get b not 0?
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Re M11-26  [#permalink]

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New post 23 Jun 2016, 03:30
I think this is a high-quality question and I agree with explanation. I need one point clarification from Bunuel is:

when you say bc < 0 it is possible that c as well not equal to zero along with b. So we have some information on C also right.
May be I am not getting your point.
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Re: M11-26  [#permalink]

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New post 23 Jun 2016, 03:33
dharan wrote:
I think this is a high-quality question and I agree with explanation. I need one point clarification from Bunuel is:

when you say bc < 0 it is possible that c as well not equal to zero along with b. So we have some information on C also right.
May be I am not getting your point.


Yes, bc < 0 means that none of them is 0. But we need to know the sign of c not just that it's not 0, that's why we say that there is not sufficient info on c there.
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Re M11-26  [#permalink]

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New post 20 Aug 2016, 04:48
I think this is a high-quality question and I agree with explanation.
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Re M11-26  [#permalink]

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New post 16 Jan 2017, 11:37
I think this is a high-quality question and I agree with explanation.
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M11-26  [#permalink]

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New post 05 Jun 2018, 04:35
Bunuel wrote:
Is \(a^7*b^2*c^3 \gt 0\)?


(1) \(bc \lt 0\)

(2) \(ac \gt 0\)


Hi Bunuel

If a^7 = that can indicate A can be (+\-) going ahead , * B2 = this means B will be every time positive, C^3 , C may be +\- values

coming back to the main equation , if we multiply Negative * positive * Negative = this gives us a positive value . Is my mistake only that I haven't considered Zero in my values ? As by even / odd concept , I had marked this D .
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Re: M11-26  [#permalink]

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New post 05 Jun 2018, 04:39
loserunderachiever wrote:
Bunuel wrote:
Is \(a^7*b^2*c^3 \gt 0\)?


(1) \(bc \lt 0\)

(2) \(ac \gt 0\)


Hi Bunuel

If a^7 = that can indicate A can be (+\-) going ahead , * B2 = this means B will be every time positive, C^3 , C may be +\- values

coming back to the main equation , if we multiply Negative * positive * Negative = this gives us a positive value . Is my mistake only that I haven't considered Zero in my values ? As by even / odd concept , I had marked this D .


x^odd can be positive, negative or 0.
x^even can only be positive, or 0.

Not sure I understand what's your question though.
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Re: M11-26  [#permalink]

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New post 05 Jun 2018, 04:41
Bunuel wrote:
loserunderachiever wrote:
Bunuel wrote:
Is \(a^7*b^2*c^3 \gt 0\)?


(1) \(bc \lt 0\)

(2) \(ac \gt 0\)


Hi Bunuel

If a^7 = that can indicate A can be (+\-) going ahead , * B2 = this means B will be every time positive, C^3 , C may be +\- values

coming back to the main equation , if we multiply Negative * positive * Negative = this gives us a positive value . Is my mistake only that I haven't considered Zero in my values ? As by even / odd concept , I had marked this D .


x^odd can be positive, negative or 0.
x^even can only be positive, or 0.

Not sure I understand what's your question though.


I got your point , as I didn't consider X to be Zero .

Thanks.
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Re: M11-26  [#permalink]

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New post 29 Sep 2018, 02:03
Bunuel wrote:
Official Solution:


Inequality \(a^7*b^2*c^3 \gt 0\) to be true \(a\) and \(c\) must be either both positive or both negative AND \(b\) must not be zero (in order \(a^7*b^2*c^3\) not to equal zero).

(1) \(bc \lt 0\). Hence, \(b \ne 0\). Don't know about \(a\) and \(c\). Not sufficient.

(2) \(ac \gt 0\). Hence, \(a\) and \(c\) are either both positive or both negative. Don't know about \(b\): if \(b=0\), then the expression will be equal 0. Not sufficient.

(1)+(2) Sufficient.


Answer: C


Hi,
How can we say 1 + 2 is sufficient?(What if a=0 or c=0)
Because we have not considered a=0 or c=0 case.
Why have we not considered this and only considered b=0 case?
Can you please explain?
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Re: M11-26  [#permalink]

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New post 29 Sep 2018, 07:08
Akshit03 wrote:
Bunuel wrote:
Official Solution:


Inequality \(a^7*b^2*c^3 \gt 0\) to be true \(a\) and \(c\) must be either both positive or both negative AND \(b\) must not be zero (in order \(a^7*b^2*c^3\) not to equal zero).

(1) \(bc \lt 0\). Hence, \(b \ne 0\). Don't know about \(a\) and \(c\). Not sufficient.

(2) \(ac \gt 0\). Hence, \(a\) and \(c\) are either both positive or both negative. Don't know about \(b\): if \(b=0\), then the expression will be equal 0. Not sufficient.

(1)+(2) Sufficient.


Answer: C


Hi,
How can we say 1 + 2 is sufficient?(What if a=0 or c=0)
Because we have not considered a=0 or c=0 case.
Why have we not considered this and only considered b=0 case?
Can you please explain?


How can either of them be 0 if it's given that ac > 0?
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Re M11-26  [#permalink]

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New post 22 Apr 2019, 20:44
I think this is a high-quality question. I solved it like this:
a^7*b^2*c^3=a^6*(bc)^2* ac
using both statements; bc<0;so, (bc)^2 >0 & ac>0

also a^6 being even power will be positive so the value as a whole will be greater than zero.
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Re M11-26   [#permalink] 22 Apr 2019, 20:44
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