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# M11-26

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Math Expert
Joined: 02 Sep 2009
Posts: 52385

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15 Sep 2014, 23:45
1
12
00:00

Difficulty:

85% (hard)

Question Stats:

35% (00:40) correct 65% (00:41) wrong based on 133 sessions

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Is $$a^7*b^2*c^3 \gt 0$$?

(1) $$bc \lt 0$$

(2) $$ac \gt 0$$

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Math Expert
Joined: 02 Sep 2009
Posts: 52385

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15 Sep 2014, 23:45
3
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.

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Manager
Joined: 01 Feb 2013
Posts: 115
Location: India
Schools: Anderson '18 (M)

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23 Oct 2014, 23:32
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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Joined: 25 Apr 2012
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24 Oct 2014, 01:08
2
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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Location: India
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24 Oct 2014, 01:42
Oh right... thanks a lot. Simply overlooked the zero case.
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10 Dec 2014, 19:20
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?
Math Expert
Joined: 02 Sep 2009
Posts: 52385

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11 Dec 2014, 03:04
1
mvictor wrote:
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?

Can b be 0 if bc < 0? NO! If b = 0, then bc = 0, not < 0.
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Joined: 07 Mar 2011
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23 Jun 2016, 02:30
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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Posts: 52385

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23 Jun 2016, 02:33
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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20 Aug 2016, 03:48
I think this is a high-quality question and I agree with explanation.
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16 Jan 2017, 10:37
I think this is a high-quality question and I agree with explanation.
Manager
Joined: 26 Feb 2018
Posts: 57
WE: Sales (Internet and New Media)

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05 Jun 2018, 03:35
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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Joined: 02 Sep 2009
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05 Jun 2018, 03:39
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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05 Jun 2018, 03:41
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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Intern
Joined: 07 Jul 2018
Posts: 29

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29 Sep 2018, 01:03
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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 52385

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29 Sep 2018, 06:08
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.

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?

How can either of them be 0 if it's given that ac > 0?
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Re: M11-26 &nbs [#permalink] 29 Sep 2018, 06:08
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# M11-26

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