GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2018, 17:02

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

M11-26

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50002

Show Tags

16 Sep 2014, 00:45
1
12
00:00

Difficulty:

85% (hard)

Question Stats:

33% (00:39) correct 67% (00:41) wrong based on 129 sessions

HideShow timer Statistics

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

(1) $$bc \lt 0$$

(2) $$ac \gt 0$$

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50002

Show Tags

16 Sep 2014, 00:45
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.

_________________
Current Student
Joined: 01 Feb 2013
Posts: 117
Location: India
Schools: Anderson '18 (M)

Show Tags

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.
Director
Joined: 25 Apr 2012
Posts: 692
Location: India
GPA: 3.21

Show Tags

24 Oct 2014, 02:08
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
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Current Student
Joined: 01 Feb 2013
Posts: 117
Location: India
Schools: Anderson '18 (M)

Show Tags

24 Oct 2014, 02:42
Oh right... thanks a lot. Simply overlooked the zero case.
Board of Directors
Joined: 17 Jul 2014
Posts: 2657
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)

Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 50002

Show Tags

11 Dec 2014, 04:04
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.
_________________
Intern
Joined: 07 Mar 2011
Posts: 25

Show Tags

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.
Math Expert
Joined: 02 Sep 2009
Posts: 50002

Show Tags

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.
_________________
Senior Manager
Joined: 31 Mar 2016
Posts: 390
Location: India
Concentration: Operations, Finance
GMAT 1: 670 Q48 V34
GPA: 3.8
WE: Operations (Commercial Banking)

Show Tags

20 Aug 2016, 04:48
I think this is a high-quality question and I agree with explanation.
Intern
Status: Single
Affiliations: None
Joined: 25 Dec 2016
Posts: 10
Sricharan: A

Show Tags

16 Jan 2017, 11:37
I think this is a high-quality question and I agree with explanation.
Manager
Joined: 26 Feb 2018
Posts: 59
WE: Sales (Internet and New Media)

Show Tags

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 .
_________________

" Can't stop learning and failing"

Math Expert
Joined: 02 Sep 2009
Posts: 50002

Show Tags

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.
_________________
Manager
Joined: 26 Feb 2018
Posts: 59
WE: Sales (Internet and New Media)

Show Tags

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.
_________________

" Can't stop learning and failing"

Intern
Joined: 07 Jul 2018
Posts: 11

Show Tags

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.

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: 50002

Show Tags

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.

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?
_________________
Re: M11-26 &nbs [#permalink] 29 Sep 2018, 07:08
Display posts from previous: Sort by

M11-26

Moderators: chetan2u, Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.