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This topic is locked. If you want to discuss this question please repost it in the respective forum. Is \(A^7 B^2 C^3 > 0\) ? 1. \(BC < 0\) 2. \(AC > 0\) Source: GMAT Club Tests  hardest GMAT questions



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Re: M11 #26 [#permalink]
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24 Jan 2009, 14:38
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i will go with C
1) tells us that either C or B is <0
insuff we dont know about A..
2) AC>0 good...we dont know if B=0
together sufficient..we know B is not 0 and AC>0



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Re: M11 #26 [#permalink]
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25 Apr 2012, 21:53
charlemagne wrote: ilhom1986 wrote: From the given question I found that IF A>0 than C>0 IF A<0 than C<0 (I answered this question in less than a minute and choose B, because I didn't consider B to be equal to zero) Good question for GMAT starter, easy to get into trap... I did this sometime back...bt I dont seem to have considered that B may be equal to 0, and still chose C. CAn anyone show how B=0 case make a difference? Sure. For example if we put \(b\neq{0}\) in the stem then the answer would become B, instead of C. IF THE QUESTION WERE:If \(b\neq{0}\) is \(a^7*b^2*c^3>0\) ? Since \(b\neq{0}\) then \(b^2>0\), so we can reduce by it (b^2 does not affect given inequality at all) and the question becomes: is \(a^7*c^3>0\)? So, the question basically asks whether \(a\) and \(c\) have the same sign. (Notice that if \(b\neq{0}\) were not given then \(b^2\geq{0}\), and we could not reduce by it) (1) \(bc<0\). Not sufficient. (2) \(ac>0\) > \(a\) and \(c\) have the same sign. Sufficient. Answer: B. Hope it's clear. P.S. Solution to he original question is given here: m1175085.html#p1073868
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Re: M11 #26 [#permalink]
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statement 1 : ========== We can get combinations of B & C bt no clue abt A.So insuff
Statement 2: ========== We can get combinations about A & C bt no clue abt B.So insuff
Combining both we get Case 1: ====== A ve C ve B +ve
For the above combination,we get the answer as YES
Case 2: ====== A +ve C +ve B ve
For case 2 combination also we get the answer as YES.
So I will go with option C
Deepak.



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15 Apr 2012, 00:51



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21 Apr 2012, 10:41



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topmbaseeker wrote: Is \(A^7 B^2 C^3 > 0\) ? 1. \(BC < 0\) 2. \(AC > 0\) Source: GMAT Club Tests  hardest GMAT questions 1. BC < 0 implies either B or C is negative, but not both 2. AC > 0 implies neither A nor C are negative, but both A and C may be negative Using both 1 and 2, we have two options: I  A is negative; B is positive; C is negative => \(A^7 B^2 C^3 > 0\) is positive II  A is positive; B is negative; C is positive => \(A^7 B^2 C^3 > 0\) is positive Hence Option C.! :D
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Re: M11 #26 [#permalink]
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26 Apr 2012, 22:58
charlemagne wrote: Yes....much clearer....Thank you!!! Another kudos to you.... BTW, with so many of these already on your name, you must be going crazy with the amount of autonotification emails coming your way?? That's not a problem. Also one should consider kudos not only as a "thank you" to user whose post was helpful, but also as a tool to distinguish a valuable post. Notice that posts with more than 1 kudos have different color, also notice that total # of kudos is shown just beside the topic name, so by giving a kudos to a post you are drawing an attention of other users to the helpful material and thus are contributing to the community.
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Re: M11 #26 [#permalink]
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23 Apr 2013, 06:59
vshrivastava wrote: I'm sorry if I'm missing something, but I think the right answer is B.
Here is how: Question: Is (A^7) * (B^2) * (C^3) > 0?
Statement 1: BC < 0 Evaluate the Y/N question: Is (A^7) * (B*C)^2 * (C) > 0? (B*C)^2 > 0 But, if A > 0 and C > 0 then expression > 0 => Yes However, if A > 0 and C < 0 then expression < 0 => No So, S1 is not sufficient. Eliminate A and D.
Statement 2: AC > 0 Evaluate the Y/N question: Is (A^7) * (B^2) * (C^3) > 0?
Combine A and C.
Is (A*C)^3 * A^4 * B^2 > 0
S2 says A*C > 0 ; so (A*C)^3 > 0 A^4 is always positive even if A were negative; so A^4 > 0 B^2 is always positive even if B were negative; so B^2 > 0
So, the expression is always positive even if A and/or B were negative. S2 is sufficient.
B is correct.
What do you guys think? Notice that when we consider the second statement we know nothing about the value of b, so if b=0, then \(a^7*b^2*c^3=0\) (\(a^7*b^2*c^3\) is NOT greater than 0). That's why (2) is not sufficient. Similar questions to practice: isx2y5z01xzy02yz98341.htmlisx7y2z301yz02xz127692.htmlm21q3096613.htmlHope it helps.
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Re: M11 #26 [#permalink]
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24 Jan 2009, 17:16
topmbaseeker wrote: Is \(A^7 B^2 C^3 \gt 0\) ?
1. \(BC \lt 0\) 2. \(AC \gt 0\)
(C) 2008 GMAT Club  m11#26
* Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient * Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient * BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient * EACH statement ALONE is sufficient * Statements (1) and (2) TOGETHER are NOT sufficient both will be reqd. just need to determine if both are adequate. B^2*C^2>0 AC>0 So AB^2C^3>0 Now, A is also nonzero from 2. So, A^6>0 Thus, A^6*A*B^2*C^3>0 Hence, sufficient. C.
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Re: M11 #26 [#permalink]
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14 Apr 2010, 07:57
I think answer is "C' A^7B^2C^3 >0
1.BC<0 2.AC>0
sol 1 assume B>0 C<0 then BC<0
if C<0, A also <0 bcs AC>0 from 1&2 A^7B^2C^3 >0
Assume B<0 C>0 then BC<0
if C>0, A also >0 bcs AC>0 from 1&2 A^7B^2C^3 >0



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Re: M11 #26 [#permalink]
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14 Apr 2010, 09:59
My pick is C
Must have both statements to ensure that (1.) at least 1 variable is > 0 (2.) none of the other variables = 0



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Re: M11 #26 [#permalink]
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15 Apr 2010, 02:02
IMO C. A^7B^2C^3 can be reduced to AC as whatever be the value of B, B^2 will always be >0 while A and C have odd powers. 1) BC<0 (Insufficient) as we dont know the value of A. 2) AC>0 (InSufficient) as discussed above. AC can be >0 only if both A and C are +ve or are ve, but wait what if B=0. I hope this helps.
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Re: M11 #26 [#permalink]
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18 Apr 2011, 05:32
Considering only 1. since BC < 0 we dont know about A for 2. AC>0 (both negative or both positive) but B could be zero. If we take both 1. and 2.  if C < 0, B > 0 and A < 0 therefore \(A^7B^2C^3 > 0\) if C > 0, B < 0 and A > 0 and still \(A^7B^2C^3 > 0\) Therefor the answer is (C)
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Re: M11 #26 [#permalink]
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18 Apr 2011, 18:36
I simplified this equation to A*B^2*C > 0 to make it slightly less daunting. B will always be positive unless it is zero. 1) BC < 0 means either B or C is Negative, but they can't both be negative. Also, neither can be zero. No other clues are given about A. Insufficient. 2) AC > 0 means A and C are either both negative or both positive. Can't be zero. Insufficient. (2) states that the product of AC is always positive, since B^2 is also always positive and B isn't zero, then the equation must be positive. (C) is the answer.
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Re: M11 #26 [#permalink]
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18 Apr 2011, 19:24
I too had missed that B could be equal to 0 in (2). (1) says : BC < 0, So B is +ve and C is ve, or B is ve and C is +ve, we don't know about A, so not sufficient (2) AC > 0, so odd powers of A * odd powers of C are > 0 Because A^7 * C^3 = (AC)^3 * A^4 (AC is +ve and A^4 is always +ve) B^2 is always nonnegative, but B can be equal to 0, so not sufficient. (1) and (2) (1) indicates B is nonzero So A^7 * B^2 * C^3 > 0 Answer  C
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Re: M11 #26 [#permalink]
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20 Apr 2011, 18:06
(A^7 B^2 C^3)>0?
1. Not sufficient as we dont know anything about A. (B<0,C>0 or B>0 , C<0)
2. Not sufficient as we dont know anything about B. ( A>0,C>0 or A<0, C<0)
Together we have B<0 , C>0 , A>0 (case 1) or B> 0 , C<0, A<0(Case 2)
In both the cases we have (A^7 B^2 C^3)>0. So thats sufficient.
Answer is C.



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Re: M11 #26 [#permalink]
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15 Apr 2012, 00:39
Here 3 unknown in equations i.e. A, B and C. so to solve this equations require details of all three. (1) statement 1 provides information about B and C (2) Statement 2 provides information about A and C
Over all by multiplication using statement 1 and 2 we can get the answers.
so my answer is C.



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Re: M11 #26 [#permalink]
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21 Apr 2012, 06:42
topmbaseeker wrote: Is \(A^7 B^2 C^3 > 0\) ? 1. \(BC < 0\) 2. \(AC > 0\) Source: GMAT Club Tests  hardest GMAT questions i followed graph method( it takes time, i dont know any easier method to do this), i got the answer C
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Re: M11 #26 [#permalink]
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23 Apr 2012, 07:48
I will split the question as [(A)^6]*[(BC)^2]*(AC) So (BC)^2>0 or =0 A^6>0 or =0 AC can be either >0 <0 or 0 so {[(A)^6]*[(BC)^2]*(AC)} will look like {(+/0) * (+/0) *(+//0)} 1:)BC<0 =>[(BC)^2]>0 but we are unsure about AC wheter its >0 or <0 so reject strike off options A,D Remaining options B,C,E 2.)AC>0 now this implies [(A)^6]>0 (as A,C!=0) [(BC)^2]>=0(we are unsure of B, whether its 0 or not) (AC)>0 so result will be >=0, but its insufficient, as its not >0 but we have dual case of >=0 Strike off option B options E,C are left, lets go for C ,combining BC<0 and AC>0 implies that [(BC)^2]>0 [(A)^6]>0 [AC]>0 so end result will be >0 So C is the ANS...
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