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76% (00:26) wrong based on 23 sessions
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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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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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: m11-75085.html#p1073868
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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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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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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 auto-notification 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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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: is-x-2-y-5-z-0-1-xz-y-0-2-y-z-98341.htmlis-x-7-y-2-z-3-0-1-yz-0-2-xz-127692.htmlm21-q30-96613.htmlHope it helps.
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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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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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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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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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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 > 0if C > 0, B < 0 and A > 0 and still A^7B^2C^3 > 0Therefor the answer is (C)
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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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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 non-negative, but B can be equal to 0, so not sufficient. (1) and (2) (1) indicates B is non-zero So A^7 * B^2 * C^3 > 0 Answer - C
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(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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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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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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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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