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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 _________________

Inequality \(a^7*b^2*c^3>0\) 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 to zero).

(1) \(bc<0\) --> \(b\neq{0}\). Don't know about \(a\) and \(c\). Not sufficient.

(2) \(ac>0\) --> \(a\) and \(c\) are either both positive or both negative. Don't know about \(b\). Not sufficient.

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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KUDOS-ing does'nt cost you anything, but might just make someone's day!!!

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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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.

* 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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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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Want to improve your CR: http://gmatclub.com/forum/cr-methods-an-approach-to-find-the-best-answers-93146.html Tricky Quant problems: http://gmatclub.com/forum/50-tricky-questions-92834.html Important Grammer Fundamentals: http://gmatclub.com/forum/key-fundamentals-of-grammer-our-crucial-learnings-on-sc-93659.html

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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"What we obtain too cheap, we esteem too lightly." -Thomas Paine

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.

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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