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GmatKiss GMAT Titan
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X and Y Sun May 27, 2012 12:10 am
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• Lap #[LAPCOUNT] ([LAPTIME])
IMO: B
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Anurag@Gurome GMAT Instructor
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Sun May 27, 2012 2:13 am
The sign of (x^7)*(y^2)*(z^3) will mainly depend upon the sign of x and z as y^2 ≥ 0

Statement 1: y and z are of opposite sign and none of them are equal to zero. But the sign of (x^7)*(y^2)*(z^3) will depend upon x also as the power of x is odd.

Not Sufficient

Statement 2: x and z are of same sign and none of them are equal to zero.
Hence, the signs of (x^7) and (z^3) are also same, i.e. (x^7)*(z^3) > 0

But, y² is either positive or equal to zero.
Hence, (x^7)*(y^2)*(z^3) ≥ 0

Not Sufficient

1 & 2 Together: Now we know that neither x nor y nor z are equal to zero and (x^7)*(z^3) > 0. Hence, (x^7)*(y^2)*(z^3) is also greater than zero.

Sufficient

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ankita1709 Really wants to Beat The GMAT!
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Sun May 27, 2012 10:07 pm
Sorry Anurag but I think the answer is B

See we can re group (x^7)(y^2)(z^3) as ((xyz)^2)(xz)(x^4)

Applying the common logic as taking out the even powers

checking this just the statement 2 is sufficient to answer

Hence B

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Sun May 27, 2012 10:18 pm
Hi ankita1709:

Anurag is right. I got the same answer.
Your logic of even powers is fine and we need to check for xz. However, you are missing a critical piece of information.

we are asked if (x^7)(y^2)(z^3) > 0 (Strictly greater than 0).
This means that we need to ascertain whether even one of x, y, z can be zero. (if one of x, y, z is zero then we can't find the answer from B, which says xz<0).

yz<0 tells us that neither y nor z is 0.
xz<0 tells us that (xz) one of xz is less than 0 and that none of x or z is equal to 0. That's why C is the correct answer.

Now, if the question asked us (x^7)(y^2)(z^3)>=0, then the answer would have been B because we would not have been concerned with any or all of x,y,z being 0s.

Let me know if this helps

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Sun May 27, 2012 10:54 pm
ankita1709 wrote:
See we can re group (x^7)(y^2)(z^3) as ((xyz)^2)(xz)(x^4)
That is a very good way to tackle the problem. But you're missing the point I was trying to make. As eagleeye noted, statement 2 is sufficient to answer that the expression is greater than or equal to zero but NOT greater than zero.

We need both statements to conclude that none of the variables are equal to zero, so that we can conclude the given expression is greater than zero.

Hope that helps.

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