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
The correct answer is C.
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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
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
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
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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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.ankita1709 wrote:See we can re group (x^7)(y^2)(z^3) as ((xyz)^2)(xz)(x^4)
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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