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achieve_dream wrote:Source: Gmatclub Tests
Is X^3Y^2Z^3 >0
1. XY > 0
2. XZ > 0
I can get to answer but it takes me more than 3 minutes.
So, what is the most quick way to solve these kind of problems.
E
dabral wrote:With these types of inequalities, always rephrase the question by pulling out the even powers:
(x^3)(y^2)(z^3)>0 is equivalent to (x^2)(y^2)(z^2)(xz)>0, here the product (x^2)(y^2)(z^2) is always positive irrespective of whether x, y, and z are positive or negative, therefore the original question is equivalent to
Is xz>0?
1) xy>0
Insufficient: If x and y are both positive then we satisfy the statement, however if z is positive then the answer to the question is Yes, but if z is negative then the answer is No.
2) Sufficient, the statement xz>0 is identical to the question being posed.
Answer should be A.
Dabral
I think you meant to say the answer is B (since you said Statement 2 was sufficient alone), but that's not quite right. With Statement 2 alone, there is still the possibility that y=0, in which case the answer to the question would be 'no'. That is, with Statement 2 alone, all we can be sure of is that x^3 * y^2 * z^3 > 0. When we combine the two statements, we know from Statement 1 that y cannot be 0, and the two Statements together are sufficient. So the answer should be C.dabral wrote:With these types of inequalities, always rephrase the question by pulling out the even powers:
(x^3)(y^2)(z^3)>0 is equivalent to (x^2)(y^2)(z^2)(xz)>0, here the product (x^2)(y^2)(z^2) is always positive irrespective of whether x, y, and z are positive or negative, therefore the original question is equivalent to
Is xz>0?
1) xy>0
Insufficient: If x and y are both positive then we satisfy the statement, however if z is positive then the answer to the question is Yes, but if z is negative then the answer is No.
2) Sufficient, the statement xz>0 is identical to the question being posed.
Answer should be A.
Dabral
dabral wrote:With these types of inequalities, always rephrase the question by pulling out the even powers:
(x^3)(y^2)(z^3)>0 is equivalent to (x^2)(y^2)(z^2)(xz)>0, here the product (x^2)(y^2)(z^2) is always positive irrespective of whether x, y, and z are positive or negative, therefore the original question is equivalent to
Is xz>0?
1) xy>0
Insufficient: If x and y are both positive then we satisfy the statement, however if z is positive then the answer to the question is Yes, but if z is negative then the answer is No.
2) Insufficient, if y>0, then the statement xz>0 is identical to the question being posed, however, if y=0, then the answer to the question is no.
1)&2) Sufficient, the condition xy>0, means y is non-zero and from statement 2 xz>0, which is equivalent to the question in the main stem.
Modified answer is indeed C!
Dabral
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