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Is X^3Y^2Z^3 >0

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by achieve_dream » Tue Nov 29, 2011 6:13 pm
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.

C
Last edited by achieve_dream on Sat Dec 03, 2011 1:14 pm, edited 1 time in total.
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by dabral » Tue Nov 29, 2011 8:02 pm
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
Last edited by dabral on Wed Nov 30, 2011 12:25 am, edited 1 time in total.
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by HSPA » Tue Nov 29, 2011 8:07 pm
we do not need A as we donot know about Z

Using 2:
as y^2 is always positive
xz > 0 is either both are positive or both negitive

if both are negitive it gives imaginary values
if both are positive xz > 0

Hence inconclusive.
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
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Second take: coming soon..
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by HSPA » Tue Nov 29, 2011 8:09 pm
Dear poster,

Is the stem (x^3) ^ (y^2)^ (z^3) or x^3 X y^2 X z^3 ??????
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
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by dabral » Tue Nov 29, 2011 8:17 pm
He wrote it as Is X^3Y^2Z^3 >0? which I interpreted as (X^3)(Y^2)(Z^3), but writing exponents using ^ is always a problem, and is probably a good idea to use the parentheses.

Dabral
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by Ian Stewart » Wed Nov 30, 2011 12:04 am
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.

The 'trap' in this question (noticing that there is one exceptional value of y, y=0, which makes Statement 2 insufficient alone) is not the 'style' of trap I see in real GMAT questions, however. In every similar real GMAT question I've seen, the question always tells you in advance the letters represent nonzero numbers, and the question is testing if you understand the more mathematically important fact that odd powers can be negative, but even powers cannot.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by dabral » Wed Nov 30, 2011 12:23 am
Ian, good catch. I agree that of all the inequalities that I have seen on the GMAT, I have yet to see this option for insufficiency. This is a very close copy of an actual GMAT question, I have a feeling the writers left out the condition, xyz not equal to zero in the main stem, but who knows. The answer to the original question in the format it is presented is indeed C.

Dabral
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by achieve_dream » Sat Dec 03, 2011 12:59 pm
Dear poster,

Is the stem (x^3) ^ (y^2)^ (z^3) or x^3 X y^2 X z^3 ??????



The question is (x^3).(y^2).(z^3) >0
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by achieve_dream » Sat Dec 03, 2011 1:05 pm
Thanks for the tip. I also changed the answer. I mistyped it before. Also, may I ask you where did you learn this technique. Was it from any book?
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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