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## If (x^2)y=z^3, is z^3>0?

This topic has 3 expert replies and 0 member replies

### Top Member

NandishSS Master | Next Rank: 500 Posts
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#### If (x^2)y=z^3, is z^3>0?

Mon May 22, 2017 6:25 am
If (x^2)y=z^3, is z^3>0?

(1) x(y^2)>0

(2) yz > 0

OA:E

Source:GMATPrep EP2

### GMAT/MBA Expert

DavidG@VeritasPrep Legendary Member
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Mon May 22, 2017 7:10 am
NandishSS wrote:
If (x^2)y=z^3, is z^3>0?

(1) x(y^2)>0

(2) yz > 0

OA:E

Source:GMATPrep EP2
Notice that x^2 must be nonnegative. Therefore, if x and z and are nonzero numbers, z^3, will be positive if y is positive, and z^3 will be negative if y is negative. The upshot is that y is the key.

1) Because y^2 must be nonnegative, this tells us that x is positive. However, we don't know if y is positive or negative - if y is positive, z^3 will be positive, giving us a YES. if y is negative, z^3 will be negative, giving us a NO. so this statement alone is not sufficient.

2) All this tells us is that z and y are both positive or both negative. But, unless both sides of the equation are equal to zero, we already knew that! Statement 2 alone is insufficient (and basically useless.)

Together: y could be positive or negative, and so z^3 could be positive or negative, meaning we can still get a YES or a NO. Together the statements are not sufficient. The answer is E

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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon May 22, 2017 3:35 pm
Hi NandishSS,

This question can be solved by TESTing VALUES (you just have to do the necessary work on the pad to keep track of the "signs" of each variable).

We're told that (Y)(X^2) = (Z^3). We're asked if Z^3 is greater than 0. This is a YES/NO question.

1) X(Y^2) > 0

IF....
X = 1, Y = 1... then Z = 1 and the answer to the question is YES
X = 1, Y = -1... then Z = -1 and the answer to the question is NO
Fact 1 is INSUFFICIENT

2) (Y)(Z) > 0

We can use the two TESTs from Fact 1 here....

IF....
X = 1, Y = 1... then Z = 1 and the answer to the question is YES
X = 1, Y = -1... then Z = -1 and the answer to the question is NO
Fact 2 is INSUFFICIENT

Combined, we already have two TESTs that fit both Fact 1 and Fact 2 (and produce different answers - one YES and one NO).
Combined, INSUFFICIENT

GMAT assassins aren't born, they're made,
Rich

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### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
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Thu Dec 07, 2017 7:11 am
NandishSS wrote:
If (x^2)y=z^3, is z^3>0?

(1) x(y^2)>0

(2) yz > 0
We are given that (x^2)y = z^3, and we need to determine whether z^3 > 0. Recall that the values of z^3 and z have the same sign; thus, we need to determine whether z > 0.

Statement One Alone:

x(y^2) > 0

Since y^2 is always nonnegative, x(y^2) > 0 means x > 0. However, since we cannot determine the sign of y, we cannot determine whether z^3 = (x^2)y is greater than 0.

For example, if y > 0, then z^3 > 0; however, if y < 0, then z^3 < 0. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

yz > 0

Since yz > 0, we know that either both y and z are positive or both y and z are negative. However, since we cannot determine the sign of y, we cannot determine whether z^3 = (x^2)y is greater than 0.

For example, if y > 0, then z > 0, and hence z^3 > 0; however, if y < 0, then z < 0, and hence z^3 < 0. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.

Statements One and Two Together:

Using the two statements together, we still cannot determine the sign of y and thus cannot determine whether z^3 > 0.

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