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Is Z less than 0?

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Is Z less than 0? [#permalink] New post 20 Mar 2012, 01:03
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Question Stats:

85% (01:27) correct 14% (00:48) wrong based on 1 sessions
Is z less than 0?

(1) xy>0 and yz<0
(2) x>0
[Reveal] Spoiler: OA
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Re: Is Z less than 0? [#permalink] New post 20 Mar 2012, 01:21
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Is z less than 0?

(1) xy>0 and yz<0 --> first inequality is useless for us since it has no z. From yz<0 we can say that y and z have opposite sings, but we don't know the sign of y to deduce something about z. Not sufficient.

(2) x>0. Not sufficient.

(1)+(2) From xy>0 we can say that x and y have the same sign, and since from (2) x>0 then y>0 too. Now, from yz<0 we have that y and z have opposite sings and as y>0 then z<0. Sufficient.

Answer: C.

Hope it's clear.
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Re: Is Z less than 0? [#permalink] New post 20 Mar 2012, 01:28
Hi,

I hope this helps

We have to prove that Is z < 0?
Statement 1. xy>0 and yz<0
=> x & y are negative / x & y are positive
=> z is postive / z is negative
Hence Insufficient

2. x>0
Insufficient since nothing said about y or z

Combine
X is positive
= >X is positive Y is positive Thus Z is negative

Hence sufficient
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Re: Is Z less than 0? [#permalink] New post 14 Mar 2013, 19:28
Bunuel wrote:
Is z less than 0?

(1) xy>0 and yz<0 --> first inequality is useless for us since it has no z. From yz<0 we can say that y and z have opposite sings, but we don't know the sign of y to deduce something about z. Not sufficient.

(2) x>0. Not sufficient.

(1)+(2) From xy>0 we can say that x and y have the same sign, and since from (2) x>0 then y>0 too. Now, from yz<0 we have that y and z have opposite sings and as y>0 then z<0. Sufficient.

Answer: C.

Hope it's clear.


for the first statement I concluded that x and y have the same signs and since y times z is negative so z is the opposite sign . I made a chart trying +/- signs for each until I got A ... still cannot quite understand why C ?
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Re: Is Z less than 0? [#permalink] New post 15 Mar 2013, 01:14
TheNona wrote:
Bunuel wrote:
Is z less than 0?

(1) xy>0 and yz<0 --> first inequality is useless for us since it has no z. From yz<0 we can say that y and z have opposite sings, but we don't know the sign of y to deduce something about z. Not sufficient.

(2) x>0. Not sufficient.

(1)+(2) From xy>0 we can say that x and y have the same sign, and since from (2) x>0 then y>0 too. Now, from yz<0 we have that y and z have opposite sings and as y>0 then z<0. Sufficient.

Answer: C.

Hope it's clear.


for the first statement I concluded that x and y have the same signs and since y times z is negative so z is the opposite sign . I made a chart trying +/- signs for each until I got A ... still cannot quite understand why C ?


Yes, xy > 0, means that x and y are either both positive or both negative. But this does not help us much.

yz < 0 means that y and z have the opposite signs. So, if y is negative then z is positive and if y is positive then z negative. Hence from the first statement z could be positive as well as negative.

Hope it's clear.
_________________

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. NEW!!!

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set. NEW!!!


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Re: Is Z less than 0?   [#permalink] 15 Mar 2013, 01:14
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