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# Is Z less than 0?

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Manager
Joined: 06 Jul 2011
Posts: 214
Location: Accra, Ghana
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Kudos [?]: 29 [0], given: 39

Is Z less than 0? [#permalink]  20 Mar 2012, 00:03
00:00

Difficulty:

15% (low)

Question Stats:

90% (01:28) correct 10% (00:54) wrong based on 51 sessions
Is z less than 0?

(1) xy>0 and yz<0
(2) x>0
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 27468
Followers: 4308

Kudos [?]: 42162 [1] , given: 5957

Re: Is Z less than 0? [#permalink]  20 Mar 2012, 00:21
1
KUDOS
Expert's post
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.

Hope it's clear.
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Senior Manager
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 291
Location: India
Concentration: General Management, Entrepreneurship
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Kudos [?]: 114 [0], given: 16

Re: Is Z less than 0? [#permalink]  20 Mar 2012, 00:28
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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Manager
Joined: 12 Dec 2012
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Kudos [?]: 51 [0], given: 181

Re: Is Z less than 0? [#permalink]  14 Mar 2013, 18:28
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.

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]  15 Mar 2013, 00:14
Expert's post
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.

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.
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Re: Is Z less than 0?   [#permalink] 15 Mar 2013, 00:14
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