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If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0

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If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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If xyz > 0, is x > 0?

(1) xy > 0
(2) xz > 0
[Reveal] Spoiler: OA
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Re: If XYZ>0 is X>0 [#permalink]

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New post 10 Jan 2010, 21:12
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DestinyChild wrote:
If XYZ>0 is X>0

XY > 0
XZ > 0

Obviously the answer is Yes or No;
Get your kudos for reasoning out why the answer is C and keep an eye on time too :)

Triple kudos for someone suggesting quicker technique for DS stems with triple variables...!


xy > 0 both are positive or both negative
xz > 0 both are positive or both negative

if x < 0 then z < 0 and y < 0 but xyz < 0 so this doesn't work
if x > 0 then y > 0 and z > 0 and xyz > 0 so this works and x > 0
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Re: If XYZ>0 is X>0 [#permalink]

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New post 10 Jan 2010, 21:29
cheers lagomez

will give you one...!
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Re: If XYZ>0 is X>0 [#permalink]

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New post 11 Apr 2011, 09:51
1) x and y both are positive or negative, so x could be -ve, or +ve insuff.
2) x and z both are positive or negative, so x could be -ve, or +ve insuff.

For C
as xyz > 0, so if y and z both -ve, then x has to be +ve, and
if y and z become +ve then x has to be +ve to become xyz > 0.
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Re: If XYZ>0 is X>0 [#permalink]

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Following chart lists down the possible scenarios in which XYZ > 0

X Y Z
1) - - +
2) - + -
3) + - -
4) + + +

As per statement I --> 1 & 4 have to be true for XY > 0. So I alone is insufficient as X can be +ve or -ve
As per statement II --> 2& 4 have to be true for XZ > 0 So II alone is insufficient as X can be +ve or -ve
If we combine both statements then only 4 is true and X has to be +ve

Hence C.
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DestinyChild wrote:
If XYZ>0 is X>0

XY > 0
XZ > 0

Obviously the answer is Yes or No;
Get your kudos for reasoning out why the answer is C and keep an eye on time too :)

Triple kudos for someone suggesting quicker technique for DS stems with triple variables...!


Certainly each statement is not sufficient alone (the logic is identical for each: for S1, x and y can both be negative or both positive, and for S2, x and z can both be negative or both positive). You might notice that S1 tells us z is positive, and S2 tells us y is positive, but that's not what we're looking for.

Now, together, the inequality xy > 0 means 'x and y have the same sign'. So from the two statements we know x and y have the same sign, and x and z have the same sign, so x, y and z all have the same sign. If xyz > 0, they must all be positive, and the answer is C.
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New post 11 Apr 2011, 18:41
C. For XYZ > 0 either all are positive or two of them negative. From St1 and St2 it is clear that both xy and xz has to be positive or both xz and xy has to be negative. in the latter case XYZ > 0 will be false.
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Re: If XYZ>0 is X>0 [#permalink]

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New post 11 Apr 2011, 22:53
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XYZ > 0 => X > 0 and YZ > 0 OR x < 0 and YZ < 0


(1)

XY > 0 means x > 0 and Y > 0 OR X < 0 and Y < 0

So (1) is not sufficient

(2)

XZ > 0 means X > 0 and Z > 0 OR X < 0 and Z < 0

So (2) is not sufficient

So if x < 0 then y < 0 and z < 0

=> xyz < 0 which is contrary to what is given in question

=> x > 0

Answer C.
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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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New post 11 Feb 2016, 10:38
This one is pure fun!

xyz>0 this means that we need two number with same sign and the Notre number must be positive. otherwise we would get a negative number.

1-xy>0
Both x and y are positive or negative. NS

2-xz>0
Both x and y are positive or negative. NS

1 and 2 - xz>0 and xy>0 - SUFFICIENT
Lets assume that x is negative: if x is negative, then y must be negative and z must be negative. This would result in a negative number. This is not possible.
So we are sure that X is positive.
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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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New post 12 Feb 2016, 05:57
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If xyz > 0, is x > 0?

(1) xy > 0
(2) xz > 0


When you modify the original condition and the question, they become xyz>0 -> x>0? -> yz>0?. There are 3 variables(x,y,z) and 1 equation(xyz>0), which should match with the number of equations. So, you need 2 more equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), they become x(y^2)z>0. When dividing x(y^2)z>0 with y^2, it becomes yz>0, which is yes and sufficient.
Therefore, the answer is C.


l For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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New post 19 May 2016, 02:26
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I solved this question "algebraically":

Question: xyz > 0 => x>0

(1) if xy > 0
dividing xyz > 0 by xy (inequality sign is not flipped)
=> z > 0 insufficient

(2) if xz > 0
dividing xyz > 0 by xz (inequality sign is not flipped)
=> y > 0 insufficient

(1&2) if z,y > 0
diving xyz > 0 by yz (inequality sign is not flipped)
=> x>0 sufficient

Is this a valid approach?
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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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New post 19 May 2016, 03:16
Expert's post
benni089 wrote:
I solved this question "algebraically":

Question: xyz > 0 => x>0

(1) if xy > 0
dividing xyz > 0 by xy (inequality sign is not flipped)
=> z > 0 insufficient

(2) if xz > 0
dividing xyz > 0 by xz (inequality sign is not flipped)
=> y > 0 insufficient

(1&2) if z,y > 0
diving xyz > 0 by yz (inequality sign is not flipped)
=> x>0 sufficient

Is this a valid approach?


Yes, that's a valid approach.
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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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New post 24 May 2016, 05:06
xyz > 0
x > 0?

Stem: yz ? 0

a) xz > 0 : Says nothing about y
b) xy > 0 : says nothing about z

Combining both L

a * b ( Since both are + ve)

x^2 * yz > 0

x^2 always positive. So yz > 0.

Answer C
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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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New post 31 May 2016, 14:06
DestinyChild wrote:
If xyz > 0, is x > 0?

(1) xy > 0
(2) xz > 0


(1) xy > 0 --> If xy > 0, x can be both positive or negative but z has to be greater than 0
(2) xz > 0 --> If xz > 0, x can be both positive or negative but y has to be greater than 0

If z and y have to be greater than 0 then x has to be greater than 0 for xyz to be true.

Therefore, answer choice C
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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0 [#permalink]

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New post 19 Jul 2016, 13:28
DestinyChild wrote:
If xyz > 0, is x > 0?

(1) xy > 0
(2) xz > 0


If xyz > 0, is x > 0?
The only way for xyz to be positive all three are positive (x is +ve ; y is +ve and z is +ve)
Or Only two of them are negative and one is positive

(1) xy > 0
x can be negative ; y can be negative (or both x and y positive)
INSUFFICIENT

(2) xz > 0
x can be negative ; z can be negative (or both x and z positive)
INSUFFICIENT

MERGING BOTH
x, y, z are all positive {therefore x is positive}
x,y,z are all negative {therefore x is negative}; BUT ALL THREE CANNOT BE NEGATIVE; OTHERWISE INFO IN THE QUESTION STEM WILL BECOME INCORRECT. xyz>0
So, x y z can only be positive

ANSWER IS C
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Re: If xyz > 0, is x > 0? (1) xy > 0 (2) xz > 0   [#permalink] 19 Jul 2016, 13:28
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