Determine whether the following expression is POSITIVE, NEGATIVE or CANNOT BE DETERMINED with numerical examples!
Q: (-X) / (-Y)(-Z), given that xyz > 0
IS is NEGATIVE, but I have come up with CANNOT BE DETERMINED!
Please help me guys.
Number Properties!
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Ahmed MS wrote:Determine whether the following expression is POSITIVE, NEGATIVE or CANNOT BE DETERMINED with numerical examples!
Q: (-X) / (-Y)(-Z), given that xyz > 0
IS is NEGATIVE, but I have come up with CANNOT BE DETERMINED!
Please help me guys.
OA is Negative! Beg your pardon!
- neelgandham
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Determine whether the following expression is POSITIVE, NEGATIVE or CANNOT BE DETERMINED
Exp: (-X) / (-Y)(-Z) = -(x/(yz)) (As -ve *-ve = +ve), given that xyz > 0
xyz >0 implies,
x = -ve, y = -ve and z = +ve or
x = -ve, y = +ve and z = -ve or
x = +ve, y = -ve and z = -ve or
x = +ve, y = +ve and z = +ve
Let us check the sign of the expression (-X) / (-Y)(-Z)= (-(x/(yz)) (As -ve *-ve = +ve)) in all the cases.
x = -ve, y = -ve and z = +ve, (-(x/(yz)) = - ((-ve)/(-ve * +ve)) = -ve
x = -ve, y = +ve and z = -ve, (-(x/(yz)) = - ((-ve)/(+ve * -ve)) = -ve
x = +ve, y = -ve and z = -ve, (-(x/(yz)) = - ((+ve)/(-ve * -ve)) = -ve
x = +ve, y = +ve and z = +ve, (-(x/(yz)) = - ((+ve)/(+ve * +ve)) = -ve
Hence Negative ![/b]
Exp: (-X) / (-Y)(-Z) = -(x/(yz)) (As -ve *-ve = +ve), given that xyz > 0
xyz >0 implies,
x = -ve, y = -ve and z = +ve or
x = -ve, y = +ve and z = -ve or
x = +ve, y = -ve and z = -ve or
x = +ve, y = +ve and z = +ve
Let us check the sign of the expression (-X) / (-Y)(-Z)= (-(x/(yz)) (As -ve *-ve = +ve)) in all the cases.
x = -ve, y = -ve and z = +ve, (-(x/(yz)) = - ((-ve)/(-ve * +ve)) = -ve
x = -ve, y = +ve and z = -ve, (-(x/(yz)) = - ((-ve)/(+ve * -ve)) = -ve
x = +ve, y = -ve and z = -ve, (-(x/(yz)) = - ((+ve)/(-ve * -ve)) = -ve
x = +ve, y = +ve and z = +ve, (-(x/(yz)) = - ((+ve)/(+ve * +ve)) = -ve
Hence Negative ![/b]
Anil Gandham
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One point to keep in mind as you approach this problem:
Even if n=negative, the negative sign in front still changes the status therefore even if n= -1
-n= 1 OR -(-1)
Just need to know the properties as neelgandham pointed out the options.
in order for xyz to be >0, all are negative or either 2 of the 3 need to be negative.
Even if n=negative, the negative sign in front still changes the status therefore even if n= -1
-n= 1 OR -(-1)
Just need to know the properties as neelgandham pointed out the options.
in order for xyz to be >0, all are negative or either 2 of the 3 need to be negative.