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03 Jul 2012, 23:30
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A
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Difficulty:
15%
(low)
Question Stats:
75% (00:50) correct
25%
(00:58)
wrong
based on 98
sessions
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Not Attempted Yet
Is x < 0 ?
(1) -4x < 0
(2) -4x^2 < 0
What I want to know is
1) -4x < 0 ; either 4 is negative or x is negative. Hence cant say if x <0.
But explanation for this is given that
dividing both sides by -4, we get x > 0. Hence we know that x > 0.
Can anyone please help me understand why -4x is not 4 * (-x)? and in case it is 4*(-x) then why cant x<0 ?
2) Is clear to me. Hence no questions
(1) -4x < 0
(2) -4x^2 < 0
What I want to know is
1) -4x < 0 ; either 4 is negative or x is negative. Hence cant say if x <0.
But explanation for this is given that
dividing both sides by -4, we get x > 0. Hence we know that x > 0.
Can anyone please help me understand why -4x is not 4 * (-x)? and in case it is 4*(-x) then why cant x<0 ?
2) Is clear to me. Hence no questions
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
03 Jul 2012, 23:59
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jayoptimist
Hi,
-4x<0,
if x < 0, let say, x=-1, then (-4)(-1)>0
which contrary to the given inequality.
again, if x>0, let say, x=2, then (-4)(2)<0
Thus, we can say x>0
Let me know if you need any further clarification,
Regards,
04 Jul 2012, 01:32
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jayoptimist
Is x < 0 ?
(1) -4x < 0. Divide both parts by -4 and flip the sign of the inequality since we are dividing by negative number: \(x>0\). Sufficient. (Or just rewrite as \(4x>0\), which also leads to \(x>0\))
(2) -4x^2 < 0 --> \(x^2>0\). This inequality holds true for positive as well as negative values of \(x\). Not sufficient.
Answer: A.
As for your question: we CAN write \(-4x < 0\) as \(4*(-x) < 0\). Now, from \(4*(-x) < 0\) we have that the product of the positive number 4 and \(-x\) is negative, so \(-x\) must be negative: \(-x<0\) --> \(x>0\).
Hope it's clear.
P.S. Please read and follow: rules-for-posting-please-read-this-before-posting-133935.html
