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If ax + b = 0, is x > 0 ?

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geetesht
 Post subject: If ax + b = 0, is x > 0 ?
 Post Posted: Fri Jan 08, 2010 1:46 pm 
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Course Students


Posts: 16
If ax + b = 0, is x > 0 ?

(1) a + b > 0

(2) a - b > 0

The given information can be rephrased as ax = -b.

If i add statement 1 & 2, ( since two inequalities can be added) i get, a > 0 i.e a is positive . Hence i can say for the equation ax = -b to be true , x is negative. Since
positive (a) * negative(x) = negative(b)

My ans would be 'C'.

Could anyone please confirm i am thinking on the right track!
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RonPurewal
 Post subject: Re: If ax + b = 0, is x > 0 ?
 Post Posted: Sat Jan 09, 2010 6:08 am 
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ManhattanGMAT Staff


Posts: 7146
geetesht wrote:
If ax + b = 0, is x > 0 ?

(1) a + b > 0

(2) a - b > 0

The given information can be rephrased as ax = -b.

If i add statement 1 & 2, ( since two inequalities can be added) i get, a > 0 i.e a is positive . Hence i can say for the equation ax = -b to be true , x is negative. Since
positive (a) * negative(x) = negative(b)

My ans would be 'C'.

Could anyone please confirm i am thinking on the right track!


nope. incorrect.

the first thing we need to get on the table here is that "-B" is NOT necessarily a negative number. this is a very common misconception - probably the most common misconception in all of algebra, actually - but it's still a misconception.
* if "b" is positive, then "-b" is negative, as expected.
* if "b" is NEGATIVE, then "-b" is POSITIVE.

--

in this problem, we can deduce that "a" is positive (as you found), but we can't figure out anything about "b", which can be positive, negative, or zero. (for instance, if a = 3, then b can be anything between -3 and 3.)

if b is positive, then x must be negative.
if b is zero, then x must be zero.
if b is negative, then x must be positive.

so, insufficient; the answer is (e).
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geetesht
 Post subject: Re: If ax + b = 0, is x > 0 ?
 Post Posted: Sat Jan 09, 2010 7:30 am 
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Course Students


Posts: 16
Ron, Your the man ! The supreme GENIUS of GMAT :) .
Many thanks Coach! Appreciate it.
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Ben Ku
 Post subject: Re: If ax + b = 0, is x > 0 ?
 Post Posted: Wed Jan 13, 2010 12:55 am 
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ManhattanGMAT Staff


Posts: 823
Glad it helped!

_________________
Ben Ku
Instructor
ManhattanGMAT
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ishkaran88
 Post subject: Re: If ax + b = 0, is x > 0 ?
 Post Posted: Mon Jan 18, 2010 3:02 pm 
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Posts: 2
Thankyou.
It really helped me clear a serious flaw in my approach!
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RonPurewal
 Post subject: Re: If ax + b = 0, is x > 0 ?
 Post Posted: Tue Feb 09, 2010 6:40 am 
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ManhattanGMAT Staff


Posts: 7146
ishkaran88 wrote:
Thankyou.
It really helped me clear a serious flaw in my approach!

glad it helped
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