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if a + b <> 0

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by m&m » Mon Jul 27, 2009 1:59 pm
Just wrote a practice GMAT test from Knewton. I believe the following question is wrong, could someone find a flaw in my logic... OA is E -

if a+b <> 0 is (2a-b)/(2a+b) > 1
1) a>0
2) b<0

I solved this algebraically. If we assume inequality is true then:
2a/(2a+b) - b/(2a+b) >1
2a/(2a+b)>1+b/(2a+b)
2a/(2a+b)>(2a+b+b)/(2a+b)
2a/(2a+b)>(2a+2b)/(2a+b)
2a/(2a+b)>(2a)/(2a+b)+ (2b)/(2a+b)
2a/(2a+b)-(2a)/(2a+b)> (2b)/(2a+b)
0 > (2b)/(2a+b)
0 > 2b
so b<0 must be true for inequality to be true... I picked B

Am I off here?

Thanks for your help
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Source: — Data Sufficiency |
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by vinayakdl » Mon Jul 27, 2009 3:11 pm
I agree with E,

try (1,-1) and (1,-5) and the it is clear that a & 2 are not sufficient.

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by m&m » Tue Jul 28, 2009 8:43 am
thanks

Could someone please help me point out where I went wrong?
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Re: if a + b <> 0

by Ian Stewart » Tue Jul 28, 2009 9:14 am
m&m wrote:Just wrote a practice GMAT test from Knewton. I believe the following question is wrong, could someone find a flaw in my logic... OA is E -

if a+b <> 0 is (2a-b)/(2a+b) > 1
1) a>0
2) b<0

I solved this algebraically. If we assume inequality is true then:
2a/(2a+b) - b/(2a+b) >1
2a/(2a+b)>1+b/(2a+b)
2a/(2a+b)>(2a+b+b)/(2a+b)
2a/(2a+b)>(2a+2b)/(2a+b)
2a/(2a+b)>(2a)/(2a+b)+ (2b)/(2a+b)
2a/(2a+b)-(2a)/(2a+b)> (2b)/(2a+b)
0 > (2b)/(2a+b)
0 > 2b
so b<0 must be true for inequality to be true... I picked B

Am I off here?

Thanks for your help
I highlighted the mistake in red above - you appear to have multiplied on both sides by 2a + b, which you can't do, since you don't know whether 2a + b is positive or negative. If it were negative, you would need to reverse the inequality.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Re: if a + b <> 0

by fruti_yum » Tue Sep 08, 2009 11:47 am
Ian Stewart wrote:
m&m wrote:Just wrote a practice GMAT test from Knewton. I believe the following question is wrong, could someone find a flaw in my logic... OA is E -

if a+b <> 0 is (2a-b)/(2a+b) > 1
1) a>0
2) b<0

I solved this algebraically. If we assume inequality is true then:
2a/(2a+b) - b/(2a+b) >1
2a/(2a+b)>1+b/(2a+b)
2a/(2a+b)>(2a+b+b)/(2a+b)
2a/(2a+b)>(2a+2b)/(2a+b)
2a/(2a+b)>(2a)/(2a+b)+ (2b)/(2a+b)
2a/(2a+b)-(2a)/(2a+b)> (2b)/(2a+b)
0 > (2b)/(2a+b)
0 > 2b
so b<0 must be true for inequality to be true... I picked B

Am I off here?

Thanks for your help
I highlighted the mistake in red above - you appear to have multiplied on both sides by 2a + b, which you can't do, since you don't know whether 2a + b is positive or negative. If it were negative, you would need to reverse the inequality.

IAN... the way i approached it..

I assumed 2a +b to be positive .. then I get b <0
I assumed 2a +b to be negative.. then i get b >0

when i'm given b <0 then don't i already know that 2a + b is positive??

pls let me know if i'm doing anything wrong?
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