I don't think Statement 1 is sufficient.
For statement 1, using a positive fraction and a negative number as 2 examples will contradict, so it isn't sufficient on its own.
169 Easy inequality
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Katrusya
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A<B
Let's check first option:
2A>AB
A>(AB/2)
Consider these numbers:
A=1, B=1.2
1>(1*1.2)/2=0.6 - true
OR
A=-5, B=10
-5>(-5*10/2)=-25 - true
So, first option is not suffisient, because A can be <0 or >0
I think the answer is B
Let's check first option:
2A>AB
A>(AB/2)
Consider these numbers:
A=1, B=1.2
1>(1*1.2)/2=0.6 - true
OR
A=-5, B=10
-5>(-5*10/2)=-25 - true
So, first option is not suffisient, because A can be <0 or >0
I think the answer is B
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Katrusya
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samsachd,
you made a mistake:
1)2A>AB
=>2A-AB>0
=>A(2-B)>0
=>2-B>0 and A<0 - doesn't work! A must be >0 also, in order the product of these to be positive!
So, it's either
A>0 and 2-B>0, B<2
OR
A<0 and 2-B<0, B>2
Even though we are given that A<B it could satisfy both of aforementioned options, hence, A could be both <0 or >0
you made a mistake:
1)2A>AB
=>2A-AB>0
=>A(2-B)>0
=>2-B>0 and A<0 - doesn't work! A must be >0 also, in order the product of these to be positive!
So, it's either
A>0 and 2-B>0, B<2
OR
A<0 and 2-B<0, B>2
Even though we are given that A<B it could satisfy both of aforementioned options, hence, A could be both <0 or >0
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NikolayZ
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Agree with you.Katrusya wrote:samsachd,
you made a mistake:
1)2A>AB
=>2A-AB>0
=>A(2-B)>0
=>2-B>0 and A<0 - doesn't work! A must be >0 also, in order the product of these to be positive!
So, it's either
A>0 and 2-B>0, B<2
OR
A<0 and 2-B<0, B>2
Even though we are given that A<B it could satisfy both of aforementioned options, hence, A could be both <0 or >0
Is OA really "D" ?
I am refering to one of the explanations from Stuart Kovinsky here:
https://www.beatthegmat.com/inequalities ... tml#193824
If this explanation can be used here(and i am saying this considering both A and B as Intergers) then i think D is correct answer.Correct me if i am wrong.
https://www.beatthegmat.com/inequalities ... tml#193824
If this explanation can be used here(and i am saying this considering both A and B as Intergers) then i think D is correct answer.Correct me if i am wrong.
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mehravikas
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Pick numbers for statement 1 -
A = 1, B = 1.5
2A > AB - true and A > 0
A = -1, B = 6
2A > AB - true and A < 0
Statement 1 is insufficient
A = 1, B = 1.5
2A > AB - true and A > 0
A = -1, B = 6
2A > AB - true and A < 0
Statement 1 is insufficient
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Stuart@KaplanGMAT
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Let's look at (1) algebraically.ern5231 wrote:A<B. Is A<0?
(1) 2A>AB
(2) B<0
The OA given for this problem is D but I feel it is B. What is you opinion?
(1) 2A>AB
With inequalities, we have to be very careful about dividing through by variables; to be safe, we should look at both the positive and negative cases (where applicable).
If A>0, we can divide both sides by A to get:
2 > B
Now, b also has to be greater than a (according to the question stem, so we get the inequality:
2 > B > A > 0
Are there values for B and A that fit this inequality? Sure, nothing says we have to pick integer values. Therefore, A could be > 0 to give us a "no" answer.
If A<0, we can divide by sides by A to get:
2 < B
(we have to swap the direction of the inequality since we're dividing by a negative number).
So now we get the inequality:
B > 2 > 0 > A
are there values for A and B that fit this inequality? Sure - so we can get a "yes" answer as well.
Therefore, (1) is insufficient.
If we knew that A and b were integers, we could ignore the positive case (since there aren't two distinct integers between 2 and 0), and (1) would be sufficient, but we don't have that information.
Stuart Kovinsky | Kaplan GMAT Faculty | Toronto
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Talkativetree
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