Is A^2+A>B^2?
1. A^2+B^2=1
2. A>0
(B)
My thoughts:
I'm trying to pick numbers but I'm not making sense of statement 1.
I skip to statement 2.
So I know that B^2 is always negative. So This means B has to be true.
Answer is B/D
This is where I get stuck.
B^2 = 1  A^2
Any thoughts?
Tough Number properties
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IMO B
qn : is A^2 + A >  B^2
stmnt 1:
A^2 + B^2 = 1
=> A^2  1 =  B^2
Now to check whether A^2 + A >  B^2 we can check:
whether A^2 + A > A^2  1 ?
or A > 1 ?
as A could be any number, could be > 1 or < 1 or = 1
So stmnt 1 is insufficient.
qn : is A^2 + A >  B^2
stmnt 1:
A^2 + B^2 = 1
=> A^2  1 =  B^2
Now to check whether A^2 + A >  B^2 we can check:
whether A^2 + A > A^2  1 ?
or A > 1 ?
as A could be any number, could be > 1 or < 1 or = 1
So stmnt 1 is insufficient.

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So you solved for statement 2 and got stuck with either B or D.
For statement 1, go with simple numbers..
Say B^2 = 0, hence A^ = 1. A can be either 1 or 1
If A = 1
when we solve the equation A^2+A>B^2 we get 0 > 0? No.
If A = 1
when we solve the equation A^2+A>B^2 we get 2 > 0? Yes.
Hence NOT sufficient. So this will leave you with only B.
For statement 1, go with simple numbers..
Say B^2 = 0, hence A^ = 1. A can be either 1 or 1
If A = 1
when we solve the equation A^2+A>B^2 we get 0 > 0? No.
If A = 1
when we solve the equation A^2+A>B^2 we get 2 > 0? Yes.
Hence NOT sufficient. So this will leave you with only B.
Attempt 1: 710, 92% (Q 42, 63%; V 44, 97%)
Attempt 2: Coming soon!
Attempt 2: Coming soon!
Does the question say –(B^2) or (B^2)? I am assuming it is the former.
Then S2 simply says that the left side of the equation is positive. In that case, no matter what B is, the right side will be negative or 0. Sufficient.
Then S2 simply says that the left side of the equation is positive. In that case, no matter what B is, the right side will be negative or 0. Sufficient.
 cubicle_bound_misfit
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simplify
the inequality becomes
is a2 +b2+a>0
we know a2 and b2 is always >0
hence question is asking is a>0 ?
that is what stmt 2 says.
hence B
the inequality becomes
is a2 +b2+a>0
we know a2 and b2 is always >0
hence question is asking is a>0 ?
that is what stmt 2 says.
hence B
Cubicle Bound Misfit

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rahulmehra13 wrote:IMO B
qn : is A^2 + A >  B^2
stmnt 1:
A^2 + B^2 = 1
=> A^2  1 =  B^2
Now to check whether A^2 + A >  B^2 we can check:
whether A^2 + A > A^2  1 ?
or A > 1 ?
as A could be any number, could be > 1 or < 1 or = 1
So stmnt 1 is insufficient.
I disagree here 'coz A^2+B^2 = 1
as both A^2 and B^2 is positive... they need to be less than 1 or at max 1
So, A=< 1
So, 1 will be sufficient
MS

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Rephrase the questionmohitsharda wrote:rahulmehra13 wrote:IMO B
qn : is A^2 + A >  B^2
stmnt 1:
A^2 + B^2 = 1
=> A^2  1 =  B^2
Now to check whether A^2 + A >  B^2 we can check:
whether A^2 + A > A^2  1 ?
or A > 1 ?
as A could be any number, could be > 1 or < 1 or = 1
So stmnt 1 is insufficient.
I disagree here 'coz A^2+B^2 = 1
as both A^2 and B^2 is positive... they need to be less than 1 or at max 1
So, A=< 1
So, 1 will be sufficient
A^2 + B^2 + A > 0 (just adding B^2)
So at this point A could be > 0 or less than 0. You don't know. Right.
Think about A^2 + B^2 = 1. A could be positive .707107 or positive
707107. The point is that squaring a number turns it into a positive so we don't know whether A > 0 or less than 0. Don't know at all.
The question reads: Is A^2+A>B^2? We don't know if A is greater than 0 or less than 0 at this point. So if A =<1 then A is still insufficient because you can still answer Yes and No.
With statement B  after you rephrase the question A > 0. Bingo.