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from A,
a= -3 or 4
Substitute a to get b = 85, -1 ..both are integers. Thus, both values of a are ok==> still can't we determine what the value of a is.
--> insuff.

from B, b= -1 or 2
b=-1, a^3-a^2 = 49+(-1) = 48
a^3-a^2-48= > a =4
for b= 2, we find out other value of a
---> insuff

combine A and B, we find out a= 4
thus, C.

Sorry, edit: when b=2, we have a^3-a^2-51=0
There's a trick, the integer outcome of the equation can only be among factors of 51, that is to say +,- 1 ; +- 51, +- 3, +-17. As we notice that the LHS of equation involves all - , thus, negative factors of 51 can't be the solution. In fact ,there's ways for you to narrow down instead of trying these factors each by each.
Try these out and you get no integer results for a.
Thus, when b=2, there's no a.
the only value of a is 4 when b=-1

Eagerly awaiting your next 'weekly' Avtar!![/quote

What's wrong with the one I have now? Is it not "pretty" enough? _________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

What's wrong with the one I have now? Is it not "pretty" enough?

Nothing is wrong with this one. Just that I want to see more awesome ones. Frankly, your avtars make this place a whole lot more lively!

Infact, I thought your earlier avatar was your true picture! Now I know it isn't. Seeing this new one only makes me laugh everytime!!

Well, for some reason I can't upload my own custom avatar - I think the admin might have blocked that feature. We can only use what's in the upload bank. When I found this picture on the upload bank, needless to say, I couldn't resist.
Obviously, it's definitely not advisable to put your personal mugshots on public forums because of hams like me.

Okay good night guys 2:32am my time! : _________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

but when b=2, the equation a^3- a^2- 2= 49 or a^3-a^2-51= 0 has no integer solutions for a! Thus, we get only a=4 when b=-1 -----> B is suff

True! Good Catch! Laxie, I suggest you take the GMAT tomorrow

Okay I'm definitely hitting the sack - good catch Laxi.

_________________

"Wow! Brazil is big." â€”George W. Bush, after being shown a map of Brazil by Brazilian president Luiz Inacio Lula da Silva, Brasilia, Brazil, Nov. 6, 2005

What's wrong with the one I have now? Is it not "pretty" enough?

Nothing is wrong with this one. Just that I want to see more awesome ones. Frankly, your avtars make this place a whole lot more lively! Infact, I thought your earlier avatar was your true picture! Now I know it isn't. Seeing this new one only makes me laugh everytime!!

Well, for some reason I can't upload my own custom avatar - I think the admin might have blocked that feature. We can only use what's in the upload bank. When I found this picture on the upload bank, needless to say, I couldn't resist. Obviously, it's definitely not advisable to put your personal mugshots on public forums because of hams like me. Okay good night guys 2:32am my time! :

mr./ms. Titleist,

after going through the posts above, i also couldnot stop myself from asking you for your awsome and "old is gold" avatar.

but when b=2, the equation a^3- a^2- 2= 49 or a^3-a^2-51= 0 has no integer solutions for a! Thus, we get only a=4 when b=-1 -----> B is suff

a^3-a^2-b=49
a^2(a-1)=49+b
We know that a(a-1) is even, so 49+b has to be even. That's why we can determine that b=-1. Then we write 49+(-1) = 48 = 4*4*3 and determine a=4.

You could stop here. But if you want to think further, you can.
This is a polynomial equation of the third order, so we have to be able to decide whether the other two solutions are integers. We know a-1>0, in other words a>1. Also a has to be even because if a is odd then a^2 is odd and a^2(a-1)/2 is odd, which cannot be 48. Obviously a has to be smaller than 7 because 7^2=49>48. So we only need to try a=2 and a=6, which can be easily shown that they are not one of the solutions. _________________

Keep on asking, and it will be given you;
keep on seeking, and you will find;
keep on knocking, and it will be opened to you.