Author 
Message 
Director
Joined: 15 Aug 2005
Posts: 796
Location: Singapore

For integers a and b, if square root of (a^3  a^2  b) = 7, [#permalink]
Show Tags
22 Oct 2005, 22:22
Question Stats:
0% (00:00) correct
0% (00:00) wrong based on 0 sessions
HideShow timer Statistics
This topic is locked. If you want to discuss this question please repost it in the respective forum. For integers a and b, if square root of (a^3  a^2  b) = 7, what is the value of a?
A. a^2  a = 12
B. b^2  b = 2
_________________
Cheers, Rahul.



Director
Joined: 21 Aug 2005
Posts: 789

C
A) Insuff. Has 2 solutions. a=4, 3 (corresponding b=1, 85)
B) Insuff. b=2, 1
Combining, we can say a=4



SVP
Joined: 24 Sep 2005
Posts: 1885

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^3a^2 = 49+(1) = 48
a^3a^248= > 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^3a^251=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



Director
Joined: 21 Aug 2005
Posts: 789

Titleist wrote: Ditto GSR
I go with C
Eagerly awaiting your next 'weekly' Avtar!!



Director
Joined: 14 Oct 2003
Posts: 583
Location: On Vacation at My Crawford, Texas Ranch

gsr wrote: Titleist wrote: Ditto GSR
I go with C
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
http://www.nytimes.com/2005/11/21/international/asia/21prexy.html



Director
Joined: 21 Aug 2005
Posts: 789

Titleist wrote: 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!!



SVP
Joined: 24 Sep 2005
Posts: 1885

Titleist wrote: Ditto GSR
I go with C
but when b=2, the equation a^3 a^2 2= 49 or a^3a^251= 0 has no integer solutions for a!
Thus, we get only a=4 when b=1 > B is suff



Director
Joined: 14 Oct 2003
Posts: 583
Location: On Vacation at My Crawford, Texas Ranch

gsr wrote: Titleist wrote: 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
http://www.nytimes.com/2005/11/21/international/asia/21prexy.html



Director
Joined: 21 Aug 2005
Posts: 789

laxieqv wrote: Titleist wrote: Ditto GSR I go with C but when b=2, the equation a^3 a^2 2= 49 or a^3a^251= 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



Director
Joined: 14 Oct 2003
Posts: 583
Location: On Vacation at My Crawford, Texas Ranch

gsr wrote: laxieqv wrote: Titleist wrote: Ditto GSR I go with C but when b=2, the equation a^3 a^2 2= 49 or a^3a^251= 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
http://www.nytimes.com/2005/11/21/international/asia/21prexy.html



Director
Joined: 21 Aug 2005
Posts: 789

True, Titleist! Don't take this one off unless you find a better one! I guess we don't have any better ones on the forum!



VP
Joined: 13 Jun 2004
Posts: 1115
Location: London, UK
Schools: Tuck'08

Nice Laxie...fei chang hao



Director
Joined: 15 Aug 2005
Posts: 796
Location: Singapore

Antmavel wrote: Nice Laxie...fei chang hao
Though i have no clue what you meant....il surely say this.....nee hao?
_________________
Cheers, Rahul.



Current Student
Joined: 28 Dec 2004
Posts: 3357
Location: New York City
Schools: Wharton'11 HBS'12

hmm...I am not sure about B cause
if we just look at b and ignore anything we know about a, then we still dont know if 2 or 1 for B will work or not...
It only makes sense that b=1 when we know what a^3a^2 simplifies too?
laxieqv wrote: Titleist wrote: Ditto GSR
I go with C but when b=2, the equation a^3 a^2 2= 49 or a^3a^251= 0 has no integer solutions for a! Thus, we get only a=4 when b=1 > B is suff



SVP
Joined: 05 Apr 2005
Posts: 1710

Titleist wrote: gsr wrote: Titleist wrote: 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.
awaiting eagerly.....



SVP
Joined: 03 Jan 2005
Posts: 2233

laxieqv wrote: but when b=2, the equation a^3 a^2 2= 49 or a^3a^251= 0 has no integer solutions for a! Thus, we get only a=4 when b=1 > B is suff
a^3a^2b=49
a^2(a1)=49+b
We know that a(a1) 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 a1>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(a1)/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.



SVP
Joined: 03 Jan 2005
Posts: 2233

HongHu wrote: Also a has to be even because if a is odd then a^2 is odd and a^2(a1)/2 is odd, which cannot be 48.
Actually this is not right, but is ok to use for a<7. Also better change it to be a^2(a1)/4 is odd.
_________________
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.










