Author 
Message 
Manager
Joined: 24 Jun 2003
Posts: 91
Location: Moscow

R^c)(R^d)(R^e)=12^12. If R>0, and c,d and e are each
[#permalink]
Show Tags
25 Jul 2003, 07:53
(R^c)(R^d)(R^e)=12^12.
If R>0, and c,d and e are each different negative integers, what is the smalest that c could be?
A) 12
B)10
C)9
D)6
E)1 == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
_________________
Respect,
KL



Manager
Joined: 22 Jul 2003
Posts: 60
Location: CA

(R^c)(R^d)(R^e)=12^12.
If R>0, and c,d and e are each different negative integers, what is the smalest that c could be?
A) 12 B)10 C)9 D)6 E)1
My answer is (A) i.e. 12
(R^c)(R^d)(R^e)=12^12
=> r^(c+d+e) = 12^12
=> r^(c+d+e) = (2*sqrt3)^24 (see below how I got this)
so, lowest value of c+d+e = 24
which leads to the smallest value of c as 12.
12^12 = (4*3)^12 = 4^12 * 3^12 = [(2^2)]^12 * [(sqrt3) ^ 2] ^ 12 = 2^24 * (sqrt3)^24 = [2 * sqrt(3)] ^ 24



Manager
Joined: 22 Jul 2003
Posts: 60
Location: CA

If R>0, and c,d and e are each different negative integers, what is the smalest that c could be?
You are assuming that R is an interger >0. But in the problem c,d,e are defined as negative intergers. R may not be an integer  isn't it?
If we take, R=2√3; c=12, d=7, e=5
then, c+d+e=24
so, R^(c+d+e) = (2√3)^24 = 12^12
That's why I think answer is A. Feedback pls.



Manager
Joined: 25 Jun 2003
Posts: 93

prakuda2000 wrote: If R>0, and c,d and e are each different negative integers, what is the smalest that c could be?
You are assuming that R is an interger >0. But in the problem c,d,e are defined as negative intergers. R may not be an integer  isn't it?
If we take, R=2√3; c=12, d=7, e=5 then, c+d+e=24
so, R^(c+d+e) = (2√3)^24 = 12^12 That's why I think answer is A. Feedback pls.
But how can you 'guess'tify R to be a noninteger
Even if c+d+e = 24 , why C is 12 , why can't it be 22 ?
Per the question C, D and E need to be negetive integers , So each one of them may atmost be 1.
So this gives us C to be 22 ?
I feel (A) should be  22 (may be a typo ).
_________________
Brainless



Manager
Joined: 24 Jun 2003
Posts: 91
Location: Moscow

Re: Some algebra practice
[#permalink]
Show Tags
26 Jul 2003, 03:48
Lynov Konstantin wrote: (R^c)(R^d)(R^e)=12^12.
If R>0, and c,d and e are each different negative integers, what is the smalest that c could be?
A) 12 B)10 C)9 D)6 E)1
Sorry, guys. I made a typing mistake in the question.
The condition should be read as follows:
(R^c)(R^d)(R^e)=R^c+d+e= R^12
If R>0, and c,d and e are each different negative integers, what is the smalest that c could be?
A) 12
B)10
C)9
D)6
E)1
Forgive me please and give it another shot.
_________________
Respect,
KL



SVP
Joined: 30 Oct 2003
Posts: 1769
Location: NewJersey USA

R^(a+b+c) = 12^(12)
so a+b+c = 12
Given a,b and c are ve distincive integers
abc can be any of(0,0,12), (0,1,11),(1,1,10),(1,2,9)
Lowest is 11 but that choice is not given. Next lowest is
(1,2,9) where integers are distinct and c = 9



NonHuman User
Joined: 09 Sep 2013
Posts: 7755

Re: R^c)(R^d)(R^e)=12^12. If R>0, and c,d and e are each
[#permalink]
Show Tags
04 Nov 2017, 13:13
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. == Message from GMAT Club Team == This is not a quality discussion. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: R^c)(R^d)(R^e)=12^12. If R>0, and c,d and e are each &nbs
[#permalink]
04 Nov 2017, 13:13






