If x and y are positive integers, what is the value of x + y ?
(1) 2^x 3^y = 72
(2) 2^x 2^y = 32
I will post the ans after some discussion.
If x and y are positive integers
This topic has expert replies
- GMAT Hacker
- Senior | Next Rank: 100 Posts
- Posts: 48
- Joined: Sun May 30, 2010 12:35 am
- Thanked: 1 times
GMAT/MBA Expert
- lunarpower
- GMAT Instructor
- Posts: 3380
- Joined: Mon Mar 03, 2008 1:20 am
- Thanked: 2256 times
- Followed by:1535 members
- GMAT Score:800
nicely done, although you did make one mistake -- the prime factorization of 72 is (3^2)(2^3). (you had a 3 instead of the red '2'.)nicolezl wrote:(1) The prime factorization of 72 is (2^3)(3^3), which looks just like the equation given, so x=3, y=2, and x+y=5.
Sufficient
(2) Can be re-written as 2^(x+y)=32, so x+y=5.
Sufficient
Answer is D.
i'd like to point out that you don't even have to form the actual prime factorization of 72 -- i.e., you don't have to spend the time to break 72 down into 3x3x2x2x2 -- if you realize that statement (1) has the form of a prime factorization.
instead, if you just realize that prime factorizations are unique -- i.e., that there is only one way to make the prime factorization of any given number -- then you will instantly realize that there must be a single combination of x and y that satisfies statement (1). if there were two or more such combinations, then you would have a violation of the rule that prime factorizations are unique.
on the other hand, since statement (2) is not a prime factorization, you should actually do the math that nicole has done in this post.
Ron has been teaching various standardized tests for 20 years.
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron
--
Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
--
Learn more about ron