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.
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'.)
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.
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