Lucky2783 wrote:
If set A={2,2,2,....,n times} , set B={3,3,3,3....m times} and set C={11,11,11...k time} , then in terms of m,n and k , how many possible subsets from sets A,B, and C can be created ?
a) k(n+m+mn)+ k
b) (1+n+m+mn)(k+1)
c) k^2(mn+n/m)
d) kmn(k+m+n)
e) None of the above.
I'm happy to respond.
This is simply a problem testing the Fundamental Counting Principle, which is discussed in this blog:
https://magoosh.com/gmat/2012/gmat-quant-how-to-count/In the subset, of course, order doesn't matter. Notice that, in technical terms, the wording is very sloppy: "
the subsets of these three sets" is a very sloppy vague idea. Presumably, the writer means, "
the subsets of the union of these three sets." Assuming this is what is meant, then all that matters is:
a) how many 2's are included?
b) how many 3's are included?
and
c) how many 11's are included?
For the number of 2, we could have zero 2's, or one 2, or two 2's, all the way up to n 2's. That's (n + 1) possibilities for the 2's. Similarly, (m + 1) possibilities for the 3's and (k + 1) possibilities for the 11's. We simply multiply these three numbers.
NOTICE that one set, the set that includes no 2's, no 3's, and no 11's, is included. This is known in mathematics as the
null set, sometimes called the empty set, a set with no members. Technically, this is a subset of every possible set, but that's a technical detail of set theory that goes well beyond what the GMAT would expect students to know. Even the the calculation is not that difficult, some of the technical aspects of this question are not in line with the GMAT's expectations.
The number of subsets is (m + 1)(n + 1)(k + 1). The answer is not given in that form. Instead, the first two factors have been FOILed together:
(mn + m + n + 1)(k + 1).
I don't know the source. This looks like a question that was written by someone who knows a good deal of math but not necessarily a lot about the GMAT.
Does all this make sense?
Mike
thanks for your detailed explanation . it makes sense.
Is it not like a GMAT question? To be honest i created this question when i looked at prime factorization and #factors of product of Integers.
if N=2^n*3^m*11^k then #factors (n+1)*(m+1)*(k+1) , here we have 1 as one of the factor which is {} null set in your explanation.