Set consists 2n-1 element

[gchechenova]

A set consist of 2n-1 element. What is the number of subsets of this set which contain at most n-1 elements?

A. 2^(2n-2)
B. 2^(2n) - 2
C. 2^(2n) -1
D. 2^(2n)
E. 2^(2n-1)


OA A (by the way, how do we hide the OA in this forum?)
Please explain.

[sunny.jain]

Well I choose n = 3

so total number of initial element: 5

we have to find subset contain at most : 2
so subset may have 0,1,2 element

5C0 + 5C1 + 5C2 ==> 1 + 5 + 10 ==> 16

options
A) 2^(4) ==> 16
b)2^6 - 2 ==> 62
c) 2^6 -1 ==> 63
d)2^6 ==> 64
E) 2^5 ==> 32

clearly A is the answer here.

Alternatively you have to solve this equation:

Sum ( [2n-1]C[i]) with i going from 0 to n-1.

[RonPurewal]

hi -

this problem would be nice in an introductory set theory class, but it has absolutely nothing in common with authentic gmat problems. you should flag whatever source it came from as dubious.

first of all, this problem is WAY too theoretical in nature for the gmat (a test on which ALL combinatorics problems are rooted in word problems / real-life type situations).

second of all, this problem requires you to understand that a set with no elements (the "empty set") is considered a subset of any larger set.
while mathematically true, this is not the sort of thing that would ever appear on the gmat.

--

therefore, the ONLY VALUE of this question, AT ALL, is that it should prompt you to use a "plug in numbers" approach (as did the previous poster).

even then, it's still not that useful, since you have to realize that the "empty set" is a subset in order to get the count right.

therefore, "ignore this question - and be skeptical of the source it came from" is the best policy here.