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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## How many different subsets of the set {10, 14, 17, 24} are t ##### This topic has 2 expert replies and 0 member replies ## How many different subsets of the set {10, 14, 17, 24} are t How many different subsets of the set {10, 14, 17, 24} are there that contain an odd number of elements? (A) 3 (B) 6 (C) 8 (D) 10 (E) 12 OA: C What's wrong with options B and D? ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 ardz24 wrote: How many different subsets of the set {10, 14, 17, 24} are there that contain an odd number of elements? (A) 3 (B) 6 (C) 8 (D) 10 (E) 12 OA: C What's wrong with options B and D? There's only two ways that a subset can contain an odd number of elements here (assuming that each element can only be selected once): if the set contains 1 element and if the set contains 3 elements. 1 element sets: {10}, {14},{17}, {24} ---> 4 sets 3 elements sets: {10, 14, 17}, {10, 14, 24}, {10, 17, 24}, {14, 17, 24} --> 4 sets 4 + 4 = 8 sets total. The answer is C. _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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Quote:
How many different subsets of the set {10, 14, 17, 24} are there that contain an odd number of elements?

(A) 3
(B) 6
(C) 8
(D) 10
(E) 12

OA: C

What's wrong with options B and D?
Hi ardz24,
Let's take a look at your question.

We are asked to find the number of subsets of the set {10, 14, 17, 24} that contain an odd number of elements.
The subsets that have odd number of elements have either 1 or 3 elements.
Let's find those subsets.

Subsets with one element = {10}, {14}, {17}, {24}
Subsets with 3 elements = {10, 14, 17}, {10, 14, 24}, (10, 17, 24}, {14, 17, 24}

So there are 8 subsets that have odd number of elements.

Therefore, Option C is correct.

Hope this helps.
I am available if you'd like any follow up.

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