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How many different subsets of the set {10, 14, 17, 24} are t

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by DavidG@VeritasPrep » Tue Oct 24, 2017 6:05 am
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.
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How many different subsets of the set {10, 14, 17, 24} are t

by EconomistGMATTutor » Tue Oct 24, 2017 2:16 pm
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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by Scott@TargetTestPrep » Wed Nov 20, 2019 5:46 pm
BTGmoderatorAT 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?
The options are:

17

10

14

24

10, 14, 17

17, 14, 24

17, 10, 24

10, 14, 24

Alternate solution:

Fact: For a set with n elements, the number of the subsets containing r elements (where 0 ≤ r ≤ n) is nCr.

Using the above fact, the number of subsets containing 1 element is 4C1 = 4, and the number subsets containing 3 elements is 4C3 = 4. Therefore, the number of subsets containing an odd number of elements is 4 + 4 = 8.

Answer: C

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