set problem

[BTGmoderatorRO]

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 is c
How can i get the correct answer here with well detailed explanation? please help me out
Thanks

[EconomistGMATTutor]

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 is c
How can i get the correct answer here with well detailed explanation? please help me out Crying or Very sad
Thanks

Hi Roland2rule,
Let's take a look at your question.

The given set is: $$\left\{10,\ 14,\ 17,\ 24\right\}$$
The subsets that include odd number elements could have either one element or 3 elements. So let's first write all possible subsets that have only one element.
$$\left\{10\right\},\ \left\{14,\right\}\ \left\{17\right\},\left\{24\right\}$$
Therefore, there are 4 subsets that have one element.

Now let's write all possible subsets that have 3 elements.
$$\left\{10,\ 14,\ 17\right\},\ \left\{10,\ 14,\ 24\right\},\ \left\{10,\ 17,\ 24\right\},\ \left\{14,\ 17,\ 24\right\}$$
Therefore, there are 4 possible subsets of the given set that have 3 elements.

Hence the total number of subsets that have odd number of elements are 4 + 4 = 8.
So, Option C is correct.

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

[Scott@TargetTestPrep]

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 is c
How can i get the correct answer here with well detailed explanation? please help me out
Thanks

Solution:

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 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 of subsets containing 3 elements is 4C3 = 4. Therefore, the number of subsets containing an odd number of elements is 4 + 4 = 8.

Answer: C