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16 Sep 2014, 00:47
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
64% (00:59) correct
36%
(01:03)
wrong
based on 171
sessions
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How many subsets of the set \(\{a,b,c,d\}\), containing both elements \(a\) and \(c\) (order of elements does not matter), are there?
A. 3
B. 4
C. 5
D. 6
E. 7
A. 3
B. 4
C. 5
D. 6
E. 7
16 Sep 2014, 00:47
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Official Solution:
How many subsets of the set \(\{a,b,c,d\}\), containing both elements \(a\) and \(c\) (order of elements does not matter), are there?
A. 3
B. 4
C. 5
D. 6
E. 7
Since the given set is small enough, we can easily list all subsets that contain both elements \(a\) and \(c\): \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\).
Alternatively, we can use a more general approach. The subset must contain both elements \(a\) and \(c\). For each of the remaining elements, \(b\) and \(d\), there are two options: either to be included in the subset or not. This gives us a total number of possible subsets equal to \(2*2 = 4\).
Answer: B
How many subsets of the set \(\{a,b,c,d\}\), containing both elements \(a\) and \(c\) (order of elements does not matter), are there?
A. 3
B. 4
C. 5
D. 6
E. 7
Since the given set is small enough, we can easily list all subsets that contain both elements \(a\) and \(c\): \(\{a, c\}, \ \{a, b, c\}, \ \{a, c, d\}, \ \{a, b, c, d\}\).
Alternatively, we can use a more general approach. The subset must contain both elements \(a\) and \(c\). For each of the remaining elements, \(b\) and \(d\), there are two options: either to be included in the subset or not. This gives us a total number of possible subsets equal to \(2*2 = 4\).
Answer: B
riyazgilani
Joined: 14 May 2014
Last visit: 13 Jun 2016
Posts: 36
Given Kudos: 39
Schools: Broad '18 (WA$)
GMAT 1: 700 Q44 V41
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24 Jul 2015, 09:27
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Bunuel
hi, Bunuel,
can we count {a,b,c,d} as subset of {a,b,c,d}..?
