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How many subsets of (a,b,c,d) are there including a and c [#permalink]
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01 Aug 2007, 16:34
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How many subsets of (a,b,c,d) are there including a and c (order of elements doesn't matter)?
A) 3
B) 4
C) 5
D) 6
E) 7



Manager
Joined: 17 Apr 2007
Posts: 90

doesn't this mean subsets including both a & c.
In that case answer is 4  B.



Manager
Joined: 27 May 2007
Posts: 128

Is abcd a subset of abcd?
If not the answer is 3
ac
abc
adc



Director
Joined: 08 Jun 2007
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Re: PS Subsets [#permalink]
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01 Aug 2007, 20:30
ashkrs wrote: raptr wrote: How many subsets of (a,b,c,d) are there including a and c (order of elements doesn't matter)?
A) 3 B) 4 C) 5 D) 6 E) 7 I think 7  ac bc dc abc acd bcd abcd
oops ...sorry i was drunk..!
i couldnt resist laughing when i saw my answer. agree with others..!



Director
Joined: 12 Jun 2006
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Re: PS Subsets [#permalink]
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01 Aug 2007, 23:43
raptr wrote: How many subsets of (a,b,c,d) are there including a and c (order of elements doesn't matter)?
A) 3 B) 4 C) 5 D) 6 E) 7
What is the OA on this?
from dictionary.com: Mathematics. a set consisting of elements of a given set that can be the same as the given set or smaller.
that said, won't the subsets be:
a
b
c
d
ab
ac
ad
abc
abd
dcb
abcd



GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

If 1 element subset > 2 (either {a} or {c})
If 2 elements subset > 1 (can only be {a,c})
If 3 elements subset > 2 (either {a,c,b} or {a,c,d}_
Total = 5 (order doesn't matter, so {a,c} and {c,a} both mean the same subset)



Director
Joined: 12 Jun 2006
Posts: 532

I think I get this now. we're only counting subsets that include a and/or c?



SVP
Joined: 28 Dec 2005
Posts: 1557

the way the question is worded, i thought it was asking for subsets that contained BOTH a and c , in which case the answer should be 2
a, b, c
a,c,d



VP
Joined: 10 Jun 2007
Posts: 1439

pmenon wrote: the way the question is worded, i thought it was asking for subsets that contained BOTH a and c , in which case the answer should be 2
a, b, c a,c,d
I feel the same. "including a and c", to me, means both a and c
However, there are total of three:
a,c
a,b,c
a,c,d



Manager
Joined: 06 Jul 2007
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OA is B) 4
The subsets are:
(a,c)
(a,c,b)
(a,c,d)
and to my surprise (a,b,c,d).



VP
Joined: 10 Jun 2007
Posts: 1439

raptr wrote: OA is B) 4
The subsets are:
(a,c) (a,c,b) (a,c,d) and to my surprise (a,b,c,d).
What's the source of this question?
So..Is it true that any set is a subset of itself? Somebody confirm...plz.



Manager
Joined: 06 Jul 2007
Posts: 160
Schools: CBS, MIT, Kellogg, Wharton

This question is from the challenges.
According to Wikipedia ( http://en.wikipedia.org/wiki/Subset):
"Any set is a subset of itself, but not a proper subset."
I guess for GMAT purposes, (a,b,c,d) is a subset of (a,b,c,d).










