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# How many subsets of (a,b,c,d) are there including a and c

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

50% (01:09) correct 50% (00:03) wrong based on 36 sessions

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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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

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01 Aug 2007, 17:12
doesn't this mean subsets including both a & c.

In that case answer is 4 - B.
Manager
Joined: 27 May 2007
Posts: 128

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01 Aug 2007, 17:44
Is abcd a subset of abcd?

If not the answer is 3
ac
abc
Director
Joined: 08 Jun 2007
Posts: 573

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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
Posts: 532

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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
abc
abd
dcb
abcd
GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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02 Aug 2007, 01:07
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

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02 Aug 2007, 01:44
I think I get this now. we're only counting subsets that include a and/or c?
SVP
Joined: 28 Dec 2005
Posts: 1557

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02 Aug 2007, 05:09
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

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02 Aug 2007, 07:03
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
Posts: 160
Schools: CBS, MIT, Kellogg, Wharton

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02 Aug 2007, 14:41
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

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02 Aug 2007, 14:50
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

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02 Aug 2007, 16:14
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).
02 Aug 2007, 16:14
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