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

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Manager
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How many subsets of (a,b,c,d) are there including a and c [#permalink] New post 01 Aug 2007, 15:34
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A
B
C
D
E

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Question Stats:

50% (01:09) correct 50% (00:03) wrong based on 0 sessions
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
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 [#permalink] New post 01 Aug 2007, 16:12
doesn't this mean subsets including both a & c.

In that case answer is 4 - B.
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 [#permalink] New post 01 Aug 2007, 16:44
Is abcd a subset of abcd?

If not the answer is 3
ac
abc
adc
Director
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Re: PS Subsets [#permalink] New post 01 Aug 2007, 19:30
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
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Re: PS Subsets [#permalink] New post 01 Aug 2007, 22:43
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
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 [#permalink] New post 02 Aug 2007, 00:07
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
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 [#permalink] New post 02 Aug 2007, 00:44
I think I get this now. we're only counting subsets that include a and/or c?
SVP
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 [#permalink] New post 02 Aug 2007, 04:09
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
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 [#permalink] New post 02 Aug 2007, 06:03
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
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 [#permalink] New post 02 Aug 2007, 13:41
OA is B) 4

The subsets are:

(a,c)
(a,c,b)
(a,c,d)
and to my surprise (a,b,c,d).
VP
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 [#permalink] New post 02 Aug 2007, 13:50
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.
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 [#permalink] New post 02 Aug 2007, 15:14
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).
  [#permalink] 02 Aug 2007, 15:14
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How many subsets of (a,b,c,d) are there including a and c

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