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How many subsets of (a,b,c,d) are there including a and c [#permalink ]
01 Aug 2007, 15:34

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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

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

Manager

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

Director

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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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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

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

SVP

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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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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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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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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

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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).