Set theory problem.

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Vookeh dyzynah: Newbie | Next Rank: 10 Posts; Posts: 3; Joined: Tue Apr 24, 2012 1:11 am

Set theory problem.

by Vookeh dyzynah » Wed Apr 25, 2012 4:49 am

In a survey of 100 families the no. that read recent issues of a certain monthly magazine were found to be;
September only 18
September but not August 23
September & July 8
september 26
July 48
July & August 8
None of the 3 months 24.
With the help of the set theory find;
(a)How many read the August issue?
(b)How many read 2 consecutive issues?
(c)How many read the July issue if and only if they did not read the August issue?
(d)How many read September & August issues but did not read the July issue?

please atach sum explanation to your working thank you.

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Source: Beat The GMAT — Data Sufficiency | Wed Apr 25, 2012 4:49 am

Birottam Dutta: Master | Next Rank: 500 Posts; Posts: 342; Joined: Wed Jul 08, 2009 8:50 am; Thanked: 214 times; Followed by:19 members; GMAT Score:740

by Birottam Dutta » Wed Apr 25, 2012 7:55 am

According to the question,

a= 18 (September only 18 )-----(1)
a+b+d+f = 26 (september 26 )-----(2)
g+f+d+e = 48 (July 48 )-----(3)
d+e= 8 (July & August 8)-----(4)
d+f = 8 (September & July 8)-----(5)
a+f = 23 (September but not August 23)-----(6)
a+b+c+d+e+f+g = 76 (None of the 3 months 24)-----(7)
From (1) and (6), f=5---- (8)
From (8) and (5), d=3 --- (9)
From (9) and (4), e=5---- (10)
From (3), (8), (9) and (10), g= 35 --- (11)
From (2), (8), (9) and (1), b = 0
As only c is missing, putting values of all other unknowns in (7), we get c= 10.

Now let us answer the questions:

(a) August = b+c+d+e = 18
(b) Two consecutive issues will be either July August or August September = e + b = 5+ 0 = 5
(c) July minus August = g + f = 35 + 5 = 40
(d) Sept + Aug - July = b = 0.

Hope these are correct!

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Wed Apr 25, 2012 8:23 am

Hi,

I'm a bit confused about what this has to do with:

1) data sufficiency; and
2) the GMAT!

Thanks,

Stuart

Vookeh dyzynah wrote:In a survey of 100 families the no. that read recent issues of a certain monthly magazine were found to be;
September only 18
September but not August 23
September & July 8
september 26
July 48
July & August 8
None of the 3 months 24.
With the help of the set theory find;
(a)How many read the August issue?
(b)How many read 2 consecutive issues?
(c)How many read the July issue if and only if they did not read the August issue?
(d)How many read September & August issues but did not read the July issue?

please atach sum explanation to your working thank you.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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