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Of the 60 students of the IT class of 2003 at UC Berkeley, 30 use a Ma

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Of the 60 students of the IT class of 2003 at UC Berkeley, 30 use a Ma  [#permalink]

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New post Updated on: 03 Jun 2018, 14:25
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Question Stats:

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Of the 60 students of the IT class of 2003 at UC Berkeley, 30 use a Mac, 20 use a SPARC workstation, and 20 use a SGI. 13 use both Mac and SPARC, 5 uses both MAC and SGI, and 8 uses both SGI and SPARC. If 5 of the students use all three, how many don't use any of the three (not a Mac, not a SPARC, not a SGI, but maybe a crappy Intel machine)?

A. 0
B. 5
C. 10
D. 11
E. 12

with venn diagram got the answer as 11. But when i use the set theory formaulae

total = a+b+c- both -2Xall 3 + neither

i am getting neither as 26 as below

60 ( total ) =30 + 20 + 20 - 13 -5 -8 -2*5 + neither

solving this neither comes as 26

can anyone please guide where i am going wrong

Originally posted by tito411990 on 03 Jun 2018, 14:15.
Last edited by Bunuel on 03 Jun 2018, 14:25, edited 1 time in total.
Renamed the topic and edited the question.
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Of the 60 students of the IT class of 2003 at UC Berkeley, 30 use a Ma  [#permalink]

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New post 03 Jun 2018, 17:17
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tito411990 wrote:
Of the 60 students of the IT class of 2003 at UC Berkeley, 30 use a Mac, 20 use a SPARC workstation, and 20 use a SGI. 13 use both Mac and SPARC, 5 uses both MAC and SGI, and 8 uses both SGI and SPARC. If 5 of the students use all three, how many don't use any of the three (not a Mac, not a SPARC, not a SGI, but maybe a crappy Intel machine)?

A. 0
B. 5
C. 10
D. 11
E. 12

with venn diagram got the answer as 11. But when i use the set theory formaulae

total = a+b+c- both -2Xall 3 + neither

i am getting neither as 26 as below

60 ( total ) =30 + 20 + 20 - 13 -5 -8 -2*5 + neither

solving this neither comes as 26

can anyone please guide where i am going wrong

tito411990 , I drew a Venn diagram and got 11 as well.

The formula is a little different when we aren't using "exactly" or "only" two groups.
We need
\(A + B + C -(Both) + (all3) + Neither = Total\)

M = 30
SP = 20
SG = 20
M + SP = 13
M + SG = 5
SP + SG = 8
All 3 = 5

Total of "BOTH"
M + SP = 13
M + SG = 5
SP + SG = 8
(13+5+8) = 26

\(A + B + C -(Both) + (all3) + Neither = Total\)
Thus:
\(30+20+20-26+5+Neither= Total\)
\(75 - 26 + Neither = 60\)
\(49 + Neither = 60\)
\(Neither = 11\)


Answer D

Bunuel explains the formulas masterfully here, In Advanced Overlapping Sets

Hope that helps. :-)

EDIT
tito411990 , you are welcome.
Also, welcome to GMAT club!
Adding a Venn diagram.
1) Most restrictive first. All three = 5 (pink)

2) M and SP, SP and SG, M and SG are represented by
the three gray areas. In each area, use (BOTH - all three)
Mac + SP = 13: 5 from the all 3 group (pink) and 8 who use just 2 of the 3 (gray)

3) Light purple areas, M only, SP only, and SG only, use
For each: TOTAL - (gray + gray + pink)

4) Add all the numbers from inside the circle = total students who used
machines in defined categories
5) All students = 60. Students who use these machines = 49
6) None/Neither = (60 - 49) = 11
Attachment:
2018-06-03venn.png
2018-06-03venn.png [ 44.94 KiB | Viewed 391 times ]

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Of the 60 students of the IT class of 2003 at UC Berkeley, 30 use a Ma  [#permalink]

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New post Updated on: 07 Jul 2018, 05:41
I have also used the same formula used by generis above.

But the diference between two formulas mentioned by Bunuel post is quite subtle. So I would prefer to do this question via Venn diagram.

Sorry for copying the above formula. Thats strictly not my intention and I apologize for it.


Posted from my mobile device

Originally posted by push12345 on 06 Jul 2018, 20:00.
Last edited by push12345 on 07 Jul 2018, 05:41, edited 1 time in total.
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Re: Of the 60 students of the IT class of 2003 at UC Berkeley, 30 use a Ma  [#permalink]

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New post 07 Jul 2018, 05:25
push12345 wrote:
The formula is a little different when we aren't using "exactly" or "only" two groups.
We need
A+B+C−(Both)+(all3)+Neither=Total

Fill.in values and get answer

Posted from my mobile device


You just copied this from the post above - that's called plagiarism (copying someone's work to present as their own) :roll:
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Re: Of the 60 students of the IT class of 2003 at UC Berkeley, 30 use a Ma &nbs [#permalink] 07 Jul 2018, 05:25
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