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 SetsHope that helps.
EDITtito411990 , 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 [ 44.94 KiB | Viewed 1226 times ]
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