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

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