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

Question

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

generis · Accepted Answer

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 2018-06-03venn.png

push12345 · Answer

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

bb · Answer

You just copied this from the post above - that's called plagiarism (copying someone's work to present as their own)

bumpbot · Answer

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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

Prep Toolkit

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