Monday, May 24, 2010

Please help me with this venn diagram problem!?

here's the problem.





In a survey involving 800 employees, it was found that:


485 save with Banco de Oro


550 save with Metrobank


540 save with BPI


255 save with Banco de Oro and Metrobank


270 save with Banco de Oro and BPI


325 save with Metrobank and BPI


All employees save with at least one of these banks.





Using a Venn diagram, find the number of employees who save with:


a. all 3 banks


b. Banco de Oro but not BPI


c. Metrobank but not Banco de Oro


d. BPI but not Metrobank


e. Banco de Oro but not Metrobank or BPI


F. Banco de Oro or BPI but not Metrobank.





(I tried soolving this problem, but it seems that the intersection of the 3 circles is missing. Please help me with this.)

Please help me with this venn diagram problem!?
==________ Banco de Oro


==|===A===|


__|________|___


|==|=C|=D|=E|==|


|=B|__|___|__|=F|


|====|= G|====|


|_____|___|____|==H


Metrobank===BPI





= is space for above diagram





Banco de Oro = {A,C,D,E}


Metrobank = {B,C,D,G}


BPI = {D,E,F,G}


non of these = {H}





Total = 800


A + C + D + E = 485


B + C + D + G = 550


D + E + F + G = 540


C + D = 255


D + E = 270


D + G = 325


H = 0





C + 2D + E + G = (A + C + D + E) + (B + C + D + G) + (D + E + F + G) + H - Total


= 485 + 550 + 540 + 0 - 800 = 775





C + 3D + E + G = (C + D) + (D + E) + (D + G) = 255 + 270 + 325 = 850





a. all 3 banks


D = (C + 3D + E + G) - (C + 2D + E + G) = 850 -775 = 75





b. Banco de Oro but not BPI


A + C = (A + C + D + E) - (D + E) = 485 - 270 = 215





c. Metrobank but not Banco de Oro


B + G = (B + C + D + G) - (C + D) = 550 - 255 = 295





d. BPI but not Metrobank


E + F = (D + E + F + G) - (D + G) = 540 - 325 = 215





e. Banco de Oro but not Metrobank or BPI


A = (A + C + D + E) + D - (C + D) - (D + E) = 485 + 75 - 255 - 270 = 35





f. Banco de Oro or BPI but not Metrobank


Total - (B + C + D + G) = 800 - 550 = 250
Reply:I get 75 for the first answer.





The 800 figure is the sum of all sections (bdo-only,m-only,bpi-only,combo1,combo2,...


The sum of the individuals (485+550+540) is the following sum


bdo,combo1,combo2,all3


bpi,combo2,combo3,all3


m,combo1,combo3,all3





subtract to get


combo1+combo2+combo3+twice all3=775





also,


combo1+all3+


combo2+all3+


combo3+all3=


255+270+325=850





subtract gives all3=75





can then find numbers in each of the 7 individual segments of the venn diagram





Should be able to take it from there. Segment numbers are then





35,45,20,195,180,250





I guess it depends how you read the figures, but the combo1/2/3 I take to mean as follows...


255 with bdo and m means 255 with bdo and m only(=combo2 in my symbols above), plus bdo and m and all3





Other answers follow....





b)35+180=215


c)45+250=295


d)20+195


e)35


f)35+195+20=250
Reply:Here's my Venn Diagram:





http://i246.photobucket.com/albums/gg88/...





Here's my calculations:


O: Banco de Oro


P: BPI


M: Metrobank





O^P^M=x


O^P=270


O^M=255


P^M=325


O^P^M'=270-x


O^M^P'=255-x


P^M^O'=325-x


O^P'^M'=485-(270-x)-(255-x) = x-40





O'^M^P'=550-(255-x)-(325-x) = x-30





P^M'^o'=540-(325-x)-(255-x) = x-55


Add them all together:


x-40+ x-30+ x-55+270-x+255-x+325-x+x=800


x+725=800


x=75





a. 75


b. 180+35=215


c. 250+45=295


d. 195+20=215


e. 35


f. 35+195+20=250


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