Bunuel wrote:

saintforlife wrote:

vandygrad11 wrote:

The best way to tackle this question is probably the formula for three overlapping sets:

Total = Group1 + Group 2 + Group 3 - (sum of 2-group overlaps) - 2*(all three) + Neither

Total = 300(.4) + 300(.3) + 300(.75) - 300(.35) - 2*(all three) + 0

300*.1 = 30

300 = 120 + 90 + 225 - 105 - 2*(all three)

2*(all three) = 30

:. 15 experienced all three effects

So Group 1 + Group 2 + Group 3 - 2-group overlaps * 2 - 3-group overlaps * 3 is our answer

= 120 + 90 + 225 - 105*2 - 15*3

= 435 - 210 - 45

= 180

Can someone explain how we get the formula highlighted in red above? Why do we multiply the 2-group overlaps and 3-group overlaps by 2 and 3 respectively? I didn't get that part. Thanks.

Explained here:

http://gmatclub.com/forum/advanced-over ... 44260.htmlHope it helps.

Hi

dave13,

In case your doubt regarding this question is not cleared here it is .

First I will explain the derivation of both the formulas and then you can find its application.

refer to advanced-overlapping-sets-problems-144260.html for the pictorial representation.

Only A= a, only B=b, only C=c ,

only A&B =d, only A&C =e , only B&C=f, These are exactly two group overlaps.

A&B&C = g all three group over laps

Two group overlaps d+g , e+g,f+g.

Now Each element is of certain value that adds up to total of the group. ie

a+b+c+d+e+f+g+n=T, where n=none .

Now Set A= a+d+e+g, We will take into account all the elements the construct the Set which is the value of Only A+only A&B+only A&C+A&B&C. This is how set A is build.

Set B= b+d+f+g We will take into account all the elements the construct the Set which is the value of Only B+only A&B +onlyB&C+A&B&C

Set C=c+e+f+g We will take into account all the elements the construct the Set which is the value of Only C+only A&C +onlyB&C+A&B&C

Well there are two Basic Formulas for three overlapping sets

T= A+B+C- (sum of exactly two over-lapping sets)-2(all three) +none

lets understand how is it constructed

First part

A+B+C= (a+d+e+g)+(b+d+f+g)+(c+e+f+g )

A+B+C=a+b+c+2d+2e+2f+3g. To cancel out the additional (d,e,f and the two g's that we got subtract them so that our final result is T= a+b+c+ d+f+e+g+n

Second part Removing the additional d,e,f and 2g

This can be done in two ways where each way gives us a formula

Method 1

Remove the exactly two group elements and remove twice of element that belongs to all three groups )

Elements that belong to exactly two group are d,e,f and element that belongs to all three groups is "g"

T= a+b+c+2d+2e+2f+3g- d-f-e-2g

T=a+b+c+d+e+f+g

add the final element "n" to get the total T

T=a+b+c+d+e+f+g+n

Hence the formula

T= (a+d+e+g)+(b+d+f+g)+(c+e+f+g )-(d+e+f)-2(g)+n

T= A+B+C- (sum of exactly two over-lapping sets)-2(all three) +none

Method 2

Removing can also be done by removing the two overlap groups ,

So the elements of the this group are (d+g,e+g,f+g)

T= a+b+c+2d+2e+2f+3g -d-g-e-g-f-g

T= a+b+c+d+e+f We dont have element"g" which completes the total

So to undo this effecy we add an element "g" which is nothing but element belonging to all three sets

T=a+b+c+d+e+f+g+n

SO this gives us the second formula.

T= A+B+C- (sum of two over-lapping sets)+all three +none

T= (a+d+e+g)+(b+d+f+g)+(c+e+f+g ) - ( d+g+e+g+f+g)+(g)+n

No Coming back to the question

We are given certain information , is 40 % of 300 = 120, 30% of 300= 90 and 75%of 300=225 and 35 % of 300=105.

let Sweaty Palms be A= a+d+g+e=120,

Vomiting be B=b+d+f+g= 90,&

Dizziness be C=c+e+f+g=225,

also exactly two of the three effects be " sum of exactly two over-lap groups"= d+f+e= 105.

We are asked to find a+b+c=?

So first I will use the formula T= A+B+C- (sum of

exactly two over-lapping sets)- 2(all three) +none and calculate all three.

Why do we need to calculate that since T=a+b+c+d+e+f+g, we are given the values of d+f+e but not g. If we can calculate value of g we can find a+b+c= T-(d+e+f+g)

Let all three symptoms be x then,

120+90+225-105-2(x)+0=300

2(x)=30

so x=15

Now to calculate a+b+c i will use the first formula

T=a+b+c+d+e+f+g+n

we know that d+e+f= 105, and g=15

300=a+b+c+105+15

a+b+c=300-(105+15)

a+b+c= 180.

Let me know if there is something you need more help on, will try my best.

Probus