Out of 80 people, some drink tea, some drink coffee, while some drink

Let a= Who drink tea only
b= Who drink coffee only
c = Who drink both
d = Who drink none

Now, as per St. 1 c=0.6*(a+c)=>6a=4c Not sufficient as we want only sum of only a and b in answer.
From St. 2 (b+d)*0.6=a+d=>6b=10a+4d
Not sufficient for reason as in St. 1

Combining the two we have below equations -
6b=10a+4d...(1)
6a=4c...(2)
and a+b+c+d=80...(3)

We can substitute for d from eq 1 and for c from eq 2 to get the answer. We can choose choice C as the answer.We don't need to calculate till the end.

Out of 80 people, some drink tea, some drink coffee, while some drink both. There might also be some who drink neither tea nor coffee. How many drink only one drink, i.e., either only tea or only coffee?

(1) 60% of those who drink tea, also drink coffee.

(2) 60% of those who do not drink tea, also do not drink coffee.

Using complement signs here as ' in the following descriptions. Please correct me if I am wrong.

1. From 60% of n(T) also drink coffee so : n(TnC) = 60 % of n(T)
then remaining 40 % of n(T) don't drink coffee so n(only T) = 40% of n(T)
inufficient.

2. 60% of n(T') also doesnt drink coffee so n(C') which is n(TuC)' complement= 60% of n(T')
hence 40% of n(T') drink coffee so n(only C) = 40% of n(T')

Doesnt say anything how much percentage that reflects to.

1&2 combined. We have all four components of the overlapping sets :
n(TnC) = 60% of n(T)
n(TuC)' = 60% of n(T')

n(TnC) = 60% of n(T)
n(TnC) = 6/10 * { n(only T) + n(TnC)}
10*n(TnC) = 6*n(only T) + 6 * n(TnC)
4*n(TnC) = 6*n(only T)
n(TnC) = 6/4 * n(only T) ---------(a)

n(TuC)' = 60% of n(T')
n(TuC)'= 60/100 { n(only C) + n(TuC)'}
n(TuC)' = 6/10 * { n(only C) + n(TuC)'}
10*n(TuC)' = 6*n(only C) + 6 * n(TuC)'
4*n(TuC)' = 6*n(only C)
n(TuC)' = 6/4 * n(only C) --------(b)

Total = 80
n(only T) + n(only C) + n(Tnc) + n(Tuc)' = 80
Substituting values from (a) and (b)
6/4* n(only T) + n(only T) + n(only C) + 6/4* n(only C) = 80
n(only T) + n(only C) = 32
Cannot solve with to find n(T) and n(T') as only known is n(T) + n(T') = 80

Hi AmanVarma,
It was a real exercise for my brain.
Can you please mention the source of the question.

Thanks
The Graceful

Total 80
OT - unknown ...?(**60% of those who drink Tea also drink coffee) -- can not be 60% of 80
OC - unknowns
Both -- ** (can be calculated but we dont have OT)
None -- 80 - OT (60% of those who do onot drink Tea also do not drink coffee)
Hence E

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.