Fast Solution

[infamousshorty]

A+B+C+AB+BC+AC+ABC=100
A=B=C=0 (minimise the exactly 1 parameter)

So,

AB+BC+AC+ABC=100 (1)

Additionally,

70=A+AB+AC+ABC
75=B+AB+BC+ABC
80=C+AC+BC+ABC
A=B=C=0
------------------
225=2AB+2BC+2AC+3ABC (2)

We multiply the equation (1) x2 --> 2AB+2BC+2AC+2ABC=200 (3)
Subtract [(2)-(3)] and we DONE!

[Brent@GMATPrepNow]

Is this a solution to a particular GMAT question? If so, what's the question?

Cheers,
Brent

[Haldiram Bhujiawala]

A+B+C+AB+BC+AC+ABC=100
A=B=C=0 (minimise the exactly 1 parameter)

So,

AB+BC+AC+ABC=100 (1)

Additionally,

70=A+AB+AC+ABC
75=B+AB+BC+ABC
80=C+AC+BC+ABC
A=B=C=0
------------------
225=2AB+2BC+2AC+3ABC (2)

We multiply the equation (1) x2 --> 2AB+2BC+2AC+2ABC=200 (3)
Subtract [(2)-(3)] and we DONE!

ABC = 25

Cheers

Haldi

[Matt@VeritasPrep]

I was wondering that myself!

Also, if A = B = C = 0, it's impossible for A+B+C+AB+BC+AC+ABC to equal 100. What is going on here?

Is this a solution to a particular GMAT question? If so, what's the question?

Cheers,
Brent

[GMATGuruNY]

I suspect that the OP is offering a solution to following problem:

According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?

A. 15%
B. 20%
C. 25%
D. 0%
E. 35%

To MINIMIZE the percentage who like all 3 fruits, we must MAXIMIZE the percentage who like 2 of the fruits.

Since A=70, the maximum value of BC= 30.
Since B=75, the maximum value of AC = 25.
Since C=80, the maximum value of AB= 20.

Thus:
The MAXIMUM percentage who like 2 of the fruits = 30+25+20 = 75.
Thus:
The MINIMUM percentage who like all 3 fruits = 100-75 = 25.

The correct answer is C.