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!
Fast Solution
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Is this a solution to a particular GMAT question? If so, what's the question?
Cheers,
Brent
Cheers,
Brent
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ABC = 25infamousshorty wrote: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!
Cheers
Haldi
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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?
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?
Brent@GMATPrepNow wrote:Is this a solution to a particular GMAT question? If so, what's the question?
Cheers,
Brent
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I suspect that the OP is offering a solution to following problem:
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.
To MINIMIZE the percentage who like all 3 fruits, we must MAXIMIZE the percentage who like 2 of the fruits.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%
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.
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3