If 75 percent of all Americans own an automobile, 15 percent of all Am

Question

If 75 percent of all Americans own an automobile, 15 percent of all Americans own a bicycle, and 20 percent of all Americans own neither an automobile nor a bicycle, what percent of Americans own both an automobile and a bicycle?

(A) 0%
(B) 1.33%
(C) 3.75%
(D) 5%
(E) 10%

(A) 0%
(B) 1.33%
(C) 3.75%
(D) 5%
(E) 10%

LHC8717 · Answer

Formula 100% = Neither + Bike + Auto - Both => 100% = 20% + 75% + 15% - Both => Both = 10% Answer E

ScottTargetTestPrep · Answer

We can let the total number of Americans = 100 and create the following equation:

100 = number who own an automobile + number who own a bike - number who own both + number who own neither

100 = 75 + 15 - b + 20

100 = 110 - b

b = 10

Answer: E

Abhishek009 · Answer

n(A) = 75 
 n(B) = 15

n(A U B)' = 20 , So n(A U B) = 80

Now,  n(A U B) = n(A) + n(B) - n ( A ∩ B )

Or,  80 = 75 + 15 - n ( A ∩ B )

So,  n ( A ∩ B ) = 90 - 80

Or,  n ( A ∩ B ) = 10

Thus, answer must be (E) 10

KrishnakumarKA1 · Answer

100 = 75 +15 -both +20

both = 10

Option E

fskilnik · Answer

? = x\,\%

Trivial application of the  simplifier  :

80 = 75 + 15 - x\,\,\,\,\, \Rightarrow \,\,\,? = 10\,\%

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

ArjunJag1328 · Answer

Let's assume the total population of America is 100 :D

Percentage of people using bicycle and automobile will be  10%

Please see the attached matrix method explanation.

Answer:  E

Thank you
Arjun

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If 75 percent of all Americans own an automobile, 15 percent of all Am

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If 75 percent of all Americans own an automobile, 15 percent of all Am

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