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

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New post 14 Mar 2017, 09:52
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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%

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Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

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New post 14 Mar 2017, 15:39
Formula 100% = Neither + Bike + Auto - Both => 100% = 20% + 75% + 15% - Both => Both = 10% Answer E
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Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

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New post 20 Mar 2017, 06:52
SajjadAhmad wrote:
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%


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
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Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

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New post 20 Mar 2017, 10:40
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SajjadAhmad wrote:
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%


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

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

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
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Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

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New post 21 Mar 2017, 03:51
SajjadAhmad wrote:
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%



100 = 75 +15 -both +20

both = 10

Option E
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Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

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New post 16 Sep 2018, 13:25
SajjadAhmad wrote:
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%


\(? = x\,\%\)

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.
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If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

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New post 17 Sep 2018, 00:02
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   [#permalink] 17 Sep 2018, 00:02
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