GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 26 May 2019, 11:20

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Senior RC Moderator
Status: Preparing GMAT
Joined: 02 Nov 2016
Posts: 2751
Location: Pakistan
GPA: 3.39
If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

### Show Tags

14 Mar 2017, 09:52
00:00

Difficulty:

5% (low)

Question Stats:

88% (01:21) correct 12% (01:42) wrong based on 59 sessions

### HideShow timer Statistics

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%

_________________
New Project RC Butler 2019 - Practice 2 RC Passages Everyday
Final days of the GMAT Exam? => All GMAT Flashcards.
This Post Helps = Press +1 Kudos
Best of Luck on the GMAT!!
Manager
Joined: 25 Nov 2016
Posts: 53
Location: Switzerland
GPA: 3
Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

### Show Tags

14 Mar 2017, 15:39
Formula 100% = Neither + Bike + Auto - Both => 100% = 20% + 75% + 15% - Both => Both = 10% Answer E
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6241
Location: United States (CA)
Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

### Show Tags

20 Mar 2017, 06:52
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

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4488
Location: India
GPA: 3.5
Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

### Show Tags

20 Mar 2017, 10:40
1
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
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Director
Status: Come! Fall in Love with Learning!
Joined: 05 Jan 2017
Posts: 542
Location: India
Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

### Show Tags

21 Mar 2017, 03:51
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
_________________
GMAT Mentors
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

### Show Tags

16 Sep 2018, 13:25
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.
Attachments

16Set18_6q.gif [ 8.37 KiB | Viewed 474 times ]

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
Manager
Joined: 24 Dec 2017
Posts: 192
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
If 75 percent of all Americans own an automobile, 15 percent of all Am  [#permalink]

### Show Tags

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.

Thank you
Arjun
Attachments

Automobile & Bicycle question.xlsx [26.91 KiB]

If 75 percent of all Americans own an automobile, 15 percent of all Am   [#permalink] 17 Sep 2018, 00:02
Display posts from previous: Sort by