• NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    NEW! FREE Beat The GMAT Quizzes
    Hundreds of Questions Highly Detailed Reporting Expert Explanations TAKE A FREE GMAT QUIZ
  • 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

When a dentist surveyed her 250 patients, 82% reported that

This topic has 3 expert replies and 1 member reply

When a dentist surveyed her 250 patients, 82% reported that

Post
When a dentist surveyed her 250 patients, 82% reported that they had brushed their teeth that day, 64% reported that they had flossed that day, and 52% reported that they had done both that day. How many of the dentist’s patients reported that they had neither brushed nor flossed that day?

A. 15
B. 16
C. 18
D. 21
E. 24

OA is A

What is the purpose of this question ? It seems more like a time consuming question so that i get less time for another question.
My approach:-
I create a set matrix table and got the answer. However, i have found another approach which is a bit quick but is it correct approach ?

Please let me know.

Percentage of patients done both is -
82 + 64 - 52 = 94

Thus, only 6% of the patients did not brush/flossed

So, (6/100) - 250 = 15 patients neither brushed nor flossed that day.

Or any alternate approach, then please let me know

Thanks

  • +1 Upvote Post
  • Quote
  • Flag

GMAT/MBA Expert

Legendary Member
Joined
14 Jan 2015
Posted:
2667 messages
Followed by:
122 members
Upvotes:
1153
GMAT Score:
770
Top Reply
Post
vinni.k wrote:
When a dentist surveyed her 250 patients, 82% reported that they had brushed their teeth that day, 64% reported that they had flossed that day, and 52% reported that they had done both that day. How many of the dentist’s patients reported that they had neither brushed nor flossed that day?

A. 15
B. 16
C. 18
D. 21
E. 24

OA is A

What is the purpose of this question ? It seems more like a time consuming question so that i get less time for another question.
My approach:-
I create a set matrix table and got the answer. However, i have found another approach which is a bit quick but is it correct approach ?

Please let me know.

Percentage of patients done both is -
82 + 64 - 52 = 94

Thus, only 6% of the patients did not brush/flossed

So, (6/100) - 250 = 15 patients neither brushed nor flossed that day.

Or any alternate approach, then please let me know

Thanks
Just be careful about what your calculations represent. For example, when you did 82 + 64 - 52, you correctly calculated the percentage of patients who had done at least one of the two types of cleaning, not the percentage who had done both kinds. (That's given to us.) Given your subsequent calculation, it seems as though you understood this. Valid approach.

(And 18% of this dentist's patients hadn't brushed their teeth that day at all? Makes you wonder about the quality of care/instruction they're receiving.)

_________________
Veritas Prep | GMAT Instructor

Veritas Prep Reviews
Save $100 off any live Veritas Prep GMAT Course

  • +1 Upvote Post
  • Quote
  • Flag
Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now!

GMAT/MBA Expert

Elite Legendary Member
Joined
23 Jun 2013
Posted:
10197 messages
Followed by:
496 members
Upvotes:
2867
GMAT Score:
800
Most Active Expert
Top Reply
Post
Hi vinni.k,

We're told that a dentist surveyed her 250 patients and the following results were reported: 82% reported that they had brushed their teeth that day, 64% reported that they had flossed that day, and 52% reported that they had done both that day. We're asked for the number of patients who reported that they had NEITHER brushed NOR flossed that day. This is an example of a standard Overlapping Sets question (although we will have to do a little extra math involving the percents relative to the 250 person total). We can solve it in a couple of different ways (including with the Overlapping Sets Formula):

Total = (Group 1) + (Group 2) - (Both) + (Neither)

In this prompt, Group 1 is the group that brushed their teeth and Group 2 is the group that had flossed...

100% = (82%) + (64%) - (52%) + (Neither)
100% = 94% + (Neither)
6% = Neither

The 'Neither' group is 6% of the 250 person total = = (.06)(250) = 15

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

_________________
Contact Rich at Rich.C@empowergmat.com

  • +1 Upvote Post
  • Quote
  • Flag
Master | Next Rank: 500 Posts
Joined
17 Apr 2011
Posted:
421 messages
Followed by:
2 members
Upvotes:
6
Test Date:
2016
Target GMAT Score:
700+
GMAT Score:
620
Post
Rich,

Thanks for your reply. I think it is a very good approach. I tried in the following question, and it worked.
Here's the question and the explanation.

600 residents were surveyed about whether they liked 3 different candidates running for certain offices in their town. 35% of those surveyed liked candidate A, 40% liked candidate B, and 50% liked candidate C. If all residents liked at least one of three candidates and 18% liked exactly 2 of the three candidates, then how many of the residents liked all three of the candidates?

A. 150
B. 108
C. 42
D. 21
E. 7

Approach
100 = 35 + 40 + 50 - 18 - 2x + 0
x = 3.5%
Now 3.5% of 600 = 21

Thanks

  • +1 Upvote Post
  • Quote
  • Flag
Post
vinni.k wrote:
When a dentist surveyed her 250 patients, 82% reported that they had brushed their teeth that day, 64% reported that they had flossed that day, and 52% reported that they had done both that day. How many of the dentist’s patients reported that they had neither brushed nor flossed that day?

A. 15
B. 16
C. 18
D. 21
E. 24

We can create the equation:

Total = #brushed + #flossed - #both + #neither

Keeping everything in percents, we have:

100 = 82 + 64 - 52 + n

100 = 94 + n

6 = n

So 6% or 0.06 x 250 = 15 of the patients neither brushed nor flossed.

Answer: A

_________________

Scott Woodbury-Stewart
Founder and CEO
scott@targettestprep.com



See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

  • +1 Upvote Post
  • Quote
  • Flag
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep

Top First Responders*

1 Ian Stewart 50 first replies
2 Brent@GMATPrepNow 37 first replies
3 Jay@ManhattanReview 33 first replies
4 GMATGuruNY 29 first replies
5 ceilidh.erickson 14 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description Scott@TargetTestPrep

Target Test Prep

209 posts
2 image description Max@Math Revolution

Math Revolution

92 posts
3 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

79 posts
4 image description Ian Stewart

GMATiX Teacher

57 posts
5 image description GMATGuruNY

The Princeton Review Teacher

49 posts
See More Top Beat The GMAT Experts