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

This topic has expert replies
User avatar
Master | Next Rank: 500 Posts
Posts: 421
Joined: 17 Apr 2011
Location: India
Thanked: 6 times
Followed by:2 members
GMAT Score:620
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

User avatar
Legendary Member
Posts: 2663
Joined: 14 Jan 2015
Location: Boston, MA
Thanked: 1153 times
Followed by:128 members
GMAT Score:770

by [email protected] » Tue Mar 13, 2018 9:48 am
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

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: 23 Jun 2013
Location: Palo Alto, CA
Thanked: 2867 times
Followed by:508 members
GMAT Score:800

by [email protected] » Tue Mar 13, 2018 6:49 pm
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 [email protected]
Image

User avatar
Master | Next Rank: 500 Posts
Posts: 421
Joined: 17 Apr 2011
Location: India
Thanked: 6 times
Followed by:2 members
GMAT Score:620
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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 6362
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:26 members

by [email protected] » Sun Jun 02, 2019 4:24 pm
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
[email protected]

Image

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

ImageImage