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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## When a dentist surveyed her 250 patients, 82% reported that tagged by: vinni.k ##### This topic has 3 expert replies and 1 member reply ## When a dentist surveyed her 250 patients, 82% reported that 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 dentistâ€™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) âˆ- 250 = 15 patients neither brushed nor flossed that day. Or any alternate approach, then please let me know Thanks ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 Top Reply 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 dentistâ€™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) âˆ- 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

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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

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

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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

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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 dentistâ€™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.

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