Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 24 Jan 2012
Posts: 9

A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
26 Sep 2013, 08:27
Question Stats:
60% (01:40) correct 40% (01:40) wrong based on 1078 sessions
HideShow timer Statistics
A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are summarized as below 48 like Pizza 45 like Hoagies 58 like tacos 28 like pizza and hoagies 37 like hoagies and tacos 40 like pizza and tacos 25 like all three food What is the number of students who like none or only one of the foods ? A. 4 B. 16 C. 17 D. 20 E. 23 I got this one right but I spent a lot of time playing with numbers. Can someone please show a faster way.
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 49303

A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
28 Sep 2013, 04:35
violetsplash wrote: A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are summarized as below
48 like Pizza 45 like Hoagies 58 like tacos 28 like pizza and hoagies 37 like hoagies and tacos 40 like pizza and tacos 25 like all three food
What is the number of students who like none or only one of the foods ?
A. 4 B. 16 C. 17 D. 20 E. 23
I got this one right but I spent a lot of time playing with numbers. Can someone please show a faster way. \(Total = A + B + C  (sum \ of \ 2group \ overlaps) + (all \ three) + Neither\). 75 = 48 + 45 + 58  (28 + 37 + 40) + 25 + Neither > Neither = 4. Only Pizza = P  (P and H + P and T  All 3) = 48  (28 + 40  25) = 5; Only Hoagies = H  (P and H + H and T  All 3) = 45  (28 + 37  25) = 5; Only Tacos = T  (P and T + H and T  All 3) = 58  (40 + 37  25) = 6. The number of students who like none or only one of the foods = 4 + (5 + 5 + 6) = 20. Answer: D. For more check ADVANCED OVERLAPPING SETS PROBLEMS: advancedoverlappingsetsproblems144260.htmlHope this helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 24 Jan 2012
Posts: 9

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
27 Sep 2013, 20:30
violetsplash wrote: A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are summarized as below
48 like Pizza 45 like Hoagies 58 like tacos 28 like pizza and hoagies 37 like hoagies and tacos 40 like pizza and tacos 25 like all three food
What is the number of students who like none or only one of the foods ?
A. 4 B. 16 C. 17 D. 20 E. 23
I got this one right but I spent a lot of time playing with numbers. Can someone please show a faster way. I have edited the question. The total number of students was missing. After that I could solve it as well. The updated solution is attached.
Attachments
Solution.jpg [ 81.28 KiB  Viewed 54384 times ]




Manager
Status: How easy it is?
Joined: 09 Nov 2012
Posts: 105
Location: India
Concentration: Operations, General Management
GMAT 1: 650 Q50 V27 GMAT 2: 710 Q49 V37
GPA: 3.5
WE: Operations (Other)

A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
29 Sep 2014, 12:23
Bunuel / VeritasPrepKarishma, is there a simpler method similar to the table method used for such problems? This appeared in the first 10 questions of my test and I was stumped by the numbers involved.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
30 Sep 2014, 08:58
nitin6305 wrote: Is there a simpler method similar to the table method used for such problems? This appeared in the first 10 questions of my test and I was stumped by the numbers involved. Make a Venn diagram. The toughest of sets questions can be done easily through venn diagrams because you can visualize easily. Draw three overlapping circles (as shown by Bunuel in his post above). Mark set A as Pizzas, set B as Hoagies and set C as Tacos. The part where all three overlap (g in the diagram), mark that as 25. 28 like pizza and hoagies. 25 like all three so 3 like only pizzas and hoagies. Mark d as 3. 37 like hoagies and tacos. 25 like all three so 12 like only hoagies and tacos. Mark f as 12. 40 like pizza and tacos. 25 like all three so 15 like only pizza and tacos. Mark e as 15. From 75, subtract d, e, f and g. This will give the number of students lying in a, b, c and None. This is exactly what we want. 75  3  12  15  25 = 20
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 03 Jul 2014
Posts: 16

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
23 Nov 2014, 12:06
This one is tricky and lengthy , I guess it doesnt end there in Knowing your Formula 1 and Formula 2 :D ..... I tried solving this and then I got stuck again solving for exactly 1 like . Though it was preety straight forward for solving Neither . Also I recognize something , for the same problem I can also number of people who like exactly 2 like using Total = A+B+C  ( Exactly 2 like AB+BC+CA)  2 ABC +Neither. Hence 75 = 151  Exactly 2 like  2 (25) + 4 Exactly 2 like =26 . Correct me if I am missing something .I guess though its the right approach . Also for this we need to primarily work 1st step Using Formula 1 to find Neither . Then only its possible . Suggest me if there is any other approach Thanks. Bunuel wrote: violetsplash wrote: A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are summarized as below
48 like Pizza 45 like Hoagies 58 like tacos 28 like pizza and hoagies 37 like hoagies and tacos 40 like pizza and tacos 25 like all three food
What is the number of students who like none or only one of the foods ?
A. 4 B. 16 C. 17 D. 20 E. 23
I got this one right but I spent a lot of time playing with numbers. Can someone please show a faster way. \(Total = A + B + C  (sum \ of \ 2group \ overlaps) + (all \ three) + Neither\). 75 = 48 + 45 + 58  (28 + 37 + 40) + 25 + Neither > Neither = 4. Only Pizza = P  (P and H + P and T  All 3) = 48  (28 + 40  25) = 5; Only Hoagies = H  (P and H + H and T  All 3) = 45  (28 + 37  25) = 5; Only Tacos = T  (P and T + H and T  All 3) = 58  (40 + 37  25) = 5. The number of students who like none or only one of the foods = 4 + (5 + 5 + 6) = 20. Answer: D. For more check ADVANCED OVERLAPPING SETS PROBLEMS: advancedoverlappingsetsproblems144260.htmlHope this helps.



Intern
Joined: 03 Jul 2014
Posts: 16

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
23 Nov 2014, 12:23
How are we assuming about the neither part to be . I mean when we are subtracting (All three) from each of the (2 like region ) we assume that its part of the bigger a , b and c . I mean suppose we try solving for Exactly two like using the approach above then we have , All 2 like = (2825)= 3 ; (3725)=12 ; (4025)=15 ; Therefore 3+12+15=30 .....But I guess its wrong as I am missing out on the Neither Part. Now If I consider the approach used by Bruneal then I know that Neither =4 ; so Exactly liking 2 items would be 304=26 . Please correct me if I am wrong , also what approach should I take for Neither. VeritasPrepKarishma wrote: nitin6305 wrote: Is there a simpler method similar to the table method used for such problems? This appeared in the first 10 questions of my test and I was stumped by the numbers involved. Make a Venn diagram. The toughest of sets questions can be done easily through venn diagrams because you can visualize easily. Draw three overlapping circles (as shown by Bunuel in his post above). Mark set A as Pizzas, set B as Hoagies and set C as Tacos. The part where all three overlap (g in the diagram), mark that as 25. 28 like pizza and hoagies. 25 like all three so 3 like only pizzas and hoagies. Mark d as 3. 37 like hoagies and tacos. 25 like all three so 12 like only hoagies and tacos. Mark f as 12. 40 like pizza and tacos. 25 like all three so 15 like only pizza and tacos. Mark e as 15. From 75, subtract d, e, f and g. This will give the number of students lying in a, b, c and None. This is exactly what we want. 75  3  12  15  25 = 20



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
23 Nov 2014, 20:39
hanschris5 wrote: How are we assuming about the neither part to be . I mean when we are subtracting (All three) from each of the (2 like region )
we assume that its part of the bigger a , b and c .
I mean suppose we try solving for Exactly two like using the approach above then we have ,
All 2 like = (2825)= 3 ; (3725)=12 ; (4025)=15 ; Therefore 3+12+15=30 .....But I guess its wrong as I am missing out on the Neither Part.
Now If I consider the approach used by Bruneal then I know that Neither =4 ; so Exactly liking 2 items would be 304=26 .
Please correct me if I am wrong , also what approach should I take for Neither.
The question asks you the sum of 'None' and 'Only 1' i.e. it asks you 'None + Only 1' (irrespective of how many are in None and how many are in Only 1). You just need the sum. You have that the total number of students = 75 75 = None + Only 1 + Only 2 + All 3 To get 'None + Only 1', all you need to do is subtract 'Only 2' and 'All 3' from 75. 'Only 2' =3 + 12 + 15 = 30 (as correctly calculated by you. It does not include 'None') 'All 3' = 25 So None + Only 1 = 75  30  25 = 20
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT selfstudy has never been more personalized or more fun. Try ORION Free!



Intern
Joined: 12 Aug 2014
Posts: 11
Location: United States
Concentration: Strategy, General Management
GMAT 1: 710 Q50 V35 GMAT 2: 720 Q49 V40
WE: Other (Consulting)

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
25 Dec 2014, 05:00
There's a faster way of doing it. Let x= total with 3 foods Total with with 2 foods only => (37x) + (28x) + (40x) = 1053x= 30 Total with 3 = x = 25
Total 0 and 1 = Total  (Total 2 and Total 3) = 75  30  25 = 20



Manager
Status: PLAY HARD OR GO HOME
Joined: 25 Feb 2014
Posts: 153
Location: India
Concentration: General Management, Finance
GPA: 3.1

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
12 Feb 2015, 07:20
Dear Bunuel, I think in your solution, you intended to use the second formula from the gmatclub mathbook,but wrote the first formula.
_________________
ITS NOT OVER , UNTIL I WIN ! I CAN, AND I WILL .PERIOD.



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
12 Feb 2015, 07:33



Intern
Joined: 02 Jan 2015
Posts: 32
GMAT Date: 02082015
GPA: 3.7
WE: Management Consulting (Consulting)

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
03 Jul 2015, 04:08
I'd appreciate further clarification on why we use the version of the formula where we add back in the 'all' category? I'm not sure why we are able to assume that the 'all' category also includes numbers from the 'two items' sections? Thanks



Math Expert
Joined: 02 Sep 2009
Posts: 49303

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
03 Jul 2015, 04:11



Director
Status: Professional GMAT Tutor
Affiliations: AB, cum laude, Harvard University (Class of '02)
Joined: 10 Jul 2015
Posts: 669
Location: United States (CA)
Age: 38
GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42
WE: Education (Education)

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
03 Jun 2016, 10:15
When you draw the Venn diagram, I suggest starting with the "triple overlap" number of 25 and working your way out from there. Don't forget to adjust the numbers as you go. Attached is a visual that should help.
Attachments
Screen Shot 20160603 at 10.14.20 AM.png [ 112.84 KiB  Viewed 31845 times ]
_________________
Harvard grad and 99% GMAT scorer, offering expert, private GMAT tutoring and coaching, both inperson (San Diego, CA, USA) and online worldwide, since 2002.
One of the only known humans to have taken the GMAT 5 times and scored in the 700s every time (700, 710, 730, 750, 770), including verified section scores of Q50 / V47, as well as personal bests of 8/8 IR (2 times), 6/6 AWA (4 times), 50/51Q and 48/51V (1 question wrong).
You can download my official testtaker score report (all scores within the last 5 years) directly from the Pearson Vue website: https://tinyurl.com/y94hlarr Date of Birth: 09 December 1979.
GMAT Action Plan and Free EBook  McElroy Tutoring
Contact: mcelroy@post.harvard.edu



Director
Joined: 12 Nov 2016
Posts: 759
Location: United States
GPA: 2.66

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
12 Oct 2017, 19:16
violetsplash wrote: A survey was conducted to determine the popularity of 3 foods among students. The data collected from 75 students are summarized as below
48 like Pizza 45 like Hoagies 58 like tacos 28 like pizza and hoagies 37 like hoagies and tacos 40 like pizza and tacos 25 like all three food
What is the number of students who like none or only one of the foods ?
A. 4 B. 16 C. 17 D. 20 E. 23
I got this one right but I spent a lot of time playing with numbers. Can someone please show a faster way. The thing that's important to remember with this time of problem is that it says "37 like hoagies and tacos" not "37 like only hoagies and tacos" > knowing this we can apply the first of 2 formulas used for 3 overlapping sets total= A + B + C  [sum of 2] + [all three] + neither 75= 71 + x Neither= 4 Work in reverse to find the number of exactly 2 D



Senior Manager
Joined: 12 Feb 2015
Posts: 432

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
20 Jul 2018, 10:54
The question could be solved in two parts: 1) First 75 minus the number contained in union of the three sets will give the number of students who like none of the foods.(i.e. 7571=4) 2) In second part, number of students who like only one of the foods = (7155=16) Total = 4+16 = 20 Option D is the correct answer.
_________________
"Please hit +1 Kudos if you like this post"
_________________ Manish
"Only I can change my life. No one can do it for me"



Manager
Joined: 31 Jul 2017
Posts: 126
Location: Tajikistan
Concentration: Finance, Economics
GPA: 3.85
WE: Accounting (Investment Banking)

Re: A survey was conducted to determine the popularity of 3 food
[#permalink]
Show Tags
01 Sep 2018, 23:39
CAMANISHPARMAR wrote: The question could be solved in two parts:
1) First 75 minus the number contained in union of the three sets will give the number of students who like none of the foods.(i.e. 7571=4) 2) In second part, number of students who like only one of the foods = (7155=16)
Total = 4+16 = 20
Option D is the correct answer. CAMANISHPARMAR, how do you find 4 from first part (or 71)?




Re: A survey was conducted to determine the popularity of 3 food &nbs
[#permalink]
01 Sep 2018, 23:39






