Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 09 Feb 2013
Posts: 121

A company conducted a survey about its two brands, A and B. [#permalink]
Show Tags
25 Feb 2013, 02:25
2
This post received KUDOS
2
This post was BOOKMARKED
Question Stats:
65% (03:08) correct
35% (02:17) wrong based on 161 sessions
HideShow timer Statistics
A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company? A. 46 B. 80 C. 90 D. 100 E. 200
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Kudos will encourage many others, like me. Good Questions also deserve few KUDOS.
Last edited by Bunuel on 26 Feb 2013, 01:43, edited 1 time in total.
Edited the question.



Moderator
Joined: 02 Jul 2012
Posts: 1223
Location: India
Concentration: Strategy
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: A company conducted a survey about its two brands, A and B [#permalink]
Show Tags
25 Feb 2013, 02:39
2
This post received KUDOS
emmak wrote: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company?
46
80
90
100
200 100 = x + x  20 + 23  23 x = 60, So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23% 23% of the total no. of people should be an integer. So, A,B & C are out. 60% of D and 40% of D are both integers. So, D satisfies all conditions. So, answer is D.
_________________
Did you find this post helpful?... Please let me know through the Kudos button.
Thanks To The Almighty  My GMAT Debrief
GMAT Reading Comprehension: 7 Most Common Passage Types



Intern
Joined: 08 Nov 2012
Posts: 8

Re: A company conducted a survey about its two brands, A and B [#permalink]
Show Tags
25 Feb 2013, 03:46
1
This post received KUDOS
MacFauz wrote: emmak wrote: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company?
46
80
90
100
200 100 = x + x  20 + 23  23 x = 60, So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23% 23% of the total no. of people should be an integer. So, A,B & C are out. 60% of D and 40% of D are both integers. So, D satisfies all conditions. So, answer is D. Even if it does not affect the result and the reasoning, in this case, I believe that the sentence is not completely clear because it should clarify if:  x contains people who likes ONLY A, or not;  (x  20) contains people who likes only B, or not. The result in this case is not affected (D in both cases), but the computation of x and x20 is. Patrizio



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: A company conducted a survey about its two brands, A and B [#permalink]
Show Tags
26 Feb 2013, 01:41
Patrizio wrote: MacFauz wrote: emmak wrote: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company?
46
80
90
100
200 100 = x + x  20 + 23  23 x = 60, So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23% 23% of the total no. of people should be an integer. So, A,B & C are out. 60% of D and 40% of D are both integers. So, D satisfies all conditions. So, answer is D. Even if it does not affect the result and the reasoning, in this case, I believe that the sentence is not completely clear because it should clarify if:  x contains people who likes ONLY A, or not;  (x  20) contains people who likes only B, or not. The result in this case is not affected (D in both cases), but the computation of x and x20 is. Patrizio x percent of respondents liked product A means that x% contains those who also liked product B. No further clarification is needed here. Otherwise it would be written: x percent of respondents liked ONLY product A. Hope it's clear.
_________________
New to the Math Forum? Please read this: 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: 20 Feb 2013
Posts: 20

Re: A company conducted a survey about its two brands, A and B. [#permalink]
Show Tags
26 Feb 2013, 02:12
AUB = 100 – 23 = 77 % = A + B – A and B 77 = x + x – 20 – 23 X = 60 A – 40 B – 60 Both – 23 Now the only key is that number of people cannot be fraction. All the percentages are integers for option D. Hence answer is D.
_________________
Pushpinder Gill



Intern
Joined: 20 Feb 2013
Posts: 20

Re: A company conducted a survey about its two brands, A and B. [#permalink]
Show Tags
26 Feb 2013, 03:33
vinaymimani wrote: emmak wrote: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company?
A. 46 B. 80 C. 90 D. 100 E. 200 This question doesn't require us to calculate the value of x also. We know that 23 % of something(the number of people) has to be an integer. Thus, as 23 is prime, the "something" should be a multiple of 100. Now to minimize this "something" we can only choose 100. D. What if the value of x is 23.5% then 100 would also not suffice. So you need to calculate all the values to make sure that you don't get an integer.
_________________
Pushpinder Gill



Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 629

Re: A company conducted a survey about its two brands, A and B. [#permalink]
Show Tags
26 Feb 2013, 03:40
Pushpinder wrote: vinaymimani wrote: emmak wrote: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company?
A. 46 B. 80 C. 90 D. 100 E. 200 This question doesn't require us to calculate the value of x also. We know that 23 % of something(the number of people) has to be an integer. Thus, as 23 is prime, the "something" should be a multiple of 100. Now to minimize this "something" we can only choose 100. D. What if the value of x is 23.5% then 100 would also not suffice. So you need to calculate all the values to make sure that you don't get an integer. true. agreed. oversight from my end.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



Intern
Joined: 16 Feb 2012
Posts: 27
GPA: 3.57

Re: A company conducted a survey about its two brands, A and B [#permalink]
Show Tags
27 Feb 2013, 13:24
MacFauz wrote: emmak wrote: A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company?
46
80
90
100
200 100 = x + x  20 + 23  23 x = 60, So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23% 23% of the total no. of people should be an integer. So, A,B & C are out. 60% of D and 40% of D are both integers. So, D satisfies all conditions. So, answer is D. 200 also satisfies the condition, but why do you prefer D. Since, 23%, 40% and 60% of 200 is some integer.



Intern
Joined: 06 Feb 2013
Posts: 23

Re: A company conducted a survey about its two brands, A and B [#permalink]
Show Tags
27 Feb 2013, 14:35
Quote: 100 = x + x  20 + 23  23
Hi, could you please clarify the formula? why do you subtract 23? thanks



Intern
Joined: 06 Feb 2013
Posts: 23

Re: A company conducted a survey about its two brands, A and B [#permalink]
Show Tags
28 Feb 2013, 08:17
vinaymimani wrote: Because it mentions to find out the MINIMUM number of people surveyed. sorry, still don't get it is there a formula you are referring to when finding a minimum? thanks



Veritas Prep GMAT Instructor
Joined: 11 Dec 2012
Posts: 313

Re: A company conducted a survey about its two brands, A and B [#permalink]
Show Tags
28 Feb 2013, 09:33
LinaNY wrote: vinaymimani wrote: Because it mentions to find out the MINIMUM number of people surveyed. sorry, still don't get it is there a formula you are referring to when finding a minimum? thanks Hi LinaNY, there's no formula for finding minimum. The formula used above is: Total = Set X + Set Y  Both + Neither 100 = x + (x20)  23 + 23 Since 23 is a prime number, the total cannot be less than 100 and keep it as an integer. Your only two options are 100 and 200. Which one is the minimum? The smaller one. 200 works as well, you'd have 120 people who like X, 80 who like Y, 46 who like both and 46 who like neither. But you can get smaller than this, much like 2/4 can be reduced to 1/2. This yields 60 people who like X, 40 who like Y, 23 who like both and 23 who like neither. Must be D if you want the minimum. Hope this helps Ron
_________________
Ron Awad Veritas Prep  GMAT Instructor Save $100 on Veritas Prep GMAT Courses and Admissions Consulting Services Veritas Prep Reviews



Intern
Joined: 06 Feb 2013
Posts: 23

Re: A company conducted a survey about its two brands, A and B [#permalink]
Show Tags
28 Feb 2013, 10:57
VeritasPrepRon wrote: Since 23 is a prime number, the total cannot be less than 100 and keep it as an integer. Your only two options are 100 and 200. Which one is the minimum? The smaller one.
Thank you very much, Ron. It totally makes sense now.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16026

Re: A company conducted a survey about its two brands, A and B. [#permalink]
Show Tags
19 Jun 2014, 08:18
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Current Student
Joined: 03 Jul 2013
Posts: 95

A company conducted a survey about its two brands [#permalink]
Show Tags
04 Oct 2014, 01:16
A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number of people surveyed by the company? 1)46 2)80 3)90 4)100 5)200
_________________
Sometimes standing still can be, the best move you ever make......



Math Expert
Joined: 02 Sep 2009
Posts: 39753

Re: A company conducted a survey about its two brands, A and B. [#permalink]
Show Tags
04 Oct 2014, 04:12




Re: A company conducted a survey about its two brands, A and B.
[#permalink]
04 Oct 2014, 04:12







