Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 May 2012
Posts: 95
Location: United Kingdom
WE: Account Management (Other)

According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
15 Oct 2012, 02:00
Question Stats:
42% (02:05) correct 58% (02:22) wrong based on 422 sessions
HideShow timer Statistics
According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three? A. 15% B. 20% C. 25% D. 0% E. 35%
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
In the study cave!




Math Expert
Joined: 02 Sep 2009
Posts: 49964

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
15 Oct 2012, 03:58
Skientist wrote: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15% B. 20% C. 25% D. 0% E. 35%
I'm really interested in a detailed explaination of how to approach this problem.
Thanks
Skientist First of all, let's simplify the question: say there are 100 people. So, we have that at least 70 people like apples, at least 75 like bananas and at least 80 like cherries. Since we want to minimize the group which likes all three, then let's minimize the groups which like each fruit: 80 people like cherries; 75 people like bananas; 70 people like apples. () 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries); () 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas). So, we can see that minimum 55 people like both cherries and bananas (11 dashes). To have minimum overlap of 3, let 20 people who don't like cherries and 25 who don't like bananas to like apples. So, we distributed 20+25=45 people who like apples and 7045=25 people still left to distribute. The only 25 people who can like apples are those who like both cherries and bananas. Consider the diagram below: () 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries); () 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas); () 70 people like apples and 30 don't (each green dash represents 5 people who like apples). Therefore the minimum number of people who like all three is 25. Answer: C (OA is not correct).
_________________
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: 26 Dec 2011
Posts: 1

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
15 Oct 2012, 05:47
I guess it can be solved a bit quicker. 30 people out of 100 don't like apples. As we must consider the worst case scenario, let's assume that 25 people who don't like bananas are among 70 who like apples. So, 7025=45. Also, let's assume that 20 people who don't like cherry is among these 45. So 4520=25. It is the worst case scenario and the minimum number of people who like all three fruits is 25.




Director
Joined: 22 Mar 2011
Posts: 601
WE: Science (Education)

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
15 Oct 2012, 08:28
Skientist wrote: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15% B. 20% C. 25% D. 0% E. 35%
I'm really interested in a detailed explaination of how to approach this problem.
Thanks
Skientist Let's consider 100 people and drop using %. Since we are looking for the minimum overlap, let's consider the case with exactly 70, 75 and 85. If the numbers are bigger, then the overlap between the three sets increases. Since 70 + 75 = 145 >100, at least 45 people like both A(pple) and B(anana). Again, we take the minimum overlap. It means that there are 70  45 = 25 who like A and not B, and 75  45 = 30 who like B and not A. If all these people like C(herries), then 80  (25 + 30) = 25, who are in neither of the above two categories, they must like all (A, B, and C). Those who like C, necessarily must be among those who like either A or B, because 70 + 75  45 = 100, are all the people. Answer 25  should be C and not B.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Intern
Joined: 30 May 2012
Posts: 19
Concentration: Finance, Strategy
GPA: 3.39

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
16 Jul 2013, 12:37
Skientist wrote: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15% B. 20% C. 25% D. 0% E. 35% To find the minimal intersection of the people who like apples and the people who like bananas, we need a number x such that 70+(75x)=100. x=45. The group of people who like both apples and bananas and the group of people who like cherries must intersect because 45+80 > 100. So we need a number y such that 45+(80y)=100. y=25. Answer is C.



Intern
Joined: 15 Jul 2013
Posts: 9

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
17 Jul 2013, 15:07
I got the right answer but not sure why it worked. I added up 80%+75%+70% = 225%. Thought of this in my head as a three level venn diagram, with 100% being the maximum. 225 is 125 above the maximum, so going to the first intersect level is 125, which is still above the maximum of 100, so going to the second and final intersect level is 25, which was my answer, and I have no idea if this was just luck.



Intern
Joined: 02 Feb 2012
Posts: 26
GPA: 4

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
17 Jul 2013, 20:34
Bunuel wrote: Skientist wrote: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15% B. 20% C. 25% D. 0% E. 35%
I'm really interested in a detailed explaination of how to approach this problem.
Thanks
Skientist First of all, let's simplify the question: say there are 100 people. So, we have that at least 70 people like apples, at least 75 like bananas and at least 80 like cherries. Since we want to minimize the group which likes all three, then let's minimize the groups which like each fruit: 80 people like cherries; 75 people like bananas; 70 people like apples. () 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries); () 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas). So, we can see that minimum 55 people like both cherries and bananas (11 dashes). To have minimum overlap of 3, let 20 people who don't like cherries and 25 who don't like bananas to like apples. So, we distributed 20+25=45 people who like apples and 7045=25 people still left to distribute. The only 25 people who can like apples are those who like both cherries and bananas. Consider the diagram below: () 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries); () 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas); () 70 people like apples and 30 don't (each green dash represents 5 people who like apples). Therefore the minimum number of people who like all three is 25. Answer: C (OA is not correct). Hi Bunuel, Can the explanation be given with a diagram.. I m still confused



Math Expert
Joined: 02 Sep 2009
Posts: 49964

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
17 Jul 2013, 22:33
avinashrao9 wrote: Bunuel wrote: Skientist wrote: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15% B. 20% C. 25% D. 0% E. 35%
I'm really interested in a detailed explaination of how to approach this problem.
Thanks
Skientist First of all, let's simplify the question: say there are 100 people. So, we have that at least 70 people like apples, at least 75 like bananas and at least 80 like cherries. Since we want to minimize the group which likes all three, then let's minimize the groups which like each fruit: 80 people like cherries; 75 people like bananas; 70 people like apples. () 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries); () 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas). So, we can see that minimum 55 people like both cherries and bananas (11 dashes). To have minimum overlap of 3, let 20 people who don't like cherries and 25 who don't like bananas to like apples. So, we distributed 20+25=45 people who like apples and 7045=25 people still left to distribute. The only 25 people who can like apples are those who like both cherries and bananas. Consider the diagram below: () 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries); () 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas); () 70 people like apples and 30 don't (each green dash represents 5 people who like apples). Therefore the minimum number of people who like all three is 25. Answer: C (OA is not correct). Hi Bunuel, Can the explanation be given with a diagram.. I m still confused It's a hard question (62% of the users got it wrong!), so I can understand that. We have a similar question on the site to which Karishma gave a venn diagram solution: inavillageof100households75haveatleastonedvd98257.html#p825632Hope it 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



Director
Joined: 17 Dec 2012
Posts: 634
Location: India

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
18 Jul 2013, 01:40
EvaJager wrote: Skientist wrote: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15% B. 20% C. 25% D. 0% E. 35%
I'm really interested in a detailed explaination of how to approach this problem.
Thanks
Skientist It seems to me the answer is D. Here's how: 1. Let us keep the number as 70, 75 and 80 to minimize the likes. 2. Number of people who like apples is formed by the people who like A only, who like both A and B only , who like both A and C only and who like A, B and C. This is what is equal to 70. i.e., A + AB+AC+ABC =70 3. Similarly B +AB+BC+ABC= 75 and C+AC+BC+ABC=80 4. Summing all the three we have A+B+C+2AB+2BC+2AC+3ABC=225 5. If A=0, B=5, C=10, AB=BC=CA=35, ABC can be 0. That is the minimum number of people who like all the 3 can be 0.
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



Math Expert
Joined: 02 Sep 2009
Posts: 49964

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
18 Jul 2013, 01:48
SravnaTestPrep wrote: EvaJager wrote: Skientist wrote: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15% B. 20% C. 25% D. 0% E. 35%
I'm really interested in a detailed explaination of how to approach this problem.
Thanks
Skientist It seems to me the answer is D. Here's how: 1. Let us keep the number as 70, 75 and 80 to minimize the likes. 2. Number of people who like apples is formed by the people who like A only, who like both A and B only , who like both A and C only and who like A, B and C. This is what is equal to 70. i.e., A + AB+AC+ABC =70 3. Similarly B +AB+BC+ABC= 75 and C+AC+BC+ABC=80 4. Summing all the three we have A+B+C+2AB+2BC+2AC+3ABC=225 5. If A=0, B=5, C=10, AB=BC=CA=35, ABC can be 0. That is the minimum number of people who like all the 3 can be 0. The correct answer is C, not D. In your case total = 3*35+10+5 = 120%.
_________________
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



Director
Joined: 17 Dec 2012
Posts: 634
Location: India

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
18 Jul 2013, 04:17
Quote: The correct answer is C, not D.
In your case total = 3*35+10+5 = 120%. OOPS! sorry about the oversight. There is actually a straightforward solution based on the line of reasoning in my previous post. 1. we have A+B+C+AB+BC+CA+ABC=100  (1) 2. We also have A+B+C+2AB+2BC+2CA+3ABC= 225  (2) Just plug in the values: ABC = 0 we have from (1) and (2) the impossibility AB+BC+CA=125 i.e., >100 for ABC=20 we have the impossibility AB+BC+CA +ABC=105 i.e., >100 similarly for ABC=15 Only for ABC=25 we have AB+BC+CA+ABC=100. It is easy to figure out the values and verify. Though for ABC=35, there is nothing contradictory, 25 is smaller and hence the solution.
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



Director
Joined: 17 Dec 2012
Posts: 634
Location: India

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
18 Jul 2013, 07:05
Here's another quick way to arrive at the solution: 1. A+B+C+AB+BC+CA+ABC=100  (1) 2. A+B+C+2AB+2BC+2CA+3ABC = 225  (2) (2) (1) > AB+BC+CA+2ABC = 125  (3) (3)  (1) > ABCABC = 25 (4) As A, B and C are >=0, the minimum value of ABC is 25. Therefore the number of people who like all the three is 25%.
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



VP
Joined: 07 Dec 2014
Posts: 1102

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
14 Apr 2016, 14:59
30% don't like apples + 25% don't like bananas + 20% don't like cherries = 75%=maximum % of people who don't like at least one fruit 100%75%=25%=minimum % of people who like all three fruits



Manager
Joined: 14 May 2014
Posts: 62
Location: India
GPA: 3.44

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
17 Apr 2016, 07:46
Bunuel wrote: Skientist wrote: According to a survey, at least 70% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
A. 15% B. 20% C. 25% D. 0% E. 35%
I'm really interested in a detailed explaination of how to approach this problem.
Thanks
Skientist First of all, let's simplify the question: say there are 100 people. So, we have that at least 70 people like apples, at least 75 like bananas and at least 80 like cherries. Since we want to minimize the group which likes all three, then let's minimize the groups which like each fruit: 80 people like cherries; 75 people like bananas; 70 people like apples. () 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries); () 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas). So, we can see that minimum 55 people like both cherries and bananas (11 dashes). To have minimum overlap of 3, let 20 people who don't like cherries and 25 who don't like bananas to like apples. So, we distributed 20+25=45 people who like apples and 7045=25 people still left to distribute. The only 25 people who can like apples are those who like both cherries and bananas. Consider the diagram below: () 80 people like cherries and 20 don't (each red dash represents 5 people who like cherries); () 75 people like bananas and 25 don't (each blue dash represents 5 people who like bananas); () 70 people like apples and 30 don't (each green dash represents 5 people who like apples). Therefore the minimum number of people who like all three is 25. Answer: C (OA is not correct). Brunel I have a second part of this question and want to ask if I am going right What is the max number of overlapping sets for all 3 selection My answer is 55. Am I right?



Manager
Joined: 16 Mar 2016
Posts: 129
Location: France
GPA: 3.25

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
23 Oct 2016, 06:06
apples 70% like 30% dislike bananas 75% like 25% dislike cherries 80% like 20% dislike
We want the minimum of people who like for all this fruits.
Imagine that all the people who dislike bananas like apple : 7025 = 45 idem for cherries, 45  20 = 25, answer choice C



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12639
Location: United States (CA)

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
07 Apr 2018, 11:15
Hi All, We're told that according to a survey, AT LEAST 70% of people like apples, AT LEAST 75% like bananas and AT LEAST 80% like cherries. We're asked for the MINIMUM percentage of people who like ALL THREE. For this type of question, you can draw pictures and/or do math. Your goal is to find a way to make the MINIMUM number occur... Here's how you can TEST VALUES. If there are 100 people, then we have 70 who like apples 75 who like bananas 80 who like cherries Clearly, some people have been counted in more than 1 category. Here's how to figure out the minimum number who like all 3.... There are 80 who like cherries; that means there are 20 who DON'T. Of the 75 who like bananas, we can say that 20 DON'T like cherries (this helps to minimize the number who like cherries AND bananas). Now we have: 55 who like cherries AND bananas 25 who like just cherries 20 who like just bananas Next, we factor in the apples. Of those 70 people, we can spread them around and maximize the number who like apples AND cherries OR apples and bananas, BUT NOT ALL 3. So, let's split the 70 into: 25 who like apples and cherries 20 who like apples and bananas That leave's 25 who MUST like cherries, bananas AND apples. 25/100 = 25% Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Intern
Joined: 16 Jun 2017
Posts: 14

Re: According to a survey, at least 70% of people like apples
[#permalink]
Show Tags
07 Apr 2018, 23:08
Attachment:
graphpapergraphpapertemplategraphpapera4graphpaperprintableFavim.com4736346.jpeg [ 107.02 KiB  Viewed 2409 times ]
I was able to solve this pretty much instantly by just picturing this is my head. The green representing apples, yellow for bananas, and red for cherries. The minimum overlap of the 3 is solid.
Attachments
solution.jpeg [ 107.02 KiB  Viewed 2403 times ]




Re: According to a survey, at least 70% of people like apples &nbs
[#permalink]
07 Apr 2018, 23:08






