Last visit was: 15 Jul 2024, 01:24 It is currently 15 Jul 2024, 01:24
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640906 [72]
Given Kudos: 85011
Send PM
Most Helpful Reply
User avatar
Senior Manager
Senior Manager
Joined: 15 Sep 2011
Posts: 256
Own Kudos [?]: 1377 [17]
Given Kudos: 46
Location: United States
WE:Corporate Finance (Manufacturing)
Send PM
Director
Director
Joined: 21 May 2013
Posts: 539
Own Kudos [?]: 231 [12]
Given Kudos: 608
Send PM
General Discussion
Intern
Intern
Joined: 28 May 2013
Posts: 14
Own Kudos [?]: 28 [9]
Given Kudos: 18
Schools: Mannheim"17
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
6
Kudos
3
Bookmarks
consider total 100 people.
we minimize the of people who solved only X puzzle and the of people who solved only Y. This would maximize # people who solved both.
So, X min will be (100-89) =11...(89 is #people solving Y)
Y min will be (100-79) = 21...(79 is #people solving X)

Thus, Xmin + Ymin = 32. Thus XY min(#people solving both)= 100-32, i.e 68 or 68%.


Also, to maximize the number of people solving both, we need to find # people with maximum overlap.
i.e 79 people can be the # people solving X and both. In other words, none of the people solved only X. Then, we have Xonly=0, XY=79, X=79, Y=89, Yonly= 100-79, i.e 21.

Thus, we have XY max =79%

Answer:D

Tx
Kindly correct me if it's wrong.
User avatar
Manager
Manager
Joined: 10 May 2014
Posts: 116
Own Kudos [?]: 342 [2]
Given Kudos: 28
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
1
Kudos
1
Bookmarks
Overlapping Sets formulas
Formula 1: Total = X total + Y total - Both + Neither
Formula 2: Total = X only + Y only + Both + Neither

You are given that
100 = 79 + 89 - Both + Neither


Maximum "Both"
Total = X only + Y only + Both + Neither
100 = 0 + 79 + 10 + 11

Minimum "Both"
Total = X only + Y only + Both + Neither
100 = 11 + 68 + 21 + 0

Hence, option D (79, 68)
Manager
Manager
Joined: 14 Mar 2014
Posts: 135
Own Kudos [?]: 450 [4]
Given Kudos: 124
GMAT 1: 710 Q50 V34
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
4
Kudos
Bunuel wrote:
A group of people were given 2 puzzles. 79% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?

(A) 11%, 0%
(B) 49%, 33%
(C) 68%, 57%
(D) 79%, 68%
(E) 89%, 79%

Kudos for a correct solution.


IMO : D

Max Overlap we can obtain from two values i.e. 79 and 89 will be 79.
Only Option D has Max = 79.
Thus We need not calculate the min. value
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640906 [2]
Given Kudos: 85011
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
2
Kudos
Expert Reply
Bunuel wrote:
A group of people were given 2 puzzles. 79% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?

(A) 11%, 0%
(B) 49%, 33%
(C) 68%, 57%
(D) 79%, 68%
(E) 89%, 79%

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

The first thing to note here is that we do not know the % of people who could not solve either puzzle. All we know is that puzzle X was solved by 79% of the people and puzzle Y was solved by 89% of the people.



Let’s first try to maximize the % of people who solved both the puzzles. We want to make these two sets overlap as much as possible i.e. we need to get them as close to each other as possible. Region of overlap can be 79% at most since we know that only 79% people solved puzzle X. In this case, the venn diagram will look something like this.



Hence, the maximum % of people who could have solved both the puzzles is 79%.

Now, let’s try to minimize the % of people who solved both the puzzles. We want the sets to be as far apart as possible. In this case, the % of people who solved neither puzzle must be 0. Only then will the overlap of the sets be as little as possible.



In this case, 68% people must have solved both the puzzles.

Hence, the answer is (D)
Intern
Intern
Joined: 23 Oct 2017
Posts: 46
Own Kudos [?]: 20 [0]
Given Kudos: 23
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
2 puzzles: X & Y.
Let x be the the no. of people who solved both.
100= (79+89) - x + neither (=> taking the component of neither is key here)

lets try to express x as f(neither)

x= 68 + neither
Now neither can takes values of 0 till (100-89)
min: x= 68+0 =68
max: x= 68+11 =79
Director
Director
Joined: 24 Oct 2016
Posts: 581
Own Kudos [?]: 1365 [1]
Given Kudos: 143
GMAT 1: 670 Q46 V36
GMAT 2: 690 Q47 V38
GMAT 3: 690 Q48 V37
GMAT 4: 710 Q49 V38 (Online)
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
1
Kudos
Bunuel wrote:
A group of people were given 2 puzzles. 79% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?

(A) 11%, 0%
(B) 49%, 33%
(C) 68%, 57%
(D) 79%, 68%
(E) 89%, 79%

Kudos for a correct solution.



Method: Direct Formula (Better)


Max (A&B) = Min(A, B) = 79
Min (A&B) = A + B - Total + None (To minimize Both, minimize None by taking None=0 except when there's a min constraint on None.)
Min (X&Y) = A + Y - 100 + None = 79 + 89 - 100 + 0 = 68 (None has no constraint)

Since there’s only one choice with max=79, no need to calculate min. => D

Alternate Method for Min (A&B):


Min (A & B) = (A + B) % Total + None
Since None has no constraint, minimize None by taking it equal to 0 => Min (A & B) = (79 + 89)%100 + 0 = 168%100 = 68

ANSWER: D
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6049
Own Kudos [?]: 4764 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
Bunuel wrote:
A group of people were given 2 puzzles. 79% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?

(A) 11%, 0%
(B) 49%, 33%
(C) 68%, 57%
(D) 79%, 68%
(E) 89%, 79%

Kudos for a correct solution.

79 + 89 = 168 > 100

So, both x & y = 68

Now, if all people in sent X solves questions of Y, then max is 79

Hence, Answer must be (D)
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19130
Own Kudos [?]: 22631 [2]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
2
Bookmarks
Expert Reply
Bunuel wrote:
A group of people were given 2 puzzles. 79% people solved puzzle X and 89% people solved puzzle Y. What is the maximum and minimum percentage of people who could have solved both the puzzles?

(A) 11%, 0%
(B) 49%, 33%
(C) 68%, 57%
(D) 79%, 68%
(E) 89%, 79%


Solution:

We can use the formula:

Total = Puzzle X + Puzzle Y - Both + Neither

Assuming Neither = 0 (since 0 is the minimum value of any nonnegative quantities), we have:

100 = 79 + 89 - Both

100 = 168 - Both

Both = 68

Assuming Neither = 11 (since we know 89 percent solved puzzle Y), we have:

100 = 79 + 89 - Both + 11

100 = 179 - Both

Both = 79

We see that the maximum value is 79 percent and the minimum value is 68 percent.

Answer: D
VP
VP
Joined: 11 Aug 2020
Posts: 1247
Own Kudos [?]: 207 [0]
Given Kudos: 332
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
Didn't see how I could post tables here, but set matrices are super helpful for these types of questions. First thing that one needs to do is in the absence of any count, assume the total number of entities is 100.

There's two scenarios:
1. Maximum: 79 (This is the highest possible b/c we know that 79 people solved puzzle X)
2. Minimum: 68 (This is the lowest possible b/c we know that 21 people did not solve X)

Answer is D.
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33970
Own Kudos [?]: 851 [0]
Given Kudos: 0
Send PM
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
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 Club Bot
Re: A group of people were given 2 puzzles. 79% people solved puzzle X and [#permalink]
Moderator:
Math Expert
94342 posts