Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
GMAT Club

 It is currently 29 Mar 2017, 16:06

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Each of 90 students participated at least 1 of the track try

Author Message
TAGS:

### Hide Tags

Manager
Status: struggling with GMAT
Joined: 06 Dec 2012
Posts: 225
Concentration: Accounting
GMAT Date: 04-06-2013
GPA: 3.65
Followers: 15

Kudos [?]: 359 [2] , given: 46

Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

19 Feb 2013, 10:39
2
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

65% (02:05) correct 35% (01:25) wrong based on 305 sessions

### HideShow timer Statistics

Each of 90 students participated at least 1 of the track tryouts: High jump, long jump, 100 meter dash. If 20 students participated in high jump tryout, 40 students participated in the long jump tryout and 60 students participated in the 100 meter dash tryout, and if 5 students participated in all 3 tryouts, how many students participated in only two of these tryouts?

(A) 25
(B) 20
(C) 15
(D) 10
(E) 5
[Reveal] Spoiler: OA
Manager
Joined: 27 Jan 2013
Posts: 230
GMAT 1: 780 Q49 V51
Followers: 48

Kudos [?]: 216 [3] , given: 32

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

19 Feb 2013, 11:56
3
KUDOS
Expert's post
4
This post was
BOOKMARKED
Hi,

So the formula that we can work from is: Group A + Group B + Group C + Neither - Doubles - 2(Triples) = Total

So 20 + 40 + 60 + 0 - Doubles - 2(5) = 90

110-Doubles = 90

Doubles = 20

The above formula is critical. Although it is simple, it is important to really understand it. Once you do, groups will be much easier.

Happy Studies,

HG.
_________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

GMAT vs GRE Comparison

If you found my post useful KUDOS are much appreciated.

Here is the first set along with some strategies for approaching this work: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151479.html

MBA Section Director
Status: Back to work...
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 4225
Location: India
City: Pune
GMAT 1: 680 Q49 V34
GPA: 3.4
Followers: 419

Kudos [?]: 3040 [2] , given: 2259

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

19 Feb 2013, 12:08
2
KUDOS
Expert's post
its B

We are asked how much are in only two tryouts that means what is (H and L only) + (L and 100m only) + (H and 100m only)
Total = H + L + 100m - both + All + None
90 = 20 + 40 + 60 - both + 5 + 0
90 = 125 - both ----------> both = 35

35 = (H and L) + (L and 100m) + (H and 100m)

H and L only = H and L - all ------> H and L - 5
L and 100m only = L and 100m - all ------> L and 100m - 5
H and 100m only = H and 100m - all ------> H and 100m - 5

so (H and L only) + (L and 100m only) + (H and 100m only) = (H and L) + (L and 100m) + (H and 100m) - 15 ---------> 35 - 15 = 20.

Regards,

Abhijit.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7256
Location: Pune, India
Followers: 2205

Kudos [?]: 14372 [6] , given: 222

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

19 Feb 2013, 21:48
6
KUDOS
Expert's post
5
This post was
BOOKMARKED
mun23 wrote:
Each of 90 students participated at least 1 of the track tryouts: High jump, long jump, 100 meter dash. If 20 students participated in high jump tryout, 40 students participated in the long jump tryout and 60 students participated in the 100 meter dash tryout, and if 5 students participated in all 3 tryouts, how many students participated in only two of these tryouts?

(A) 25
(B) 20
(C) 15
(D) 10
(E) 5

A venn diagram can show you exactly what you are supposed to do.
Attachment:

Ques4.jpg [ 18.31 KiB | Viewed 7303 times ]

The high jump circle has 20 students. It includes the pink region (only High jump), d, e and 5 (students who tried all 3)
The long jump circle has 40 students. It includes the yellow region (only long jump), d, f and 5 (students who tried all 3)
The 100 meter dash circle has 60 students. It includes the green region (only 100 meter), e, f and 5 (students who tried all 3)

So when you add 20 + 40 + 60, you get 120 which is 30 more than 90. Why? Because in 20+40+60, you have counted, d, e and f twice and 5 thrice.
You need to subtract two times 5 and d+e+f once to get 90.
120 - 2*5 - (d+e+f) = 90
(d+e+f) = 20

This is how you get the formula: Group A + Group B + Group C + Neither - Doubles - 2(Triples) = Total
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 16 Nov 2012 Posts: 6 Followers: 0 Kudos [?]: 5 [0], given: 13 Re: Each of 90 students participated at least 1 of the track try [#permalink] ### Show Tags 25 Feb 2013, 04:08 VeritasPrepKarishma wrote: mun23 wrote: Each of 90 students participated at least 1 of the track tryouts: High jump, long jump, 100 meter dash. If 20 students participated in high jump tryout, 40 students participated in the long jump tryout and 60 students participated in the 100 meter dash tryout, and if 5 students participated in all 3 tryouts, how many students participated in only two of these tryouts? (A) 25 (B) 20 (C) 15 (D) 10 (E) 5 A venn diagram can show you exactly what you are supposed to do. Attachment: Ques4.jpg The high jump circle has 20 students. It includes the pink region (only High jump), d, e and 5 (students who tried all 3) The long jump circle has 40 students. It includes the yellow region (only long jump), d, f and 5 (students who tried all 3) The 100 meter dash circle has 60 students. It includes the green region (only 100 meter), e, f and 5 (students who tried all 3) So when you add 20 + 40 + 60, you get 120 which is 30 more than 90. Why? Because in 20+40+60, you have counted, d, e and f twice and 5 thrice. You need to subtract two times 5 and d+e+f once to get 90. 120 - 2*5 - (d+e+f) = 90 (d+e+f) = 20 This is how you get the formula: Group A + Group B + Group C + Neither - Doubles - 2(Triples) = Total I get your method here..however can you please explain the problem mentioned below as well... The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedies are there? In this question, we are looking for those movies that are in all 3 categories. The answer I am getting is -1 which is wrong 38=48-12(i got this 12 by adding 5+3+4)-2x therefore, 2=-2x can you please help me fix this? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7256 Location: Pune, India Followers: 2205 Kudos [?]: 14372 [2] , given: 222 Re: Each of 90 students participated at least 1 of the track try [#permalink] ### Show Tags 25 Feb 2013, 05:27 2 This post received KUDOS Expert's post 1 This post was BOOKMARKED Shini1 wrote: I get your method here..however can you please explain the problem mentioned below as well... The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedies are there? In this question, we are looking for those movies that are in all 3 categories. The answer I am getting is -1 which is wrong 38=48-12(i got this 12 by adding 5+3+4)-2x therefore, 2=-2x can you please help me fix this? I am glad you asked this question. This is the reason I tell people to not use formulas in sets questions and to rely on their understanding of venn diagrams. The formula discussed above is used in case you know d, e and f i.e. no of people participating in two and only two events. In this question, the given numbers 5, 3 and 4 are not d, e, and f. They are the number of movies which fall into two groups as well as three groups. 5 movies which are both action and drama include those movies which are comedy as well i.e. which fall in all three categories. In this case, the formula we use is P(A u B u C) = P(A) + P(B) + P(C) – P(A n B) – P(A n C) – P(B n C) + P(A n B n C) 38 = 48 - 12 + x x = 2 Think about this formula. P(A) includes P(A n B) which includes P(A n B n C). To avoid double counting in case of P(A), P(B) and P(C), you subtract P(A n B), P(A n C) and P(B n C) once but now you have subtracted P(A n B n C) thrice which means you haven't accounted for it at all. Hence, you add it back. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Manager
Joined: 27 Jan 2013
Posts: 230
GMAT 1: 780 Q49 V51
Followers: 48

Kudos [?]: 216 [0], given: 32

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

25 Feb 2013, 08:33
Hi,

I'm not a big fan of Venn diagrams and have found that for groups, these formulas, once you really practice them, are big time savers. In this case, the formula would be:

Singles + Doubles + Triples = Total

24 + 12 + Triples = 38

Triples = 2

This is just a derivative of the other formula. You have to play around with this to get the hang of it. OG 13 PS #178 is a good one to practice with.

Let me know if you have any questions. Happy studies.

HG.
_________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

GMAT vs GRE Comparison

If you found my post useful KUDOS are much appreciated.

Here is the first set along with some strategies for approaching this work: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151479.html

Intern
Joined: 16 Nov 2012
Posts: 6
Followers: 0

Kudos [?]: 5 [0], given: 13

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

25 Feb 2013, 09:23
I get Karishma's method .. Thanks

@ HerrGrau- how n here do you get your singles from
tried the OG prob too thank u ..and do we have your debrief on the site as well ..your verbal is outstanding ..need to know how for that as well ..
Manager
Joined: 27 Jan 2013
Posts: 230
GMAT 1: 780 Q49 V51
Followers: 48

Kudos [?]: 216 [0], given: 32

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

25 Feb 2013, 14:39
Hi,

You can find the singles by subtracting all of the overlaps from the fake total (I call it the fake total because it is the total that counts all of the movies that are in different categories). In this case we are told that there are 12 overlaps. You have to multiply that by 2 because each overlap is in two groups (for instance, there are 5 doubles in action and in drama so those 5 doubles take up 10 slots). So the singles are 48-24 = 24. There is no doubt that the "formula" approach to groups takes practice but it does work very well once you are comfortable with the formulas and how the different groups interact. Maybe a combined approach with Venn Diagrams would work for you.

Let me know if you need more advice on this.

HG.

PS: I am planning on writing a debrief but haven't yet found the time:(
_________________

"It is a curious property of research activity that after the problem has been solved the solution seems obvious. This is true not only for those who have not previously been acquainted with the problem, but also for those who have worked over it for years." -Dr. Edwin Land

GMAT vs GRE Comparison

If you found my post useful KUDOS are much appreciated.

Here is the first set along with some strategies for approaching this work: http://gmatclub.com/forum/the-economist-reading-comprehension-challenge-151479.html

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14559
Followers: 609

Kudos [?]: 175 [0], given: 0

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

30 Jul 2014, 17:10
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.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 50

Kudos [?]: 2063 [1] , given: 193

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

31 Jul 2014, 03:01
1
KUDOS
mun23 wrote:
Each of 90 students participated at least 1 of the track tryouts: High jump, long jump, 100 meter dash. If 20 students participated in high jump tryout, 40 students participated in the long jump tryout and 60 students participated in the 100 meter dash tryout, and if 5 students participated in all 3 tryouts, how many students participated in only two of these tryouts?

(A) 25
(B) 20
(C) 15
(D) 10
(E) 5

Refer diagram below

We require to find value of shaded region = a + b + c

(Values in Blue are calculated)

Setting up the equation

20 + 55 - (b+c) + c + 35 - (a+c) = 90

a+b+c = 20

Attachments

jump.png [ 6.49 KiB | Viewed 5110 times ]

_________________

Kindly press "+1 Kudos" to appreciate

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 50

Kudos [?]: 2063 [0], given: 193

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

31 Jul 2014, 03:14
I get your method here..however can you please explain the problem mentioned below as well...

The 38 movies in the video store fall into the following three categories: 10 action, 20 drama, and 18 comedy. However, some movies are classified under more than one category: 5 are both action and drama, 3 are both action and comedy, and 4 are both drama and comedy. How many action-drama-comedies are there?

In this question, we are looking for those movies that are in all 3 categories.

The answer I am getting is -1 which is wrong

38=48-12(i got this 12 by adding 5+3+4)-2x
therefore, 2=-2x

Refer diagram below

We require to find x

10 + 11 + x + 4 - x + 11 + x = 38

x = 2
Attachments

come.png [ 5.82 KiB | Viewed 5096 times ]

_________________

Kindly press "+1 Kudos" to appreciate

Current Student
Joined: 04 Jul 2014
Posts: 291
Location: India
GMAT 1: 640 Q47 V31
GMAT 2: 640 Q44 V34
GMAT 3: 710 Q49 V37
GPA: 3.58
WE: Analyst (Accounting)
Followers: 19

Kudos [?]: 241 [0], given: 403

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

22 Nov 2014, 11:06
Hope this helps!
Attachment:

Capture.PNG [ 7.47 KiB | Viewed 4492 times ]

_________________

Cheers!!

JA
If you like my post, let me know. Give me a kudos!

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 14559
Followers: 609

Kudos [?]: 175 [0], given: 0

Re: Each of 90 students participated at least 1 of the track try [#permalink]

### Show Tags

22 Jan 2016, 20:49
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.
_________________
Re: Each of 90 students participated at least 1 of the track try   [#permalink] 22 Jan 2016, 20:49
Similar topics Replies Last post
Similar
Topics:
5 2 students from each of the 4 different B-schools participate in a deb 5 22 Jan 2017, 02:15
4 Two students A and B participate in Physics and Chemistry exams 5 30 Nov 2016, 08:57
2 A college student expects to earn at least \$1,000 in interest on an in 6 20 Aug 2016, 04:18
10 Each person in Room A is a student, and 1/6 of the students in Room A 7 02 Sep 2015, 22:56
6 In a group of 68 students, each student is registered for at least one 7 05 Dec 2009, 07:14
Display posts from previous: Sort by