Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47978

120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
24 Dec 2014, 08:53
Question Stats:
79% (02:07) correct 21% (01:27) wrong based on 157 sessions
HideShow timer Statistics



Intern
Status: Amat Victoria Curam
Joined: 13 Sep 2014
Posts: 25
Location: India

Re: 120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
24 Dec 2014, 09:09
n(A Union B) = n(A  B) + n(B  A) + n(A intersection B) Implies 120 = 24 + n(B  A) + 32 Thus n(B  A) = 64
Percentage = 64/120% = 53%
Hence D



Manager
Joined: 21 Aug 2010
Posts: 176
Location: United States

Re: 120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
24 Dec 2014, 11:55
Bunuel wrote: Tough and Tricky questions: Overlapping Sets. 120 children are participating in a summer camp and all of them must choose at least one of the French or Spanish language workshops in which to participate. 32 of the children have selected to participate in both workshops. If 24 children participate exclusively in the French workshop, what percent of all the children exclusively participate in the Spanish workshop? A. 40% B. 48% C. 50% D. 53% E. 64% Kudos for a correct solution.Total children participating = 120 = Exclusively French + Both + exclusively Spanish Exclusively Spanish = 120  (24 + 32) = 64 Percentage = (64/120) * 100 = 53 ANS D
_________________




Manager
Joined: 27 Jan 2013
Posts: 175
Location: United States
Concentration: Entrepreneurship, Marketing
GPA: 3.5
WE: Supply Chain Management (Telecommunications)

Re: 120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
25 Dec 2014, 04:23
F= French F.N= Not French Same represenation for spanish.
F F.N
S 32 64=1203256
S.N 24 0 (as one language is mandatory)
Now 64/120 %= ? Note that we know 60 is half of 120 hence % would be just above 50. Only answer that meets this is D.



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1835
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: 120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
31 Dec 2014, 01:05
Answer = D. 53% Refer diagram below: Attachment:
over.png [ 4.34 KiB  Viewed 1851 times ]
\(\frac{64}{120} * 100 = 53%\)
_________________
Kindly press "+1 Kudos" to appreciate



Math Expert
Joined: 02 Sep 2009
Posts: 47978

Re: 120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
08 Jan 2015, 09:02
Bunuel wrote: Tough and Tricky questions: Overlapping Sets. 120 children are participating in a summer camp and all of them must choose at least one of the French or Spanish language workshops in which to participate. 32 of the children have selected to participate in both workshops. If 24 children participate exclusively in the French workshop, what percent of all the children exclusively participate in the Spanish workshop? A. 40% B. 48% C. 50% D. 53% E. 64% Kudos for a correct solution. OFFICIAL SOLUTION:The best way to solve these kinds of problems is by creating a Venn diagram. Start by drawing two circles that overlap such that they share some fraction of their areas. The boundaries of the circles will encompass the number of students that participate in each language workshop. The section where they overlap represents students that take both languages. You can arbitrarily label the left lobe with an F for French and the Right lobe with an S for Spanish. The sum of the populations in each lobe must be equal to the sum of the children, or 120. Since there are 24 children exclusively taking French the F lobe should have the number 24 in it. Since there are 32 children taking both languages, the middle lobe should have a 32 in it. We will solve for the number of children taking only Spanish, so label the S lobe with an x. The sum of the lobes, as we mentioned must equal 120, so we can solve for x by solving the equation: 24 + 32 + x = 120, or x = 64. So, there are exactly 64 children exclusively participating in the Spanish workshop. Finally, to determine what percent of the student population the 64 exclusive Spanish taking students constitute, we set up the ratio: part/whole = 64/120 = 8/15, or 53 percent.
_________________
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



Manager
Joined: 08 Nov 2014
Posts: 90
Location: India
GPA: 3
WE: Engineering (Manufacturing)

Re: 120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
08 Jan 2015, 09:13
A U B = nA+nB n(A intersection B) OR = n(AB) + n(BA) + n(A intersection B) 120 = n(SF)+24+32 n(SF) = 64 64/120*100 = 53.3 % ANSWER D is closest Bunuel wrote: Tough and Tricky questions: Overlapping Sets. 120 children are participating in a summer camp and all of them must choose at least one of the French or Spanish language workshops in which to participate. 32 of the children have selected to participate in both workshops. If 24 children participate exclusively in the French workshop, what percent of all the children exclusively participate in the Spanish workshop? A. 40% B. 48% C. 50% D. 53% E. 64% Kudos for a correct solution.
_________________
"Arise, Awake and Stop not till the goal is reached"



Intern
Joined: 21 Jun 2015
Posts: 2

Re: 120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
29 May 2016, 13:06
Hi Bunuel,
Can we solve this problem using formula : Total = S1 +S2  Both +Neither? Please explain if we can.



Intern
Joined: 28 Apr 2015
Posts: 19
GMAT 1: 600 Q46 V27 GMAT 2: 630 Q47 V30

Re: 120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
20 Jul 2016, 10:12
msrivas2 wrote: Hi Bunuel,
Can we solve this problem using formula : Total = S1 +S2  Both +Neither? Please explain if we can. Yes we can. Let, S1 be all French including both French + Spanish and S2 be all Spanish including French and Spanish. Hence, S2= 32 + 24. 120 (total) = S1 + ( 32 + 24 )  32 (both) + 0 Therefore, S1 = 96. Now, Exclusive French will be 9632 = 64. 53% of 120 will be approx. 64. Hope it helps.



NonHuman User
Joined: 09 Sep 2013
Posts: 7751

Re: 120 children are participating in a summer camp and all of them must
[#permalink]
Show Tags
12 May 2018, 04:32
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




Re: 120 children are participating in a summer camp and all of them must &nbs
[#permalink]
12 May 2018, 04:32






