Author 
Message 
TAGS:

Hide Tags

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7988
Location: Pune, India

There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
12 Aug 2016, 02:40
Question Stats:
61% (01:54) correct 39% (02:22) wrong based on 208 sessions
HideShow timer Statistics
Responding to a pm: There are 51 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs? 1) 4 2) 7 3) 17 4) 21 5) 27 Total 51 people who belong to one or both clubs. "if twice as many people belong to the tennis club as belong to the golf club"  this means if there are x people who belong to golf club, 2x belong to tennis club. Say anyone who is in one club is not in the other i.e. there is no overlap.
Total = n(G) + n(T)  Both 51 = x + 2x  Both Both = 3x  51 = 3*(x  17) 'Both' has to be a multiple of 3.
Only option (D) satisfies this condition.
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews
Last edited by Bunuel on 24 Aug 2016, 04:20, edited 1 time in total.
Added the OA.



Intern
Joined: 22 Dec 2015
Posts: 4

Re: There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
12 Aug 2016, 04:26
x > Golf Club 2x > Tennis Club y > both
x+2xy = 51 3x  y =51
multiples of 3 greater than 51 54 57 60 63 66 69 72  21 = 51
IMO (D)



Intern
Joined: 23 Apr 2016
Posts: 22
Location: Finland
Concentration: General Management, International Business
GPA: 3.65

Re: There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
23 Aug 2016, 13:33
Why not E i.e. 27 which is also a multiple of 3 ?



Intern
Joined: 18 Aug 2013
Posts: 12

Re: There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
24 Aug 2016, 02:15
VeritasPrepKarishma wrote: Responding to a pm: There are 51 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs? 1) 4 2) 7 3) 17 4) 21 5) 27 Total 51 people who belong to one or both clubs. "if twice as many people belong to the tennis club as belong to the golf club"  this means if there are x people who belong to golf club, 2x belong to tennis club. Say anyone who is in one club is not in the other i.e. there is no overlap.
Total = n(G) + n(T)  Both 51 = x + 2x  Both Both = 3x  51 = 3*(x  17) 'Both' has to be a multiple of 3.
Only option (D) satisfies this condition. VeritasPrepKarishma : Why not its E..? 27 is also a multiple of 3.. As Both = 3x  51 if i assume both = 27 = 3(26)  51 ? Am i doing something wrong ?



Current Student
Status: It`s Just a pirates life !
Joined: 21 Mar 2014
Posts: 235
Location: India
Concentration: Strategy, Operations
GPA: 4
WE: Consulting (Manufacturing)

Re: There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
24 Aug 2016, 04:09
VeritasPrepKarishma wrote: Responding to a pm: There are 51 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs? 1) 4 2) 7 3) 17 4) 21 5) 27 Total 51 people who belong to one or both clubs. "if twice as many people belong to the tennis club as belong to the golf club"  this means if there are x people who belong to golf club, 2x belong to tennis club. Say anyone who is in one club is not in the other i.e. there is no overlap.
Total = n(G) + n(T)  Both 51 = x + 2x  Both Both = 3x  51 = 3*(x  17) 'Both' has to be a multiple of 3.
Only option (D) satisfies this condition. The key point in solving this question is first of all, the number of people belonging must be a non negative integer. This in turn means that if we substitute the answer choice in the equation, the resulting number must be an integer. Only Choice D suffices this condition. Cheers BALAJI
_________________
Aiming for a 3 digit number with 7 as hundredths Digit



Intern
Joined: 10 Jun 2014
Posts: 19

Re: There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
24 Aug 2016, 04:38
thapliya wrote: Why not E i.e. 27 which is also a multiple of 3 ? 27 also can be the answer. 16827



Intern
Joined: 13 Jul 2016
Posts: 48

Re: There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
25 Sep 2016, 09:12
2
This post received KUDOS
azamaka wrote: thapliya wrote: Why not E i.e. 27 which is also a multiple of 3 ? 27 also can be the answer. 16827 It is given that "twice as many people belong to the tennis club as belong to the golf club". If # of people in golf club = x Then # of people in tennis club = 2x. 2x<51 => x <26.5 Since the number of people in both clubs can not be greater then number of people in either club hence: Answer less then 26.5



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7988
Location: Pune, India

There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
16 Nov 2016, 11:01
thapliya wrote: Why not E i.e. 27 which is also a multiple of 3 ? Responding to a pm: Let's find the range of Both and hence the range of x. Minimum value of Both: Say there is no overlap in the two sets. 51 = x + 2x x = 17 In this case Both = 0 Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x. 51 = 2x But x cannot be a decimal so (x1) could be the overlap (= Both) and there could be 1 in only the Golf club. 51 = 2x + x  (x  1) x = 25 In this case Both = 25  1 = 24 So Both lies between 0 and 24.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Director
Joined: 13 Mar 2017
Posts: 572
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
13 Aug 2017, 23:07
VeritasPrepKarishma wrote: There are 51 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
1) 4 2) 7 3) 17 4) 21 5) 27
Let x be the number of people who belongs to Golf club. So, 2x is the number of people who belongs to Tennis club. Let y be the people who belongs to both clubs. So, (xy)+(2xy) +y = 51 y = 3x51......................(i) So, y must be a multiple of 3. We can eliminate option A,B,C Also, Since total number of people in a club can't be greater than 51 So, 2x <51 x<26 Now we check y = 21 and 27 in eq (i) At y = 21, x = (21+51)/3 = 24 At y = 27, x = (27+51)/3 = 26 (Not possible) So, y = 21 is correct .. Answer D
_________________
CAT 99th percentiler : VA 97.27  DILR 96.84  QA 98.04  OA 98.95 UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



Target Test Prep Representative
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2116

Re: There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
18 Aug 2017, 09:06
Quote: There are 51 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
1) 4 2) 7 3) 17 4) 21 5) 27
We can let the number of people who belong to the golf club = x, making people who belong to the tennis club = 2x, and the number who belong to both = b. Thus: 51 = x + 2x  b Note that we must subtract b from the right side of the equation because we have doublecounted the “b” individuals (those who belong to both clubs) as members of both the golf club and the tennis club. 51 = 3x  b 51 + b = 3x (51 + b)/3 = x So (51 + b) must be a multiple of 3. Since 51 is a multiple of 3, b must also be a multiple of 3. Of our answer choices, both D and E are multiples of 3, so let’s test each one. D) If b = 21, then: (51 + 21)/3 = x 24 = x So 2x = 48. E) If b = 27, then: (51 + 27)/3 = x 26 = x So 2x = 52. However, we see that answer choice E can’t be correct, since that would mean the number of people belonging to the tennis club, 52, was greater than the given total of 51 people. Thus, the correct answer choice is D. Answer: D
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

Re: There are 51 people in a certain community who belong to the local [#permalink]
Show Tags
18 Aug 2017, 11:05
If anyone was curious about the source of this problem, it's from one of my highlevel problem sets (#55 in my 2nd problem set). I'd definitely consider it a very hard problem, even if at a glance it might appear simple. The TC has twice as many members as the GC. When we count the number of people in the TC, or in the GC, we're also counting people in both clubs. So if the GC has x members, then we know the TC has 2x members. If we have b people in both clubs, a Venn diagram would look like this: only in TC: 2x  b in both TC and GC: b only in GC: x  b These add to 51, so 3x  b = 51 We care about b, so we should isolate b: b = 51  3x This equation means: "b" and "51  3x" are the exact same number. So, since 3 is a factor of "51  3x", 3 must be a factor of b, so b must be divisible by 3. Only two answer choices are candidates: 21 and 27. You don't need to use any algebra to rule out 27. If 27 people were in both clubs, all 27 of those people are in the GC, so there would naturally be at least 27 people in the GC. Since the TC has twice as many members as the GC, there would then need to be at least 54 people in the TC. But we don't have 54 people (there are only 51 people in total), so 27 is impossible, and the only possible answer is 21.
_________________
GMAT Tutor in Toronto
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com




Re: There are 51 people in a certain community who belong to the local
[#permalink]
18 Aug 2017, 11:05






