Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 30 Aug 2009
Posts: 276
Location: India
Concentration: General Management

In an ensemble of gongs, all gongs have a diameter of either
[#permalink]
Show Tags
12 Nov 2009, 13:17
Question Stats:
63% (02:25) correct 37% (03:17) wrong based on 195 sessions
HideShow timer Statistics
In an ensemble of gongs, all gongs have a diameter of either ten inches, or twelve inches or fifteen inches. In the collection there are 18 ten inch gongs. Half of the gongs in the collection are Tiger gongs. Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. Half of the twelve inch gongs are not Tiger gongs, and half of all gongs are fifteen inches in diameter. How many gongs are there in the collection? A. 18 B. 54 C. 72 D. 90 E. 108
Official Answer and Stats are available only to registered users. Register/ Login.



Intern
Joined: 24 Oct 2009
Posts: 23
Location: Russia
Schools: IESE, SDA Bocconi

Re: Set question
[#permalink]
Show Tags
12 Nov 2009, 13:49
kp1811 wrote: In an ensemble of gongs, all gongs have a diameter of either ten inches, or twelve inches or fifteen inches. In the collection there are 18 ten inch gongs. Half of the gongs in the collection are Tiger gongs. Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. Half of the twelve inch gongs are not Tiger gongs, and half of all gongs are fifteen inches in diameter. How many gongs are there in the collection? 18 54 72 90 108 IMO, the answer is 108.



Math Expert
Joined: 02 Sep 2009
Posts: 47152

Re: Set question
[#permalink]
Show Tags
12 Nov 2009, 15:08
kp1811 wrote: In an ensemble of gongs, all gongs have a diameter of either ten inches, or twelve inches or fifteen inches. In the collection there are 18 ten inch gongs. Half of the gongs in the collection are Tiger gongs. Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. Half of the twelve inch gongs are not Tiger gongs, and half of all gongs are fifteen inches in diameter. How many gongs are there in the collection? 18 54 72 90 108 If not the wording question won't be hard: Let x and y be 12 and 15 inches gongs respectively. We know that ten inches are 18. 1. \(18+x+y=S\). We want to calculate \(S\). 2. "Half of the gongs in the collection are Tiger gongs" > \(2t=S\). 3. "Half of the twelve inch gongs are not Tiger gongs" > means another half IS Tiger gongs, so x/2 is in Tiger gongs. As "Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs". > x/2+x/2+x/2=t > \(\frac{3}{2}x=t\) 4. "Half of all gongs are fifteen inches in diameter" > \(2y=S\) Four unknowns, four equations. (3) \(\frac{3}{2}x=t\) and (2) \(2t=S\) > \(x=\frac{S}{3}\) (4) \(2y=S\) > \(y=\frac{S}{2}\) (1) \(18+x+y=S\) > \(18+\frac{S}{3}+\frac{S}{2}=S\) > \(S=108\) Answer: E.
_________________
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: 22 Sep 2009
Posts: 200
Location: Tokyo, Japan

Re: Set question
[#permalink]
Show Tags
12 Nov 2009, 17:12
E. Bunuel's answer is right on spot and clear



Manager
Joined: 25 Aug 2009
Posts: 140
Location: Streamwood IL
Schools: Kellogg(Evening),Booth (Evening)
WE 1: 5 Years

Re: Set question
[#permalink]
Show Tags
13 Nov 2009, 09:43
Code: The only use I got from the Kaplan premier book is to find the best way to answer such questions. I will use different tables for the purpose of explanation but you would need just 1. We will try and create a Sum table based on the given information. You should start of like this  Diameter of gong along the horizontal axis & type of gong along the vertical axis. Also let the total number of gongs = x, we need to find x. 10 12 15 TG NTG x TG = Tiger Gong, NTG is the non tiger gong. Lets start filling this table up with the pieces of info given 1) In the collection there are 18 ten inch gongs 10 12 15 TG NTG 18 x 2) Half of the gongs in the collection are Tiger gongs. 10 12 15 TG x/2 NTG =xx/2 = x/2 18 x 3) Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. 10 12 15 TG x/6 x/6 x/6 x/2 NTG x/2 18 x 4) Half of the twelve inch gongs are not Tiger gongs. 10 12 15 TG x/6 x/6 x/6 x/2 NTG x/6 x/2 18 x 5) half of all gongs are fifteen inches in diameter 10 12 15 TG x/6 x/6 x/6 x/2 NTG x/6 x/2 18 x/2 x now we have enough info to solve the problem  total number of 12 inch gongs = x/6+x/6=x/3 now we equate the bottom horizontal row i.e. 18 + x/3 +x/2 = x x = 18*6 = 108.
_________________
Rock On



Intern
Joined: 23 Nov 2010
Posts: 2

Re: Set question
[#permalink]
Show Tags
12 Dec 2010, 15:45
If \(18+x+y=S\) > \(18+\frac{S}{3}+\frac{S}{2}=S\) > \(S=108\)
then 18, x=S/3=36, y=S/2=54
and Tiger=9+18+27
"Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs".
But we find that they are not equal. Please tell me what am I getting wrong?



Manager
Status: ==GMAT Ninja==
Joined: 08 Jan 2011
Posts: 219
Schools: ISB, IIMA ,SP Jain , XLRI
WE 1: Aditya Birla Group (sales)
WE 2: Saint Gobain Group (sales)

Re: Set question
[#permalink]
Show Tags
12 Mar 2011, 13:20
Bunuel wrote: kp1811 wrote: In an ensemble of gongs, all gongs have a diameter of either ten inches, or twelve inches or fifteen inches. In the collection there are 18 ten inch gongs. Half of the gongs in the collection are Tiger gongs. Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. Half of the twelve inch gongs are not Tiger gongs, and half of all gongs are fifteen inches in diameter. How many gongs are there in the collection? 18 54 72 90 108 If not the wording question won't be hard: Let x and y be 12 and 15 inches gongs respectively. We know that ten inches are 18. 1. \(18+x+y=S\). We want to calculate \(S\). 2. "Half of the gongs in the collection are Tiger gongs" > \(2t=S\). 3. "Half of the twelve inch gongs are not Tiger gongs" > means another half IS Tiger gongs, so x/2 is in Tiger gongs. As "Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs". > x/2+x/2+x/2=t > \(\frac{3}{2}x=t\) 4. "Half of all gongs are fifteen inches in diameter" > \(2y=S\) Four unknowns, four equations. (3) \(\frac{3}{2}x=t\) and (2) \(2t=S\) > \(x=\frac{S}{3}\) (4) \(2y=S\) > \(y=\frac{S}{2}\) (1) \(18+x+y=S\) > \(18+\frac{S}{3}+\frac{S}{2}=S\) > \(S=108\) Answer: E. Hey bunuel I got this question by an easy approach Let total gongs be G and tiger gongs be T so T=G/2 now as the question says there is a equal no of tiger gongs in each catagory hence T/3 each now it has been given in the question that gongs that have 10 inches Diameter are 18 in nos so T/3 = 18 so T =54 now T=G/2 so 54 = G/2 so G=108 it was quite easy this way just tell me if I am wrong.......... Regards Puneet Sharma [WarLocK]
_________________
WarLocK _____________________________________________________________________________ The War is oNNNNNNNNNNNNN for 720+ see my Test exp here http://gmatclub.com/forum/mytestexperience111610.html do not hesitate me giving kudos if you like my post.



Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1899

Re: Set question
[#permalink]
Show Tags
12 Mar 2011, 13:47
Please see the attached answer image.
Attachments
gongs.PNG [ 16.94 KiB  Viewed 4491 times ]
_________________
~fluke
GMAT Club Premium Membership  big benefits and savings



Retired Moderator
Joined: 16 Nov 2010
Posts: 1467
Location: United States (IN)
Concentration: Strategy, Technology

Re: Set question
[#permalink]
Show Tags
13 Mar 2011, 03:53
Let a  10 inches b  12 inches c  15 inches So we need to find a + b + c Given that # of Tiger Gongs = (a+b+c)/2 and a = 18, and there are 1/3 * (a+b+c)/2 Tiger Gongs of each type. And then b/12 = (a+b+c)/6 and (a+b+c)/2 = c So now we have 3 equations, and by substituting the value of "a" those can be simplified to: 3b = 18 + b + c c  b = 18 So b = 36, c = 54 Hence a + b + c = 18 + 36 + 54 = 108, so the answer is E.
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant)
GMAT Club Premium Membership  big benefits and savings



Manager
Joined: 14 Feb 2011
Posts: 180

Re: Set question
[#permalink]
Show Tags
13 Mar 2011, 08:34
kp1811 wrote: In an ensemble of gongs, all gongs have a diameter of either ten inches, or twelve inches or fifteen inches. In the collection there are 18 ten inch gongs. Half of the gongs in the collection are Tiger gongs. Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. Half of the twelve inch gongs are not Tiger gongs, and half of all gongs are fifteen inches in diameter. How many gongs are there in the collection? 18 54 72 90 108 Let x be the number of ten inch, twelve inch and fifteen inch Tiger gongs, so total number of tiger gongs is 3x and total number of gongs is 6x. Now half of all gongs are fifteen inches in diameter so they must number 3x and hence there are 2x fifteen inches non Tiger gongs. Also, Half of the twelve inch gongs are not Tiger gongs so there are x twelve inches non Tiger gongs. Therefore, all the non Tiger gongs (3x) are fifteen inches (2x) or twelve inches (x) Thus, all the 18 inch gongs are tiger gongs and hence x=18, so total gongs is 6*18 = 108.



Intern
Joined: 04 May 2013
Posts: 44

Re: Set question
[#permalink]
Show Tags
11 Dec 2013, 17:35
Warlock007 wrote: Bunuel wrote: kp1811 wrote: In an ensemble of gongs, all gongs have a diameter of either ten inches, or twelve inches or fifteen inches. In the collection there are 18 ten inch gongs. Half of the gongs in the collection are Tiger gongs. Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. Half of the twelve inch gongs are not Tiger gongs, and half of all gongs are fifteen inches in diameter. How many gongs are there in the collection? 18 54 72 90 108 If not the wording question won't be hard: Let x and y be 12 and 15 inches gongs respectively. We know that ten inches are 18. 1. \(18+x+y=S\). We want to calculate \(S\). 2. "Half of the gongs in the collection are Tiger gongs" > \(2t=S\). 3. "Half of the twelve inch gongs are not Tiger gongs" > means another half IS Tiger gongs, so x/2 is in Tiger gongs. As "Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs". > x/2+x/2+x/2=t > \(\frac{3}{2}x=t\) 4. "Half of all gongs are fifteen inches in diameter" > \(2y=S\) Four unknowns, four equations. (3) \(\frac{3}{2}x=t\) and (2) \(2t=S\) > \(x=\frac{S}{3}\) (4) \(2y=S\) > \(y=\frac{S}{2}\) (1) \(18+x+y=S\) > \(18+\frac{S}{3}+\frac{S}{2}=S\) > \(S=108\) Answer: E. Hey bunuel I got this question by an easy approach Let total gongs be G and tiger gongs be T so T=G/2 now as the question says there is a equal no of tiger gongs in each catagory hence T/3 each now it has been given in the question that gongs that have 10 inches Diameter are 18 in nos so T/3 = 18so T =54 now T=G/2 so 54 = G/2 so G=108 it was quite easy this way just tell me if I am wrong.......... Regards Puneet Sharma [WarLocK] This is incorrect. You cannot say T/3 = 18. T is only tiger gongs and T/3 is tiger gongs (10in). We dont know if this is 18. 18 is the total nnumber of 10in gongs.



Intern
Joined: 04 Dec 2012
Posts: 11
GMAT Date: 12262013

Re: In an ensemble of gongs, all gongs have a diameter of either
[#permalink]
Show Tags
15 Dec 2013, 08:02
Gong  Tiger  ~Tiger  Total 10  a  18a  18 12  a(=b/2)  b/2  b 15  a  c  x/2 Total  x/2  x/2  x
Note : Since half of 12inch gongs are not tiger gongs, half of them are tiger gongs(hence a=b/2 in the table above)
Now, from the table above
In the nontiger gong column,
(18a)+b/2+c=x/2 => c = x/2(18a)b/2
From this, we can add up the 15inch gong row to get the equation,
a+x/218+ab/2=x/2 (or) 2ab/2=18(1)
Adding up column 1, we get
2a+b/2=x/2(2)
Solving (1) & (2),
4a=x/2+18(3)
We know that 3a=x/2(4)
Substituting (4) in (3), we get x=108.



SVP
Joined: 06 Sep 2013
Posts: 1867
Concentration: Finance

Re: In an ensemble of gongs, all gongs have a diameter of either
[#permalink]
Show Tags
19 Mar 2014, 06:20
There are 18 of the ten inch gongs, and we also know that there are some that are tiger gongs those are equally distributed among the three types. Now, since half of them are tiger gongs and of them 1/3 are 12 inch gongs, then 12 inch gongs are 1/6X, were X represents the total number of gongs. Now we are told that the 15 inch are the remainder. Therefore we know that x/2 + x/6 = 5/6 x, so 15 inch must be 1/6x = 18, therefore x=108. Answer is E.
Hope this clarifies Cheers J



Senior Manager
Joined: 05 Jan 2017
Posts: 426
Location: India

Re: In an ensemble of gongs, all gongs have a diameter of either
[#permalink]
Show Tags
27 Feb 2017, 04:07
Number of 10 inches gong = 18 Number of 12 inches gong = x and number of 15 inches gong = y Total number of tiger gongs = (x +y +18)/2 Total number of 12 inches tiger gong = (x +y +18)/6 x/2 = (x +y +18)/6 =>2x = y +18 (1)
And 2y = x +y +18=> y = x +18 (2)
Solving we get, x =36 and y = 54 Total number of gongs = 108
Option E



Intern
Joined: 30 Jun 2017
Posts: 18
Location: India
Concentration: Technology, General Management
WE: Consulting (Computer Software)

Re: In an ensemble of gongs, all gongs have a diameter of either
[#permalink]
Show Tags
10 Sep 2017, 22:24
Bunuel wrote: kp1811 wrote: In an ensemble of gongs, all gongs have a diameter of either ten inches, or twelve inches or fifteen inches. In the collection there are 18 ten inch gongs. Half of the gongs in the collection are Tiger gongs. Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs. Half of the twelve inch gongs are not Tiger gongs, and half of all gongs are fifteen inches in diameter. How many gongs are there in the collection? 18 54 72 90 108 If not the wording question won't be hard: Let x and y be 12 and 15 inches gongs respectively. We know that ten inches are 18. 1. \(18+x+y=S\). We want to calculate \(S\). 2. "Half of the gongs in the collection are Tiger gongs" > \(2t=S\). 3. "Half of the twelve inch gongs are not Tiger gongs" > means another half IS Tiger gongs, so x/2 is in Tiger gongs. As "Of the Tiger gongs, there are equal numbers of ten inch, twelve inch and fifteen inch gongs". > x/2+x/2+x/2=t > \(\frac{3}{2}x=t\) 4. "Half of all gongs are fifteen inches in diameter" > \(2y=S\) Four unknowns, four equations. (3) \(\frac{3}{2}x=t\) and (2) \(2t=S\) > \(x=\frac{S}{3}\) (4) \(2y=S\) > \(y=\frac{S}{2}\) (1) \(18+x+y=S\) > \(18+\frac{S}{3}+\frac{S}{2}=S\) > \(S=108\) Answer: E. This is quite a complicated problem especially for it's wording. Is this a typical GMAT like question?




Re: In an ensemble of gongs, all gongs have a diameter of either &nbs
[#permalink]
10 Sep 2017, 22:24






