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In an ensemble of gongs, all gongs have a diameter of either [#permalink]
 12 Nov 2009, 13:17
Question Stats:
25% (03:10) correct
75% (03:58) wrong based on 0 sessions
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
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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.
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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=t4. "Half of all gongs are fifteen inches in diameter" --> 2y=SFour 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=108Answer: E.
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E. Bunuel's answer is right on spot and clear
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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 =x-x/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. _________________
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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?
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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=t4. "Half of all gongs are fifteen inches in diameter" --> 2y=SFour 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=108Answer: 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]
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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.
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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.
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