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Marty has a necklace that contains a total of 36 rhinestones, zirconiu

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Marty has a necklace that contains a total of 36 rhinestones, zirconiu [#permalink]

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New post 16 Aug 2017, 00:59
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Marty has a necklace that contains a total of 36 rhinestones, zirconium, and obsidian “gems.” If the ratio of obsidian to zirconium is 2:5, then which of the following could not be the number of rhinestones in Marty’s necklace?

(A) 8
(B) 12
(C) 15
(D) 22
(E) 29
[Reveal] Spoiler: OA

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Kudos [?]: 135541 [0], given: 12697

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Re: Marty has a necklace that contains a total of 36 rhinestones, zirconiu [#permalink]

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New post 16 Aug 2017, 02:43
It's a B. Rest all combinations are possible.
If it's 12 , then 36-12= 24, which is not possible

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Re: Marty has a necklace that contains a total of 36 rhinestones, zirconiu [#permalink]

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New post 16 Aug 2017, 03:22
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r+z+o= 36
o:z= 2:5=> no of obsidian gem=o= 2k
No. of zirconium gems=z= 5k
total no of o & z= 7k
r+7k=36
k= \(\frac{(36-r)}{7}\)
r=8 => k= \(\frac{28}{7}\)=4
r= 15=> k=\(\frac{24}{7}\)=3
r=22=> k= \(\frac{14}{7}\)=2
r=29=> k=\(\frac{7}{7}\)=1
r=12=> k= not an integer.

Hence \(r \neq{12}\)

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Re: Marty has a necklace that contains a total of 36 rhinestones, zirconiu [#permalink]

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New post 02 Sep 2017, 12:05
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Another way to look at the problem:
We are told that the ratio between obsidian and zirconium "gems" is 2x:5x and that the total amount of gems are 36.
We can plug in numbers to find out how many rhinestones would be possible for us to have given the limitations set by the problem.
2(1)+5(1)+r=36 -> r=29
2(2)+5(2)+r=36 -> r=22
2(3)+5(3)+r=36 -> r=15
2(4)+5(4)+r=36 -> r=8
2(5)+5(5)+r=36 -> r=1

As you can see from this list that out of the options given to us, 12 is the only number of rhinestones that isn't possible.

Kudos [?]: 1 [0], given: 739

Re: Marty has a necklace that contains a total of 36 rhinestones, zirconiu   [#permalink] 02 Sep 2017, 12:05
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Marty has a necklace that contains a total of 36 rhinestones, zirconiu

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