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

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
Marty has a necklace that contains a total of 36 rhinestones, zirconiu  [#permalink]

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16 Aug 2017, 00:59
00:00

Difficulty:

35% (medium)

Question Stats:

73% (02:05) correct 27% (02:05) wrong based on 102 sessions

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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

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Joined: 02 Nov 2015
Posts: 166
GMAT 1: 640 Q49 V29
Re: Marty has a necklace that contains a total of 36 rhinestones, zirconiu  [#permalink]

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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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Joined: 22 Apr 2015
Posts: 28
WE: Business Development (Internet and New Media)
Re: Marty has a necklace that contains a total of 36 rhinestones, zirconiu  [#permalink]

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16 Aug 2017, 03:22
2
1
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 $$r \neq{12}$$
Intern
Joined: 04 Aug 2017
Posts: 10
Re: Marty has a necklace that contains a total of 36 rhinestones, zirconiu  [#permalink]

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02 Sep 2017, 12:05
1
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.
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Re: Marty has a necklace that contains a total of 36 rhinestones, zirconiu  [#permalink]

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20 Sep 2018, 02:26
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Re: Marty has a necklace that contains a total of 36 rhinestones, zirconiu &nbs [#permalink] 20 Sep 2018, 02:26
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# Marty has a necklace that contains a total of 36 rhinestones, zirconiu

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