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An imperial scepter is mounted with diamonds, rubies, emeralds, and

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An imperial scepter is mounted with diamonds, rubies, emeralds, and sapphires in the ratio of w : x : y : z. If w, x, y, and z are distinct single digit primes, then how many gems could be on the imperial scepter if it only contains the gems listed above?

(A) 19

(B) 58

(C) 85

(D) 97

(E) Cannot be determined from the information provided above.
[Reveal] Spoiler: OA

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An imperial scepter is mounted with diamonds, rubies, emeralds, and [#permalink]

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New post 16 Aug 2017, 06:31
The four distinct single digit prime possible are 2,3,5,7
Hence, the scepter is mounted with diamonds, rubies, emeralds, and sapphires in the ratio 2:3:5:7
So we could have 2x+3x+5x+7x or 17x gems.

If x=5, Option C(17*5 = 85) is the number of gems on the imperial scepter.
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New post 16 Aug 2017, 09:45
Bunuel wrote:
An imperial scepter is mounted with diamonds, rubies, emeralds, and sapphires in the ratio of w : x : y : z. If w, x, y, and z are distinct single digit primes, then how many gems could be on the imperial scepter if it only contains the gems listed above?

(A) 19

(B) 58

(C) 85

(D) 97

(E) Cannot be determined from the information provided above.

There are only 4 single digit-prime numbers. The ratio must be 2x : 3x : 5x: 7x.
Total = 17x

The answer must be a multiple of 17.

Answer C, 85 = 17 * 5

Answer C

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Re: An imperial scepter is mounted with diamonds, rubies, emeralds, and [#permalink]

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New post 16 Aug 2017, 12:22
Answer should be E, since as per the given information, any multiple of 17 could be the total number of gems.

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New post 22 Aug 2017, 23:03
Hi,

Why the value of X=5 ? it can be any multiple of 17 i guess

So the answer should be option E

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Re: An imperial scepter is mounted with diamonds, rubies, emeralds, and [#permalink]

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New post 22 Aug 2017, 23:58
There are only 4 distinct single digit primes viz 2,3,5,7.
Hence the ratio might be 2x:3x:5x:7x.

total is 17x.
Answer can be any multiple of 17.
Of the available choices only option C is a multiple of 17. Hence answer is C

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Re: An imperial scepter is mounted with diamonds, rubies, emeralds, and [#permalink]

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New post 08 Sep 2017, 22:04
pushpitkc wrote:
The four distinct single digit prime possible are 2,3,5,7
Hence, the scepter is mounted with diamonds, rubies, emeralds, and sapphires in the ratio 2:3:5:7
So we could have 2x+3x+5x+7x or 17x gems.

If x=5, Option C(17*5 = 85) is the number of gems on the imperial scepter.



Hi pushpitkc
How did you determine that the value of x= 5 ? It could be any value.
I think the ans must be (E). However, the OA is "C", so i think i am missing something.
Can you please guide..?

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Re: An imperial scepter is mounted with diamonds, rubies, emeralds, and [#permalink]

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New post 09 Sep 2017, 00:55
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Hi @Kevinjoshi,

Option E reads it cannot be determined from the information given but 85 is a possibility for the total number of gems on the scepter and therefore, it can be determined!

Hence, the answer has to be Option C

Hope that helps you.
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Re: An imperial scepter is mounted with diamonds, rubies, emeralds, and [#permalink]

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New post 09 Sep 2017, 03:52
The single digit prime numbers are 2 , 3 , 5 , 7
Therefore the ration is w : x : y : z
The number of gems will be multiple of 2a+3a+5a+7a=17a
only 85 is divisible by 17 therefore it is our answer
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Re: An imperial scepter is mounted with diamonds, rubies, emeralds, and   [#permalink] 09 Sep 2017, 03:52
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