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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.

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16 Aug 2017, 05:31

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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16 Aug 2017, 08:45

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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08 Sep 2017, 21:04

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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08 Sep 2017, 23:55

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This post received KUDOS

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!

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09 Sep 2017, 02:52

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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