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The jewels in a certain tiara consist of diamonds, rubies, and emerald

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The jewels in a certain tiara consist of diamonds, rubies, and emerald  [#permalink]

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New post 06 Feb 2019, 02:03
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Question Stats:

85% (01:14) correct 15% (01:44) wrong based on 13 sessions

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The jewels in a certain tiara consist of diamonds, rubies, and emeralds. If the ratio of diamonds to rubies is 5/6 and the ratio of rubies to emeralds is 8/3, what is the least number of jewels that could be in the tiara?

A. 16
B. 22
C. 40
D. 53
E. 67

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Re: The jewels in a certain tiara consist of diamonds, rubies, and emerald  [#permalink]

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New post 06 Feb 2019, 04:59
Bunuel wrote:
The jewels in a certain tiara consist of diamonds, rubies, and emeralds. If the ratio of diamonds to rubies is 5/6 and the ratio of rubies to emeralds is 8/3, what is the least number of jewels that could be in the tiara?

A. 16
B. 22
C. 40
D. 53
E. 67


d:r:e
D:R= 5:6
R:E= 8:3
we can say
keeping R as common and taking its LCM = 8,6 = 24
we will have
20:24:9
total
20+24+9 = 53
IMO D
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Re: The jewels in a certain tiara consist of diamonds, rubies, and emerald  [#permalink]

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New post 06 Feb 2019, 11:00
Ratio of Diamond/Rubi=5/6
Ratio of Rubi/Emerald=8/3

Since Rubi is common in both the cases, take LCM of 6 and 8=24

So new ratios are
Rubi/Diamond=24/20
Rubi/Emerald=24/9

So the new ratio of Rubi/Diamond/Emerald=24/20/9

Take minimum of 1 for each.
Ans should be 53
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Re: The jewels in a certain tiara consist of diamonds, rubies, and emerald  [#permalink]

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New post 06 Feb 2019, 11:27
Bunuel wrote:
The jewels in a certain tiara consist of diamonds, rubies, and emeralds. If the ratio of diamonds to rubies is 5/6 and the ratio of rubies to emeralds is 8/3, what is the least number of jewels that could be in the tiara?

A. 16
B. 22
C. 40
D. 53
E. 67


D:R
5:6
R:E
8:3

Now make R same in both ratios (LCM=24)

D:R:E
20:24:9

So, least no. of jewels=20+24+9=53
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Re: The jewels in a certain tiara consist of diamonds, rubies, and emerald   [#permalink] 06 Feb 2019, 11:27
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