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# The value of a precious stone is directly proportional to the cube of

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BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2282
Location: India
GPA: 3.12
The value of a precious stone is directly proportional to the cube of [#permalink]

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19 Nov 2017, 12:47
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Difficulty:

35% (medium)

Question Stats:

63% (01:24) correct 37% (01:02) wrong based on 46 sessions

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The value of a precious stone is directly proportional to the cube of its weight. If a big stone broke into three parts in the ratio 1:4:5, what was the percentage drop in the value of the stone?

A. 10%
B. 40%
C. 71%
D. 81%
E. 93%

source: Experts Global
[Reveal] Spoiler: OA

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PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1008
Location: India
GPA: 3.82
The value of a precious stone is directly proportional to the cube of [#permalink]

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19 Nov 2017, 13:24
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pushpitkc wrote:
The value of a precious stone is directly proportional to the cube of its weight. If a big stone broke into three parts in the ratio 1:4:5, what was the percentage drop in the value of the stone?

A. 10%
B. 40%
C. 71%
D. 81%
E. 93%

source: Experts Global

Let the original weight of the stone be $$10$$ units

so original price $$P=10^3k=1000k$$, where $$k$$ is any constant

as the stone broke in the ratio $$1:4:5$$, so the weight of the three stones will be $$1$$, $$4$$ & $$5$$. Revised price will be

$$P_1=1^3k=k$$

$$P_2=4^3k=64k$$

$$P_3=5^3k=125K$$

So Total new price $$= k+64k+125k=190k$$

Hence reduction in price $$= 1000k-190k=810k$$

Reduction % $$= \frac{810k}{1000k}*100=81$$%

Option D
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Joined: 16 Aug 2016
Posts: 15
Location: India
GMAT 1: 460 Q35 V19
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WE: Brand Management (Retail)
Re: The value of a precious stone is directly proportional to the cube of [#permalink]

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19 Nov 2017, 13:48
Let's assume initial weight of the precious stone as 10 (1+4+5) and original value as 1000.
As the stone gets broken into 3 parts in the ratio of 1: 4: 5, therefore, the weights of the pieces will be in the same ratio.
Let the value of these 3 pieces be x, y, and z respectively, hence, we get that:
$$\frac{1000}{x}=\frac{10^3}{1^3}$$, or, x=1.
Similarly, $$\frac{1000}{y}=\frac{10^3}{4^3}$$, giving y=64, and
$$\frac{1000}{z}=\frac{10^3}{5^3}$$, giving z=125

Therefore, the new value of the stone will be x+y+z, or, 1+64+125 = 190.

%age change = $$\frac{Old Value - New Value}{Old Value}$$*100

%age change = $$\frac{1000-190}{1000}$$*100 = $$\frac{810}{1000}$$*100 = 81%
Re: The value of a precious stone is directly proportional to the cube of   [#permalink] 19 Nov 2017, 13:48
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