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The value of a diamond is proportional to the square of its weight. A

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The value of a diamond is proportional to the square of its weight. A  [#permalink]

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New post 09 Feb 2019, 12:36
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The value of a diamond is proportional to the square of its weight. A diamond weighing 4 gms falls and breaks into two pieces. What are the weights of the pieces if the value of the diamond reduces by 37.5%?

(A) 1 gm, 3 gm
(B) 1.5 gm, 2.5 gm
(C) 2 gm, 2 gm
(D) 1.2 gm, 2.8 gm
(E) 1.4 gm, 2.6 gm
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Re: The value of a diamond is proportional to the square of its weight. A  [#permalink]

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New post 09 Feb 2019, 13:01
cfc198 wrote:
The value of a diamond is proportional to the square of its weight. A diamond weighing 4 gms falls and breaks into two pieces. What are the weights of the pieces if the value of the diamond reduces by 37.5%?

(A) 1 gm, 3 gm
(B) 1.5 gm, 2.5 gm
(C) 2 gm, 2 gm
(D) 1.2 gm, 2.8 gm
(E) 1.4 gm, 2.6 gm


v proportional to the square of its weight = w^2

Now value 16 is reduced by {375 *1/1000* 16} = 10

Now i need to get a 10
1+9 = 10

Only A does that
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The value of a diamond is proportional to the square of its weight. A  [#permalink]

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New post Updated on: 13 Feb 2019, 22:28

Solution


Given:
    • The value of a diamond is proportional to the square of its weight.
    • A diamond weighing 4 gms falls and breaks into two pieces.
    • The value of the diamond reduces by 37.5%.

To find:
    • The weights of the two broken pieces.

Approach and Working:
Let us assume that original value V = 100.

As the value of a diamond is proportional to the square of its weight, we can say V/w^2 = constant
    • As w = 4 and V = 100, V/w^2 = 100/16 = 25/4

Now, in the individual broken pieces also, this ratio will be maintained.
Considering the first option,
    • If weights are 1 and 3, and corresponding values are V1 and V2, then
    V1/1 = 25/4 indicates V1 = 25/4
    V2/9 = 25/4 indicates V2 = 225/4

Therefore, new value = 25/4 + 225/4 = 250/4 = 62.5, which is 37.5% less than the original value.

Hence, the correct answer is option A.

Answer: A

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Originally posted by EgmatQuantExpert on 10 Feb 2019, 05:55.
Last edited by EgmatQuantExpert on 13 Feb 2019, 22:28, edited 1 time in total.
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Re: The value of a diamond is proportional to the square of its weight. A  [#permalink]

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New post 10 Feb 2019, 09:53
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cfc198 wrote:
The value of a diamond is proportional to the square of its weight. A diamond weighing 4 gms falls and breaks into two pieces. What are the weights of the pieces if the value of the diamond reduces by 37.5%?

(A) 1 gm, 3 gm
(B) 1.5 gm, 2.5 gm
(C) 2 gm, 2 gm
(D) 1.2 gm, 2.8 gm
(E) 1.4 gm, 2.6 gm



value 4 gms = 16
after fall its value = 16*.625 ~ 10

option A = 1^2 + 3^2 = 10
IMO A
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Re: The value of a diamond is proportional to the square of its weight. A  [#permalink]

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New post 12 Feb 2019, 11:54
cfc198 wrote:
The value of a diamond is proportional to the square of its weight. A diamond weighing 4 gms falls and breaks into two pieces. What are the weights of the pieces if the value of the diamond reduces by 37.5%?

(A) 1 gm, 3 gm
(B) 1.5 gm, 2.5 gm
(C) 2 gm, 2 gm
(D) 1.2 gm, 2.8 gm
(E) 1.4 gm, 2.6 gm


_________
It is beneficial to see that 37.5% is equal to 3/8, and 8 is a factor of 16. Thus, computation becomes relatively simple.

4^2 = 16
16 x 3/8 = 6
16 - 6= 10

3^2=9 and 1^2= 1
9+1=10
The only solution that creates 10 is option A.
________
Hope this helps somebody!

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Re: The value of a diamond is proportional to the square of its weight. A   [#permalink] 12 Feb 2019, 11:54
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