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

Question

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

(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

KanishkM · Answer

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

EgmatQuantExpert · Answer

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

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

Archit3110 · Answer

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

option A = 1^2 + 3^2 = 10 
IMO A

ckadams · Answer

_________
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!

All the best,
Rumi

Kinshook · Answer

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.

Asked: What are the weights of the pieces if the value of the diamond reduces by 37.5%?

Let the diamond be broken in x & (4-x) gm pieces

New Value / Previous value = {x^2 + (4-x)^2}/4^2 = (2x^2 - 8x + 16)/4^2 = (1-.375)/1 = .625
x^2 - 4x + 8 = .625*8 = 5
x^2 - 4x + 3 = 0
(x-3)(x-1) = 0
x = 3 or 1
4-x = 1 or 3
The broken pieces are 1 and 3 gms.

IMO A

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

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