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# The value of an alloy varies directly with the concentration of metal

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Manager
Joined: 07 Jun 2017
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The value of an alloy varies directly with the concentration of metal  [#permalink]

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22 Oct 2017, 22:34
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55% (hard)

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59% (01:48) correct 41% (02:15) wrong based on 270 sessions

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The value of an alloy varies directly with the concentration of metal A and inversely with the square of the concentration of metal B. If the concentration of metal B has been increased by 30%, by approximately what percentage should the concentration of metal A be increased to avoid a drop in the value of the alloy?

A. 15%
B. 30%
C. 60%
D. 70%
E. 80%

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Re: The value of an alloy varies directly with the concentration of metal  [#permalink]

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22 Oct 2017, 22:42
16
IMO option D.
Let the value = V
v=k*x/$$y^{2}$$
The concentration of y has increased by 30%
New value =v=k*x/1.69 $$y^{2}$$
So to compensate the drop in value the concentration of A should approximately increase by 70%.
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Re: The value of an alloy varies directly with the concentration of metal  [#permalink]

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14 Nov 2017, 05:20
2
Plug in numbers
As per the question
V=value is directly proportional to conc of A and inversely prop of square of B or V=kA/B^2. (k is constant)
Let A=10 and B=10
we have V=10/(10)^2=10/100=1/10.
We have value of V =1/10
and
the new value of Y which is 30% more ie it is 13 now (10+30% of 10)
and
we now need to find the new A so that V remains=1/10
(1/10)=A/(13)^2=1/10=A/(169) or New A=16.9 which is 6.9 more than earlier A or approx 70% more. Answer D
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Re: The value of an alloy varies directly with the concentration of metal  [#permalink]

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14 Nov 2017, 05:36
2
let the initial concentration of A & B = 100 each
Value = K *100/ 100^2
New value = K * x /130^2
Equating we get x = 169
increase required in A = 69% that is approx 70%. Hence Answer is D
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The value of an alloy varies directly with the concentration of metal  [#permalink]

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18 Nov 2017, 12:35
nkmungila wrote:
The value of an alloy varies directly with the concentration of metal A and inversely with the square of the concentration of metal B. If the concentration of metal B has been increased by 30%, by approximately what percentage should the concentration of metal A be increased to avoid a drop in the value of the alloy?

A. 15%
B. 30%
C. 60%
D. 70%
E. 80%

hi

former expression

B^2
_____
A

later expression

(1.3 B)^2
_________
A

to keep the later expression approximately the same in value as the former expression, A should be increased by 70% , as (1.3)^2 = 1.69

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Joined: 25 Feb 2018
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Re: The value of an alloy varies directly with the concentration of metal  [#permalink]

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23 May 2018, 00:11
consider A = B = 100
Value = x*100/ 100^2
New value = x * y /130^2
Equating we get y = 169
A=70%.
Intern
Joined: 11 Jun 2018
Posts: 1
Re: The value of an alloy varies directly with the concentration of metal  [#permalink]

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27 Jun 2018, 16:12
I have a question on the theory behind this. If Value =AB and since (1.3)^2 New Value = A(1.69B), wouldn't A have to be multiplied by 1/1.69 such that such that value = constant? 1/1.69 translates into ~60%. Why is the answer not C?

Wouldn't D be wrong because 1.69 x (7/10) not equal to 1?
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Joined: 07 Dec 2014
Posts: 1129
Re: The value of an alloy varies directly with the concentration of metal  [#permalink]

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27 Jun 2018, 18:01
nkmungila wrote:
The value of an alloy varies directly with the concentration of metal A and inversely with the square of the concentration of metal B. If the concentration of metal B has been increased by 30%, by approximately what percentage should the concentration of metal A be increased to avoid a drop in the value of the alloy?

A. 15%
B. 30%
C. 60%
D. 70%
E. 80%

let x=increase in concentration of A
A/B^2=Ax/(1.3B)^2
➡Ax*B^2=A*1.69B^2
➡x=1.69≈70% increase
D
Re: The value of an alloy varies directly with the concentration of metal &nbs [#permalink] 27 Jun 2018, 18:01
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