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# A coin made of alloy of aluminum and silver measures 2 x 15

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Director
Joined: 11 Jun 2007
Posts: 566
A coin made of alloy of aluminum and silver measures 2 x 15  [#permalink]

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27 Nov 2007, 19:14
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Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 25 sessions

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A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

(A) 36 grams
(B) 40 grams
(C) 42 grams
(D) 48 grams
(E) 50 grams

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Intern
Joined: 25 Nov 2007
Posts: 37

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27 Nov 2007, 19:34
I got B..

Volume of first coin is 56.25(2pi). (volume of cylinder)

So, volume of aluminium portion 56.25 pi.

Because total weight is 30g, AL:AG ratio is 10:20.

Volume of second coin is 225(1pi) its all aluminium

56.25 pi has 10 g
So, 225 pi will have (225*10)/56.25 = 40 g

Whats the OA
SVP
Joined: 29 Mar 2007
Posts: 2433
Re: PS: Aluminium and silver  [#permalink]

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27 Nov 2007, 20:40
eyunni wrote:
A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

(A) 36 grams
(B) 40 grams
(C) 42 grams
(D) 48 grams
(E) 50 grams

V of cylinder is pir^2h ---> 7.5^2*2=112.5pi

56.25=V of S
56.25=V of A

30grams 2A=S so we have 10grams of A 20 grams of S

Vol of pure A coin. 15^2(1)(pi)=225pi

Do a ratio.

10grams/56.25pi(vol)=x/225pi(vol)

56.25pix=2250(g)pi cancel out the pi's. x=40.
Director
Joined: 09 Aug 2006
Posts: 733
Re: PS: Aluminium and silver  [#permalink]

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27 Nov 2007, 21:08
eyunni wrote:
A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is 2 mm thick and its diameter is 15 mm). The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver. What will be the weight of the coin measuring 1 x 30 mm made of pure aluminum if silver is twice heavier than aluminium?

(A) 36 grams
(B) 40 grams
(C) 42 grams
(D) 48 grams
(E) 50 grams

Get B.

Wt of 1st coin = 30 g
Since silver is twice the wt. of aluminum, wt of silver = 20 g and wt of aluminum = 10g

V = (7.5)^2 * 2*pi
Since volume of aluminum = volume of silver, volume of silver = (7.5)^2 *pi

volume of 2nd coin = (15)^2 * pi
Since (7.5)^2* pi represents 10 g of aluminum, (15)^2 * pi will represent:
(10 * 15^2*pi)/(7.5^2*pi) = 40
Director
Joined: 11 Jun 2007
Posts: 566

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29 Nov 2007, 06:16
sorry for the delay. OA is B.
CEO
Joined: 21 Jan 2007
Posts: 2624
Location: New York City

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19 Dec 2007, 00:18
1
A coin is essentially a very flat cylinder.
Volume of a cylinder = Area of circle * Height

Volume of 1st coin
V = pi* (r^2) * H
V = pi * 56.25 * 2
V = 112.5pi

Volume of 2nd coin
V = pi* (r^2) * H
V = pi 225
Thus, the volume of the second coin is twice the first coin.

A + S = 30 grams
A + 2A = 30
A = 10 grams

Since the second coin is all aluminum, we can assume the first coin is all aluminum and that it would weigh 20 grams. Since the second coin is twice the weight of the first coin, the second coin is 40 grams.
Non-Human User
Joined: 09 Sep 2013
Posts: 8848
Re: A coin made of alloy of aluminum and silver measures 2 x 15  [#permalink]

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02 Oct 2017, 01:08
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Re: A coin made of alloy of aluminum and silver measures 2 x 15 &nbs [#permalink] 02 Oct 2017, 01:08
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# A coin made of alloy of aluminum and silver measures 2 x 15

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