Author 
Message 
TAGS:

Hide Tags

Senior Manager
Joined: 11 Jun 2007
Posts: 307

A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
Updated on: 02 May 2020, 04:51
Question Stats:
69% (03:15) correct 31% (03:04) wrong based on 219 sessions
HideShow timer Statistics
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). If 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 a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum? A. 36 grams B. 40 grams C. 42 grams D. 48 grams E. 50 grams
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by eyunni on 27 Nov 2007, 19:14.
Last edited by Bunuel on 02 May 2020, 04:51, edited 1 time in total.
Renamed the topic and edited the question.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10477
Location: Pune, India

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
13 Sep 2011, 04:25
bibha 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). If 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 a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum? 36 grams 40 grams 42 grams 48 grams You need to do very few calculations if you understand the relation between the variables. Let's consider the first coin: Volume of Silver = Volume of Aluminum Weight of Silver = 2* Weight of Aluminum Total weight is 30 gms. Since they are in equal volume but silver is twice as heavy, out of 30 gms, silver must be 20 gms and aluminum must be 10 gms. (Think what would happen if it was given that volume of aluminum was twice the volume of silver) Now we need to figure out the relation between the volumes of the two coins. Volume of first coin \(= pi * (15/2)^2 * 2 = (225/2)*pi\) Volume of second coin \(= pi * (15)^2 * 1 = (225)*pi\) Volume of second coin is twice the volume of the first coin. If volume of aluminum in the first coin is V, the volume of the first coin is 2V. The volume of the second coin is 4V. Since it is all Aluminum, volume of Aluminum in the second coin is 4V. Since weight of Aluminum of weight V was 10 gms, weight of Aluminum of volume 4V will be 40 gms.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Manager
Joined: 20 Mar 2010
Posts: 58

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
03 Aug 2010, 00:20
bibha 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). If 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 a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum? 36 grams 40 grams 42 grams 48 grams Coin is in the shape of a cylinder. Coin 1Volume = pi* \(7.5^2\)*2 = 112.5pi cubic mm Total coin weight(including both Aluminium and Silver)= 30g but Silver is twice as heavy as aluminium. So weight of silver = 20g and weight of aluminium =10g Volume of aluminium = Volume of silver volume of aluminium = volume of silver = 112.5pi/2 = 56.25pi So 56.25pi cubic mm of aluminium weighs 10g Coin 2Volume = pi* \(15^2\)*1 = 225pi cubic mm Coin is made of pure aluminium . Also 56.25pi cubic mm of aluminium weighs 10g from above So total weight of the second coin = (10/56.25pi)*225pi = 40g




CEO
Joined: 17 Nov 2007
Posts: 2926
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
09 May 2009, 13:29
Let's move from one coin to another: 1) m1 = 30 g. 2) decrease in thick from 2mm to 1mm: m = 30 * 1/2 3) increase in diameter from 15mm to 30mm: m= 30 * 1/2 * 2^2 4) substitute 1/2 of silver to 1/2 of aluminum: it reduces weight by 3/2 times: m = 30 * 1/2 * 4 * 2/3 = 40 g.
_________________
HOT! GMAT Club Forum 2020  GMAT ToolKit 2 (iOS)  The OFFICIAL GMAT CLUB PREP APPs, musthave apps especially if you aim at 700+



Director
Joined: 05 Jul 2008
Posts: 822

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
09 May 2009, 15:12
walker wrote: Let's move from one coin to another:
1) m1 = 30 g. 2) decrease in thick from 2mm to 1mm: m = 30 * 1/2 3) increase in diameter from 15mm to 30mm: m= 30 * 1/2 * 2^2 4) substitute 1/2 of silver to 1/2 of aluminum: it reduces weight by 3/2 times: m = 30 * 1/2 * 4 * 2/3 = 40 g. You make it look so simple but I am afraid I did not get the tail or head of what you tried to explain. How are you relating weight thickness and diameter? In 2 Are you saying that as thickness decreases weight also decreases and hence divide by 2?? Diameter increased by 2 but why are you multiplying by 2^2 rather than 2? Is it because to account for 2 sides of coin? What really perplexed me is this Sentence The weight of the coin is 30 grams and the volume of aluminum in the alloy equals that of silver.
Can you explain why the weight reduces by 3/2 times? It is talking about weight of the coin and then says volume of AL and Si are same. Its not like they are 15 gms each. Here is the OE and OA Denote S the weight of silver and A the weight of aluminum in the first coin. We can compose an equation: S + A = 30 or 2A + A = 30. Thus, the aluminum half of the coin weighs 10 grams. If the coin were made of pure aluminum, the second half of the coin would also weigh 10 grams and the whole coin would weigh 20 grams. If we look at the proportions of the second coin, we will see that it is twice as large as the first coin (volume2 = \(1(\frac{30}{2})^2 \pi\) ; volume1 = \(2(\frac{15}{2})^2 \pi)\) . The second coin were made of pure aluminum would be twice as heavy as the first coin made of pure aluminum. The answer to the question is therefore 20*2 = 40 grams. The correct answer is B. While the OE makes a lot of sense in the first part, I dont understand what kind of an object are they considering the coin to be? Sphere?



CEO
Joined: 17 Nov 2007
Posts: 2926
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth)  Class of 2011

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
10 May 2009, 06:00
There is a direct way to solve it, as you've posted here: to write a formula of weight for first coin and second coin. After that, express weight of first coin through weight of second coin. I used indirect way. I actually transform our first coin to second coin by means of a few steps as a blacksmith. It seems obvious for me that if we change the thickness of a coin from 2mm to 1mm we have 1/2 m (or 2 coins instead). The same with radius, changing the radius of a coin from 15mm to 30mm we increase area of the coin by 4 and volume (weight) by the same factor. In the case of [Al][Ag] coin, it has weight that equals to [Al][Al][Al] coin, or coin with volume that 3/2 times more. So, we need use 2/3. Anyway, it was the fastest way for me, but if it is not so obvious or fast for you, it would be better to use the direct way.
_________________
HOT! GMAT Club Forum 2020  GMAT ToolKit 2 (iOS)  The OFFICIAL GMAT CLUB PREP APPs, musthave apps especially if you aim at 700+



Manager
Joined: 14 Apr 2010
Posts: 124

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
03 Aug 2010, 02:07
Volume of aluminium = Volume of silver Would you please explain this step??



Manager
Joined: 20 Mar 2010
Posts: 58

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
03 Aug 2010, 18:07
bibha wrote: Volume of aluminium = Volume of silver Would you please explain this step?? See the 2nd statement in the question "volume of aluminum in the alloy equals that of silver". Coin 1 is a mixture of aluminium and silver and in that mixture volume of aluminium is equal to the volume of the silver. So if the total volume of the coin is 112.5pi cubic mm , volume of aluminium in coin1 is 112.5pi/2 cubic mm



Senior Manager
Joined: 03 Mar 2010
Posts: 316

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
12 Sep 2011, 08:26
Coin is basically a cylinder. So volume of coin T= pi r^2 h = pi (7.5)^2 * 2 Coin=Silver+Aluminum Now total volume of coin(T) = volume of silver + volume of aluminum Also, volume of silver(Vs)= volume of aluminum(Va) T= Va+Vb T=2Va Va=T/2= pi (7.5)^2 * 2 /2 = pi (7.5)^2 Silver is twice as heavy as aluminum. Let the weight of aluminum in coin be x Weight of Silver = 2x Total weight of coin = 30 x+2x=30 x=10 Weight of Aluminum in coin is 10gm Wright of Silver in coin is 20gm. Weight of Aluminum in coin is 10gm and volume is pi (7.5)^2 Now new Aluminum coin is made with dimension 1x30mm. Volume of this new coin = pi (15)^2*1. Volume of pi (7.5)^2 contains weight of 10gm of aluminum Volume of pi (15)^2*1 will contain = 10/ pi(7.5)^ * pi (15)^2 * 1= 40gm B.
_________________
My dad once said to me: Son, nothing succeeds like success.



Manager
Joined: 06 Jun 2011
Posts: 66

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
12 Sep 2011, 08:41
Total volume 225*2pi/4 volume of aluminum in the alloy equals that of silver so volume of only aluminum is half of 225*2pi/4 which is 225*pi/4
Total weight 30 gm Silver is twice as heavy as aluminium. So Silver weight in the coin 20 gm and aluminium weight 10 gm
so weight of 225*pi/4 cubic mm of aluminum is 10 gms
Now volume of 1 x 30 mm coin is 225 pi which is 10*4 =40 gms



VP
Joined: 07 Dec 2014
Posts: 1252

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
28 Nov 2015, 17:55
ratio of aluminum weight to volume in smaller coin=10 grams/56.25⫪ mm^3 ratio of aluminum weight to volume in larger coin=w grams/225⫪ mm^3 10/56.25=w/225 w=40 grams



Board of Directors
Joined: 17 Jul 2014
Posts: 2432
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
20 Dec 2015, 17:02
it's a tough one... was confused at the beginning with volume/gr...but since first one has diameter 15, then r=7.5 and h=2. volume is pi*r^2*h = 7.5^2 * 2 * pi = 102.50 now, volume of silver is equal to volume of aluminium, or each 56.25pi. we are told that silver is twice as heavy as aluminium. which means that S+A=30, and 2A+A=30, or A=10gr. now we know that aluminium consists of 56.25pi volume and has 10gr in the mixture.
we need to get a new coin with volume 15^2*1*h, or 225pi. now, 225pi/56,25pi = 4. so we have 4 "volumes" of aluminium. 1 volume of aluminium is 10 gr, thus 4 "volumes" is equal to 4*10=40.



Intern
Joined: 12 Nov 2015
Posts: 42

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
20 Dec 2015, 20:20
The trick is not to confuse weight and volume. They play separate roles here. V/2 measures 10 grams. So,
2V measures 40 grams.



Intern
Joined: 19 Nov 2012
Posts: 26

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
03 Jul 2018, 00:56
VeritasPrepKarishma wrote: bibha 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). If 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 a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum? 36 grams 40 grams 42 grams 48 grams You need to do very few calculations if you understand the relation between the variables. Let's consider the first coin: Volume of Silver = Volume of Aluminum Weight of Silver = 2* Weight of Aluminum Total weight is 30 gms. Since they are in equal volume but silver is twice as heavy, out of 30 gms, silver must be 20 gms and aluminum must be 10 gms. (Think what would happen if it was given that volume of aluminum was twice the volume of silver). Hi Experts: VeritasPrepKarishma, BunuelJust for understanding purposes of this really good sum, what's the ans for "(Think what would happen if it was given that volume of aluminum was twice the volume of silver)" ? Would it be 30? Va/ Vs = 2/1 so now weight 10 corresponds to 66.66% of volume and thus 100% of volume is 15 and twice that is 30. Please confirm. Thanks.



Director
Joined: 04 Aug 2010
Posts: 605
Schools: Dartmouth College

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
03 Jul 2018, 04:00
bibha 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). If 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 a coin measuring 1 x 30 mm made of pure aluminum if silver is twice as heavy as aluminum? 36 grams 40 grams 42 grams 48 grams The height of the second coin (1) is half the height of the first coin (2). The radius of the second coin (15) is twice the radius of the first coin (7.5). We can plug in ANY VALUES for the two heights and two radii such that the relationships above are satisfied. In the first coin, let h=2 and r=1, with the result that the volume of the first coin = \(πr^2h = π(1^2)(2) = 2π\). In the second coin, let h=1 and r=2, with the result that the volume of the second coin = \(πr^2h = π(2^2)(1) = 4π\). The results above indicate that the volume of the second coin is double the volume of the first coin. Implication: If the second coin had the same composition as the first coin  1/2 silver, 1/2 aluminum  the weight would double from 30 grams to 60 grams. Since silver is twice as heavy as aluminum, this 60gram coin would be composed of 40 grams of silver and 20 grams of aluminum. Since the second coin is actually 100% aluminum, the 40gram silver portion above is replaced by another 20 grams of aluminum, reducing the total weight to 40 grams.
_________________
GMAT and GRE Tutor New York, NY
Available for tutoring in NYC and longdistance. For more information, please email me at GMATGuruNY@gmail.com.



NonHuman User
Joined: 09 Sep 2013
Posts: 15018

Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
Show Tags
02 May 2020, 04:18
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________




Re: A coin made of alloy of aluminum and silver measures 2 x 15 mm (it is
[#permalink]
02 May 2020, 04:18




