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Substance Ratio - Platinum GMAT Problem

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by inertia2010 » Mon Jul 18, 2011 9:27 am
Hi, Can someone provide a better explanation to this problem?

The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10, respectively. Due to a dramatic increase in the surrounding temperature, the composition of the compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the changed compound, if the total weight is 58 lbs, how much does substance x weigh?
A) 48
B) 36
C) 24
D) 12
E) 10

Thanks
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by Frankenstein » Mon Jul 18, 2011 10:01 am
Hi,
x:y:z = 4:6:10
x/y = 2/3 and x/z = 2/5
Now x/y is halved. so x/y = 1/3
y/z is tripled. so x/z = 6/5
So, x:y:z = 6:18:5
weight of x = (6/6+18+5)*58 = 12

Hence, D
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by winniethepooh » Mon Jul 18, 2011 10:05 am
Answer is 12.
Ratio as given:
X--Y---Z
4--6--10
2--3--10

Now change in the temperature causes X--Y to be halved = 2/3 * 1/2= 1--3
Also, X--Z is tripled = 2/5 * 3 = 6/5= 1--0.83333(recurring)

New Ratio:
X--Y---Z
1--3--0.833

So, weight of X in changed compound = 58/4.833(sum of all ratios) ~ 12
Hence,D.
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by GMATGuruNY » Mon Jul 18, 2011 1:48 pm
inertia2010 wrote:Hi, Can someone provide a better explanation to this problem?

The ratio of a compound, by weight, consisting only of substances x, y, and z is 4:6:10, respectively. Due to a dramatic increase in the surrounding temperature, the composition of the compound is changed such that the ratio of x to y is halved and the ratio of x to z is tripled. In the changed compound, if the total weight is 58 lbs, how much does substance x weigh?
A) 48
B) 36
C) 24
D) 12
E) 10

Thanks
Ratio of x:y = 4:6 = 2:3.
To halve a ratio means to multiply it by 1/2:
1/2 * 2/3 = 1/3.
New x:y = 1:3.

Ratio of x:z = 4:10 = 2:5.
To triple a ratio means to multiply it by 3:
3 * 2/5 = 6/5.
New x:z = 6:5.

To combine ratios, the element common to both ratios must be represented by the same value.
The element common to both ratios is x.
In order for x to be represented by 6 in x:y = 1:3, the values in the ratio must be multiplied by 6:
x:y = 1:3 = 6:18.

Combining x:y = 6:18 and x:z = 6:5, we get:
x:y:z = 6:18:5.

The sum of the values in the ratio is 6+18+5 = 29.
The total weight is 58.
Since 58 = 2*29, all the values in the ratio must be multiplied by a factor of 2.
Thus, x=12, y=36, and z=10, yielding a total weight of 12+36+10 = 58.

The correct answer is D.
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