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Mixture!

by gmatblood » Sat Nov 05, 2011 2:40 pm
A contractor combined x tons of gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x?

(1) y = 10
(2) z = 16
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Source: — Data Sufficiency |
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by GMATGuruNY » Sat Nov 05, 2011 3:49 pm
gmatblood wrote:A contractor combined x tons of gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x?

(1) y = 10
(2) z = 16
X = 10%.
Y = 2%.
Z = X+Y = 5%.

According to alligation:

The proportion needed of each ingredient in the mixture is equal to the distance between the OTHER two percentages.

Proportion needed of X = |percentage in Z - percentage in Y| = |5-2| = 3.
Proportion needed of Y = |percentage in Z - percentage in X| = |5-10| = 5.
X : Y = 3:5.

Statement 1: Y=10.
Since 3:5 = 6:10, X=6.
SUFFICIENT.

Statement 2: Z=16.
Thus, X+Y = 16.
Since X:Y = 3:5 = 6:10, X=6 and Y=10.
SUFFICIENT.

The correct answer is D.
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by [email protected] » Mon Apr 30, 2012 10:30 pm
GMATguru!!! I have found another method to figure out the answer to this question. If you do not want to solve the question using the above formula and want to use the simple weighted average method to solve the question, then here is it what I used:

The question says that: x tons of a mixture is mixed with y tones of another mixture to form a completely another mixture of z tons of a mixture.

Hence (x + y) = z

Now we come to the weighted average formula:

[10x + 2y]/(x+y) = 5 of the gravel in the z tones of the mixture.

= 10x + 2y = 5 (x+y)

= Now we come to the statement 1: We are given y and hence x can be found out.

Statement 2: since z is given to us hence we can put the values of (x+y) = z in the equation

and also put y in terms of x and z, you get x as 6 again... Substituting the values will certainly help...


The only thing to remember here is that do not divide by (x+y) at the same time equate (x+y) on the right hand side. Then you will not get the answer...

You can also not divide at all and just make the equation as 10x + 2y = 5(x+y)

as dividing is not the thing to do or dividing is not required.

I hope this is correct GMAT guruu...
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by LalaB » Mon Apr 30, 2012 10:37 pm
X-10%-Y-2%
Z-5%

X/Y=(5-2)/(10-5)=3/5

1) Y=10

X/10=3/5
SUFF

2)Z=16
X/16=3/8

SUFF

ANS IS D
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