mixtures

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Akansha: Senior | Next Rank: 100 Posts; Posts: 56; Joined: Wed Sep 01, 2010 10:04 amFollowed by: 20 members; Thanked: 1 times

by Akansha » Thu May 26, 2011 9:38 am

A contractor combined x tons of gravel mix that contained 10% gravel G
by weight, with y tons of a mixture that contained 2% gravel G by weight to
produce z tons of a mixture that was 5% gravel G by weight. What is the value of
x? D
a. y = 10
b. z = 16

OA is D

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Source: Beat The GMAT — Data Sufficiency | Thu May 26, 2011 9:38 am

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Thu May 26, 2011 11:15 am

by applying alligation method and mental math we know all percentages of mixture, so we figure average rate and we only need to know one of each mixture agent's weight
|5-10|=5 assigned to y
|2-5|=3 assigned to x
5+3=8; z/8=y/5=x/3
OR
st(1)10/5=x/3 Sufficient
st(2) 16/8=x/3 Sufficient

Akansha wrote:A contractor combined x tons of gravel mix that contained 10% gravel G
by weight, with y tons of a mixture that contained 2% gravel G by weight to
produce z tons of a mixture that was 5% gravel G by weight. What is the value of
x? D
a. y = 10
b. z = 16

OA is D

Success doesn't come overnight!

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clock60: Legendary Member; Posts: 759; Joined: Mon Apr 26, 2010 10:15 amFollowed by: 3 members; Thanked: 85 times

by clock60 » Thu May 26, 2011 11:15 am

here x+y=z, the problem says that
(10x+2y)/(x+y)=5, after little solving
5x=3y, and we need to find x-?
(1)if y=10 and 5x=3y, then it possible to find x, x=6 suff
(2) z=16. and it comes that x+y=z=16. solving with 5x=3y also possible to find x, suff

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hamadah1: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Wed Apr 06, 2011 4:07 am

by hamadah1 » Thu May 26, 2011 2:38 pm

The statement provides us with informations that can be translated into two simple equations:

First one: x+y=z and second one: 0.05z= 0.1x + 0.02y or 5z= 10x + 2y

From (1): y=10 gives us a system of two equations with two unknowns (x and z), therefore x can be found. SUFFICIENT

From (2): z=16 gives us a system of two equations with two unknowns (x and y), therefore x can be found. SUFFICIENT

Both statements are sufficient, therefore the answer is D.

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uslalas22: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Tue Feb 22, 2011 3:33 pm; Thanked: 1 times

by uslalas22 » Thu May 26, 2011 6:49 pm

What exactly is the alligation method? And is it ever beneficial to use, as the last poster broke it down pretty simply and the other two I can't say I followed completely.

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pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Thu May 26, 2011 8:15 pm

z/8=y/5=x/3

I have intentionally derived these ratios for us to see the legitimacy of alligation method.
Certainty comes with definitions.
The ways you or me would define a problem most probably are followed by
-assigning variables, the first
-finding the relationship, the second
-solving for variables, the third

with alligation method you've all three set - just need to solve one-two practice problems beforehand for applying alligation when needed.

uslalas22 wrote:What exactly is the alligation method? And is it ever beneficial to use, as the last poster broke it down pretty simply and the other two I can't say I followed completely.

Success doesn't come overnight!

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abhijit_ghonge: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Wed Oct 20, 2010 9:20 pm; Location: Mumbai, India

by abhijit_ghonge » Thu May 26, 2011 10:08 pm

I think we could have a simple approach:
from statement, we can have 2 equations straight:
1. x+y=z
2. x/10 + y/50 = z/20

From A, y= 10, which brings down above equation to "2 equations, 2 unknowns". A is sufficient.
From B, z=16, again "2 equations, 2 unknowns". Without even going ahead for the complete solution we can say that 'D' is the answer.

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