A contractor combined x tons of a gravel mixture that : GMAT Data Sufficiency (DS)
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# A contractor combined x tons of a gravel mixture that

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28 Jan 2010, 14:07
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A contractor combined x tons of a 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
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Mar 2012, 11:02, edited 1 time in total.
Edited the question
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28 Jan 2010, 15:25
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ugimba wrote:
119.A contractor combined x tons of a 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

Set the equation: $$0.1x+0.02y=0.05(x+y)$$, where $$x+y=z$$ --> $$5x=3y$$ --> Q: $$x=?$$

(1) $$y=10$$ --> $$5x=3y=30$$ --> $$x=6$$. Sufficient.

(2) $$z=x+y=16$$ --> $$y=16-x$$ --> $$5x=3y=3(16-x)$$ --> $$x=6$$. Sufficient.

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15 Jun 2010, 04:53
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What does the prompt tell us?

x + y = z

0.1x + 0.02y = 0.05z

We have to find x. If you notice, we have two equations in 3 variables, so if we are given a value for either y OR z, this is sufficient to calculate x.

1. Gives us y. Sufficient.

2. Gives us Z. Sufficient.

Pick D.
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Re: x tons of a gravel mixture [#permalink]

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15 Jun 2010, 11:19
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Goofed on this and answered B too quickly.

D it is...

we have .01x+.02y=.05z & x+y=z

1) y=10 means -> z-x=10, plug the numbers.
2) z=16 means -> x+y=16, plug the numbers
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15 Aug 2010, 23:34
lalithajob wrote:
A contractor combined x tons of a gravel mixture 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?

1. y = 10
2. z = 16

x + y = z ( x tons of mixture1 + y tons of mixture2 = z tons of combined mixture)
.1x + .02y = .05z (gravel in mixture1 + gravel in mixture2 = gravel in combined mixture)

x= ?

1) y=10. 3 equations(2 from the question + 1 from answer choice) with 3 unknowns. Can solve for x. Sufficient
2) z=16. 3 equations(2 from the question + 1 from answer choice) with 3 unknowns. Can solve for x. Sufficient

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15 Aug 2010, 23:35
Hello,

From above we have:
0.1x + 0.02y = 0.05z
x+y = z
Thus,
0.1x + 0.02y = 0.05(x+y)
0.05x=0.03y
5x=3y

Statement 1
y=10 thus x =6 sufficient

Statement 2
z=16=x+y
and we have 5x=3y
Thus we have 2 equations with 2 unknowns; we can find x. Again sufficient.
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Re: x tons of a gravel mixture [#permalink]

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17 Aug 2010, 12:05
Question:
For these types of questions can you always do
Z=X+Y?

This is the first question that I've seen like this.
I'm not sure if I would have gone with Z=X+Y, as Z could have been the combination X+Y and some other non-gravel material
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11 Oct 2010, 21:35
The answer in my opinion should be D)

By condition ,

10% X + 2% Y = 5 % Z ---(1)
Also X + Y = Z ---(2)

Option (A) is sufficient to get the value of X by substituting the value of Y = 10
Option (B) is sufficient to get the value of X by substituting the value of Z = 16
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26 Dec 2010, 22:06
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anilnandyala wrote:
a contractor combined x tons ofa gravel mixture 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 by weight. what is the value of x?

y = 10
z = 16

Using scale method here, since 10% and 2% give weighted average of 5%, x:y = 3:5
We also know x + y = z.

1. y = 10.
If y = 10, x = 6 since their ratios must be 3:5. Sufficient.

2. z = 16
If sum of x and y is 16, x must be 6 and y must be 10 to give a ratio of 3:5.

If this is not intuitive, think of it this way:
x : y...... x + y
3 : 5...... 8
Since 8 in ratio terms is actually 16, 3 is actually 6 and 5 is actually 10.

It will be worth your while if you understand the scale method. The time saving is huge and weighted average is a concept you will need to use time and again. For explanation of scale method, check this link:
http://gmatclub.com/forum/tough-ds-105651.html#p828579
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12 Mar 2011, 22:38
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I was flummoxed on this one since at first I thought it was C, then I looked at it closer and thought it was B. Now I see how A and B are sufficient.
Crazy DS - I HATE YOU!
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12 Mar 2011, 22:41
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Easy way to solve this problem:
X lbs + Y lbs = Z lbs

Given 10% X + 2% Y = 5% Z
1) Y=10
2 eqns, 2 unknowns, solve!

2)Z= given.
Same as above, solve
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13 Mar 2011, 10:38
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0.1x+0.02y=0.05(x+y)
1. suff.
2. x+y=16
y=16-x suf..

d ans
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22 Apr 2011, 23:09
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remember X+Y=Z in que statement

if you will not notice this statement you will land up to another answer
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23 Apr 2011, 07:51
Using the method of alligations,
10:2
5
3:5
The quantities of x and y = x:y=3:5
z=8
So any one of the variables y and z will give the variable x

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Re: A contractor combined x tons of a gravel mixture that [#permalink]

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15 Apr 2012, 15:37
Can anyone please explain on X+Y=Z in que statement. I definitely missed it and ended up with answer C
Where in question it says that x+y=z?
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15 Apr 2012, 15:40
Can anyone please explain on X+Y=Z in que statement. I definitely missed it and ended up with answer C
Where in question it says that x+y=z?

Sure. Question says: "A contractor combined x tons of a 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."

Hope it's clear.
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13 Jun 2013, 01:15
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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09 May 2014, 04:55
A contractor combined x tons of a gravel mixture that contained 10 percent 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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09 May 2014, 05:02
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Set the equation: 0.1x+0.02y=0.05(x+y), where x+y=z --> 5x=3y --> Q: x=?

(1) y=10 --> 5x=3y=30 --> x=6. Sufficient.

(2) z=x+y=16 --> y=16-x --> 5x=3y=3(16-x) --> x=6. Sufficient.

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09 May 2014, 05:54
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vikasogs wrote:
A contractor combined x tons of a gravel mixture that contained 10 percent 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

Merging similar topics. Please refer to the discussion above.

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