A contractor combined x tons of a gravel mixture that contained 10 per

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

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

Answer D

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.

Answer (D)

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:
https://gmatclub.com/forum/tough-ds-105651.html#p828579

The answer is D.
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!

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

remember X+Y=Z in que statement

if you will not notice this statement you will land up to another answer

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.

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.

Answer: D.

It's a weighted average problem.
X(10)....5....5.....3.....Y(2)
\(\frac{x}{y}=\frac{3}{5}\)

(1) \(\frac{x}{10}=\frac{3}{5}\), \(x=6\)
(2) \(\frac{x}{y}=\frac{3}{5}\) --> \(\frac{x}{16}=\frac{3}{8}\), \(x=6\)
Answer D

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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


When you modify the original condition and the question, they becomes x+y=z and (10/100)x+(2/100)y=(5/100)z, 10x+2y=5z. Then there are 3 variables(x,y,z) and 2 equations, which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likely to make D the answer.
For 1), when y=10, x+y=z, 10x+2y=5z → x+10=z, 10x+20=z. Since the value of x is unique, it is sufficient.
For 2), when z=16, the value of x is also unique in x+y=16, 10x+2y=80, which is unique and sufficient. Therefore, the answer is D.


 For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

x = 10% gravel
y = 2% gravel.
z = the MIXTURE of x and y = 5% gravel.

To determine the required ratio of x to y, use ALLIGATION -- a very efficient way to handle MIXTURE PROBLEMS.

Step 1: Plot the 3 percentages on a number line, with the percentages for x and y on the ends and the percentage for mixture z in the middle.
x 10%-----------5%-----------2% y

Step 2: Calculate the distances between the percentages.
x 10%-----5-----5%----3-----2% y

Step 3: Determine the ratio in the mixture.
The required ratio of x to y is equal to the RECIPROCAL of the distances in red.
x:y = 3:5.

Since x:y = 3:5, and 3+5 = 8, every 8 tons of mixture z is composed of 3 tons of x and 5 tons of y.

Statement 1: y=10
Since x:y = 3:5 = 6:10, x=6.
SUFFICIENT.

Statement 2: z=16
Since x:y = 3:5 = 6:10, and 6+10 = 16, the 16 tons of mixture z must be composed of 6 tons of x and 10 tons of y.
SUFFICIENT.

The correct answer is D.

Let's use some weighted averages to solve this question
Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...

Target question: What is the value of x ?

Given: 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.
First, we can write: x + y = z

Also, the total weight of the mixture = z (aka x + y)
So, when we apply the above formula, we get: 5% = (x/z)(10%) + (y/z)(2%)
Ignore the % symbols: 5 = (x/z)(10) + (y/z)(2)
Multiply both sides by z to get: 5z = 10x + 2y
Since x + y = z, we can rewrite the above equation as: 5(x +y) = 10x + 2y
Expand: 5x + 5y = 10x + 2y
Simplify to get: 5x - 3y = 0

Now onto the statements!!!!!

Statement 1: y = 10
Replace y with 10 to get: 5x - 3(10) = 0
Solve to get, x = 6
Since we can answer the target question with certainty, statement 1 is SUFFICIENT


Statement 2: z = 16
In other words, x + y = 16

So, we have:
5x - 3y = 0 and x + y = 16
Since we have 2 linear equations with 2 variables, we COULD solve the system for x, which means we COULD answer the target question
So, statement 2 is SUFFICIENT

Answer: D

RELATED VIDEO

Here's a visual graph for this question. This means 2 things:
There's more 2% gravel than 10%
The ratio of 2%/10% mixture is 5/3

Now if we know the values of x, y and z, we will get a sufficient answer.

Both Statement 1 and 2 gives one of those variables, so the answer is D

I think the basic assumption which everyone is undertaking i.e. ( x+y = z ). is flawed. They need to explain that only x+y =z and not 2x+y = z.

Can anyone help me out with this.

Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1

By using weighted average, we can find ratio of x and y from the question itself. Now we need to find x, we know either y or the sum of x and y, which is z. So each statement is sufficient.


[https://www.youtube.com/watch?v=MoiPuM9FEmk]