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How many green marbles in R?

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by Brent@GMATPrepNow » Thu Mar 06, 2014 9:07 am
LulaBrazilia wrote:Image

In the table above, what is the number of green marbles in jar R?

A) 70
B) 80
C) 90
D) 100
E) 110
From the table, we see that z = the number of green marbles in jar R, so our goal is to find the value of z.

There are many ways to do this. Here's one way.

Jar R: x + z = 160
Jar P: x + y = 80
SUBTRACT bottom equation from top equation: (x + z) - (x + y) = 160 - 80
Simplify: z - y = 80
Now that we have created an NEW equation involving the variables x and y, we can combine it with the equation we can create with Jar Q

So, we have:
New equation: z - y = 80
Jar Q: z + y = 120
If we ADD the two equations, we get: (z - y) + (z + y) = 80 + 120
Simplify: 2z = 200
Solve: z = 100

Answer: D

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by Patrick_GMATFix » Thu Mar 06, 2014 9:12 am
Good question. Each row corresponds to a linear equation. Write them out and isolate what you're looking for. The answer is D. I go through the question in detail in the full solution below (taken from the GMATFix App).

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by theCodeToGMAT » Thu Mar 06, 2014 9:27 am
TO find = z

x + y = 80 - (1)
y + z = 120 - (2)
x + z = 160 - (3)

Add (3) by (2)

(x + y) + 2z = 280

we know x + y = 80

So, 2z = 200 => z = 100
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by GMATGuruNY » Thu Mar 06, 2014 12:36 pm
LulaBrazilia wrote:Image

In the table above, what is the number of green marbles in jar R?

A) 70
B) 80
C) 90
D) 100
E) 110
The table implies the following equations:
x+y = 80
y+z = 120
x+z = 160.

An alternate approach is to PLUG IN THE ANSWERS, which represent the value of z.
When the correct answer choice is plugged in, x+y = 80, as indicated by the top equation.

Answer choice C: z=90
y+90 = 120 --> y=30.
x+90 = 160 --> x=70.
x+y = 70+30 = 100.
x+y is too big.
To decrease the value of x+y, we must INCREASE the value of z.
Eliminate A, B and C.

Answer choice D: z=100
y+100 = 120 --> y=20.
x+100 = 160 --> x=60.
x+y = 60+20 = 80.
Success!

The correct answer is D.
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by [email protected] » Thu Mar 06, 2014 6:50 pm
Hi LulaBrazilia,

Complex-"looking" prompts can often hide hidden patterns that will help you to reduce the amount of work you need to do to answer the question.

The question asks us for the number of green marbles in Jar R, so we're asked "what is the value of Z?"

In the table, you might notice that each variable shows up EXACTLY TWICE, so if we add all of the equations together, we have...

2X + 2Y + 2Z = 360

So...

X + Y + Z = 180

Notice in Jar P....X + Y = 80

Combining these two equations gives us the value of Z.....100

Final Answer: D

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by Scott@TargetTestPrep » Thu May 21, 2015 10:18 am
LulaBrazilia wrote:Image

In the table above, what is the number of green marbles in jar R?

A) 70
B) 80
C) 90
D) 100
E) 110
Solution:

We can create three equations from the information presented in the table.

Equation 1: x + y = 80

Equation 2: y + z = 120

Equation 3: x + z = 160

These equations present us with a good opportunity to use the "combination method" to solve multiple equations. Here, we can add equations together. Because we need the number of green marbles in jar R, we need to determine the value of z.

We can start by multiplying equation 1 by -1.

-1(x + y = 80)

-x - y = -80

Next, we add this equation to equation 2. So we have:

-x - y = -80
z + y = 120
z - x = 40

Now we can add z - x = 40 to equation 3. So we have:

-x + z = 40
x + z = 160
2z = 200
z = 100

The answer is D

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by rishab0507 » Sat Sep 07, 2019 8:39 am
This question can be solved by various ways, but some can be lengthy enough to kil time on gmat, you need to solve this under 1 min as it looks like sub 600 level question.
3 variables, 3 equations, ques can be solved. But if you try to first find value of 1 variable using 2 equation and then put in 3rd is a lengthy process.
We need to find Z ,green balls, and R .
Rather just add all 3
Adding all 3 equations:
2x+2y+2z =360
diving by 2 : x+y+z =180,
now value of x+y= 80 from eq 1
So z = 100

this is faster way to get to solution
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