How many green marbles in R?

LulaBrazilia wrote:

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

Cheers,
Brent

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

GMAT assassins aren't born, they're made,
Rich

LulaBrazilia wrote:

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