How many green marbles in R?

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LulaBrazilia: Master | Next Rank: 500 Posts; Posts: 116; Joined: Tue Mar 31, 2009 10:50 amFollowed by: 1 member

by LulaBrazilia » Thu Mar 06, 2014 8:56 am

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

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

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Source: Beat The GMAT — Problem Solving | Thu Mar 06, 2014 8:56 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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

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

Brent Hanneson - Creator of GMATPrepNow.com

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Patrick_GMATFix: GMAT Instructor; Posts: 1052; Joined: Fri May 21, 2010 1:30 amFollowed by: 98 members; Thanked: 335 times

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).

-Patrick

Check out my site: GMATFix.com

To prep my students I use this tool >> (screenshots, video)

Ask me about tutoring.

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

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

R A H U L

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Thu Mar 06, 2014 12:36 pm

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

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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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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

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

Contact Rich at [email protected]

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8152; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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rishab0507: Junior | Next Rank: 30 Posts; Posts: 25; Joined: Tue Jul 16, 2019 4:10 am

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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