# Question: Green Ball

## Comment on Green Ball

### Can you explain why you can't

Can you explain why you can't solve G / 2G + 15? Is there a rule? ### You are referring to the

You are referring to the expression we derive from statement 1. We find that the desired probability = G/(2G + 15)

When you say "solve" you are assuming that there is an equation. What is the equation that we can solve?

All we know from statement 1 is that P(ball is green) = G/(2G + 15)

So, for example, if G = 1, then P(ball is green) = 1/(2 + 15) = 1/17

Conversely, if G = 2, then P(ball is green) = 2/(4 + 15) = 2/19

And so on. Since we cannot answer the target question with certainty, statement 1 is not sufficient.

### Dear Brent, this question

Dear Brent, this question maybe slightly out of Math topic, but I think it is vital.

"There are twice as many X as there as Y", in how we can translate logically this statement? Because I write down from your question that the number of Green is bigger than the number of Red, which is wrong. ### You're not alone. Many

You're not alone. Many students will take the statement ""There are twice as many red balls as there are green balls" and will incorrectly 2R = G

To combat this mistake, first list the two variables: R and G

Then ask yourself, "Which of these numbers is bigger?"

We know that R is twice as big as G. So, R is bigger.

Now ask "What do I need to do to make the values equal?"

Well, it makes no sense to take the bigger number (R) and make it even bigger by multiplying it by 2.

Instead, since G is half as big as R, we should take the smaller number (G) and double its size by multiplying it by 2. This will make the two quantities equal.

We get: R = 2G

### what is the level of this

what is the level of this question? ### If you're referring to the

If you're referring to the video question above, I'd say it's in the 450-500 difficulty range. ### Hi Brent,

Hi Brent,

I think you have mistaken the second statement.

It says that there are twice as many red balls as green balls. So shouldn't the relationship be G=2R.

But you have selected R=2G instead.

Nonetheless, Even if you take G=R/2, the denominator equals to (3/2)G which leads to a P(G)= 2/3. Hence sufficient.

Please let me know if I am missing something?

Thank you,

Ari Banerjee ### It's a very common mistake to

It's a very common mistake to take the given information ("there are twice as many red balls as green balls") and write the equation G = 2R

One way to tell whether you've written a valid equation is to find values for the variables that meet the given condition, and then see if those same values work for the equation you wrote.

So, for example, if there are twice as many red balls as green balls, then there COULD be 6 red balls and 3 green balls.
In other words, R = 6 and G = 3 meets the given condition.

Now let's plug those values into your equation: G = 2R
We get: 3 = 2(6) . . . doesn't work.

Now let's plug those same values into my equation: R = 2G
We get: 6 = 2(3) . . . works!

Here's the process I describe in the video https://www.gmatprepnow.com/module/gmat-word-problems/video/903 :

Once we've identified our variables (G and R), we should first recognize that they are NOT EQUAL.
That is: G ≠ R
As you might imagine, this NON-equation (G ≠ R) doesn't help is at all.
We want to create an EQUATION that we can solve.

So, what do we need to do to turn the NON-equation, G ≠ R, into a useful EQUATION?
Well, we know that G ≠ R, because the value of R is TWO TIMES the value of G ('there are twice as many red balls as green balls").
So, to make these two variables EQUAL, we can take the smaller value (G) and multiply it by 2 to get: 2G = R

Does that help?

Cheers,
Brent