Official Solution:

A basket contains red, blue, and green marbles in a 2:3:5 ratio. If there are 9 more green than red marbles, how many more green marbles than blue marbles does the basket contain?

A. 3
B. 5
C. 6
D. 8
E. 9

If \(x\) is an integer, the number of red marbles can be expressed as \(2x\), the number of blue marbles as \(3x\), and the number of green marbles as \(5x\). It follows from the stem that \(5x - 2x = 3x = 9\) from where \(x = 3\). So, there are \(5*3 = 15\) green marbles and \(3*3 = 9\) marbles in the basket. The difference is \(15 - 9 = 6\).

Answer: C
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Use concept of ratios. Let the number of Red , Blue , & Green balls be 2x,3x, & 5x. Given 5x-2x=9 , i.e. 3x=9 that is x=3. We need to find out 5x-3x or 2x. The value is 2*3 or 6. The answer must be option C.
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Good question. I did the calculation in my head this way.

Adding up the ratio of the marbles the 2 + 3 + 5 = 10 total marbles. It could be any multiple of this, but it is 10 in my hypothetical world.

If the difference between the Green and the Red is (5 - 2) = 3, then the ratio of the difference is 3 marbles difference /10 total marbles. And the question gives you the difference is worth 9 marbles. So you have a mental ratio of "If 3/10 equals 9 marbles, how many total marbles are in there" - the answer is 30 marbles total.

Then you plug back in the ratio of 2:3:5 to get the numbers of each marble and do the math to get the difference.



But maybe SpetNaz's solution is a tad bit easier than mine.