Question: Minimum Number of Marbles

Comment on Minimum Number of Marbles

it should be B)16
since the ratio blue:red 4:5 so we have 9 mixed blue and red
and the ratio green:blue 4:3 and here we have 7 mixed green and blue.
and the total which can't be below 16 and thus this the minimum !!
gmat-admin's picture

Be careful. Your solution must satisfy BOTH of the given conditions:
blue : red = 4:5
green : blue = 4:3

So, for example, if the bag has 4 blue marbles and 5 red marbles, then how many green marbles are needed to ensure that green : blue = 4:3?

This situation won't work.

If we let x = the number of green marbles, we get:
x : 5 = 4 : 3
If we solve this equation, we get x = 20/3, which is impossible (the number of green marbles must be an integer)

Our goal here is to combine the two ratios so that both ratios are conserved.

For more on this, watch the video "Combining Ratios": https://www.gmatprepnow.com/module/gmat-arithmetic/video/1083

Cheers,
Brent

eyalfuhrer's picture

Nice - I like the logic!

Is there a way to eliminate some answer choices just based on the given ratios (4:3 and 4:5)?

And is this the only approach or technique that can be used to answer this question? Thanks!
gmat-admin's picture

Since we're combining two separate ratios to create one big ratio (with three parts), there's no way to eliminate answer choices based on the two given ratios, since each answer choice is referring to of the big ratio with three parts.

I hope that helps.

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