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# 1) An even number of marbles, call it "N", are distributed

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Manager
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1) An even number of marbles, call it "N", are distributed [#permalink]  19 May 2004, 10:11
1) An even number of marbles, call it "N", are distributed evenly among 4 jars. These "N" marbles are then re-allocated among the jars so that they are in a ratio now of 1:6:4:8. What is the ratio of marbles moved to the original "N"? (e.g. 3/4N, 1/6N, 1/2N, etc.)
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The question is not very clear to me.

There are N marbles and by dividing among 4 jars we have N/4 in each of them

Now the marbles are moved so that the jars contain marbles as follows

N/19, 6N/19, 4N/19, 8N/19

You can see that N/19 < N/4 and 4N/19 < N/4
All others have more marbles so they cannot be considered.
So no. of marbles moved = N/4-N/19 + N/4- 4N/19 = 9N/38

The ratio is simply 9/38
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Re: Ratio - Marbles [#permalink]  21 May 2004, 14:03
jjomalls wrote:
1) An even number of marbles, call it "N", are distributed evenly among 4 jars. These "N" marbles are then re-allocated among the jars so that they are in a ratio now of 1:6:4:8. What is the ratio of marbles moved to the original "N"? (e.g. 3/4N, 1/6N, 1/2N, etc.)

I got 9/38 too

I plugged a number that divided evenly...Assume there are 76 Marbles (I chose this because its 19*4)

Originally there were 19 in each jar.

Now there are 4, 24, 16, and 32 in jars 1,2,3 and 4 respectively.

A total of 18 marbles had to be moved to achieve the new distribution:
15 out of jar 1, of that 5 go into jar 2 and 10 into jar3
3 out of jar 2, all of which go into jar 3.

The ratio of marbles moved to total marbles is 18/76 or 9/38.
Re: Ratio - Marbles   [#permalink] 21 May 2004, 14:03
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