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# question5 of 40 inside an urn, the ratio of red to blue

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Manager
Joined: 03 Jun 2003
Posts: 84
Location: Uruguay
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question5 of 40 inside an urn, the ratio of red to blue [#permalink]  11 Jul 2003, 07:16
question5 of 40

inside an urn, the ratio of red to blue marbles is 3:8, and the ratio
of blue to green marbles is 5:8. if the sum of red, green, and blue
marbles is 238, how many of the marbles are green?

Ο 30
Ο 64
Ο 80
Ο 128
Ο 208

confirm next

I cannot get this question right. Help!!!!

of the 60 students of the i.t. class of 2003 at ucberkeley, 30 use a
mac, 20 use a sparc workstation, and 20 use an sgi. 13 use both
mac and sparc, 5 use both mac and sgi, and 8 use both sgi and
sparc. if 5 of the students use all three, how many don't use any of
the three (not a mac, not a sparc, not an sgi, but maybe a crappy
WIntel machine)?

Ο 0
Ο 5
Ο 10
Ο 11
Ο 12
Manager
Joined: 10 Jun 2003
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First Question [#permalink]  11 Jul 2003, 08:37
The first step in this problem was to make the ratio relating all there marble colors: this would be 3:8:(64/5).

Now to convert all of these to the LCD: (15/5):(40/5):(64/5)

Adding up the numerators you get 119, conveniently half of the total number of marbles! So, each of the numerators represents half of the number of that color marble. So there will be 128 Green marbles.
Manager
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Computers [#permalink]  11 Jul 2003, 08:41
For the second question I get 11 - just by setting up a Venn diagram. The tricky part was that the combination of two INCLUDES the combination of all three!
SVP
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1. 128
2. 11

Solution for the second
Let N be be the number of people who use none.
So, V-diagram shoul be

60–N=Mac + Spark + SGI – (only Mac&Spark) – (only Mac&SGI) – (only SGI&Spark) – 2*(all the three)

only Mac&Spark = 13–5 (all the three are out)=8
only Mac&SGI = 5–5=0
only SGI&Spark = 8–5=3

Finally, 60–N=30+20+20–8–3–0–2*5
N=11

Manager
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You are right.
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