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Equation with n unknowns. How to find value?

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Equation with n unknowns. How to find value?

by shenseb » Sat Jun 27, 2009 6:26 pm
This is from the OG 12th edition. (PS # : 217)
In a certain game, a container is filled with R / Y / G / B beads worth respectively 7, 5, 3 and 2 points each. A number of beads are then removed from the container. If the product of the removed beads is 147000, how many red beads were removed?
A) 5
B) 4
C) 3
D) 2
E) 0
----------
All that I could formulate is : 7R+5Y+3G+2B=147000
and I know R / Y / G / B are all integer values +
147000 should be a multiple of 7, 5, 3 and 2. But how can I deduce a definite value for R?
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by shibal » Sat Jun 27, 2009 6:53 pm
do the following, brakedown 147000 (easier if u go straight fwd to 147)
147 = 3*7*7
if we have r=7 y=5 g=3 & b=2, 2 red beads were taken, 1 green and 4 yellows & blues....

therefore IMO is 2
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by skalevar » Mon Jul 26, 2010 6:44 pm
Shibal,
I don't quite follow all the way through.

So you know that 147,000 = 7^2 x 3 x 2^3 x 5^3. How does that translate into two red beads being removed?

Can you elaborate a little further?
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by selango » Mon Jul 26, 2010 6:52 pm
shenseb wrote:This is from the OG 12th edition. (PS # : 217)
In a certain game, a container is filled with R / Y / G / B beads worth respectively 7, 5, 3 and 2 points each. A number of beads are then removed from the container. If the product of the removed beads is 147000, how many red beads were removed?
A) 5
B) 4
C) 3
D) 2
E) 0
----------
All that I could formulate is : 7R+5Y+3G+2B=147000
and I know R / Y / G / B are all integer values +
147000 should be a multiple of 7, 5, 3 and 2. But how can I deduce a definite value for R?
Given that 147000 is product of beads[not sum of beads]

So instead of 7R+5Y+3G+2B,we must use 7^R*5^Y*3^G*2^B

7^R*5^Y*3^G*2^B= 7^2x 5^3 x 3 x 2^3

Comparing the base,R=2.

Hope this clarify.
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by Rahul@gurome » Mon Jul 26, 2010 7:09 pm
r - no. of red balls.
y - no. of yellow balls.
g - no. of green balls.
b - no. of blue balls.

1 red ball has 7 points.
So if there are r red balls the product of their points is 7^r.
Similarly product of the points of y yellow balls is 5^y.
Product of the points on g green balls is 3^g.
Product of the points on b blue balls is 2^b.
Their combined product is 147000.
Or (7^r)*(5^y)*(3^g)*(2^b) = 147000. = (2^3)*(3)*(5^3)*(7^2).
To obtain r check for the power of 7 which is 2.

The correct answer is hence (D).
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by skalevar » Tue Jul 27, 2010 6:14 pm
aha. now i see. The keywords were "the product of the point values is 147,000". When I first did the question, I was operating under the assumption that 7*r * 5*y *3*g * 2*b = 147000.

I'll have to pay close attention to that wording next time.
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