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beads question

by vaivish » Wed Jun 25, 2008 10:09 am
In a certain game, a large container is filled with red, yellow, green and blue beads worth, resply 7, 5, 3 and 2 pts each. A no. of beads are then removed from the container. If the product of the point values of the removed beads is 1,47,000. How many red beads were removed?

A) 5
B) 4
C) 3
D) 2
E) 0
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by atlantic » Wed Jun 25, 2008 10:29 am
Vavish,

This is a factoring problem.

You can see that the points on the beads are prime factors.

So try do prime factor 147,000.

That can be 7*7*3*5*2*2*2......., in fact you can forget about the numbers to the right of ',' because those will not give any '7'. Notice that the product of the first three primes is in fact 7*7*3=147

So number of red beads is 2. Pick D
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by vaivish » Wed Jun 25, 2008 10:52 am
great thanks..
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by phumbert » Sun Jul 27, 2008 5:42 pm
I still am struggling with this. Can someone please point out the flaw in my following logic?

With 147,000 points, I know that i can ignore the "000" because the other beads make up those points. So I am now left with 147. With each red bead worth 7 points, I simply divided 147 by 7, getting 21. With 7 dividing into 147 equally, my assumption is that no red beads were taken away (E). Clearly I am not correct, but where am I going wrong?? Thanks in advance!
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by preetha_85 » Sun Jul 27, 2008 10:37 pm
Hi

Since the points are given as 7,5,3,2 . U need to pick up the beads in such a way that
7^x* 3^y*2^z*5^w =147000
The no can be taken as 147 since we r intrested only in the value of x (since 7 does not exactly divide 1000)

So.. 7^x* 3^y =147
THis is possible when x=2 nd y=1 . Hence D is the answer not E.

Hope this is clear
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