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purple chips

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Senior Manager
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Joined: 17 Mar 2009
Posts: 302

Kudos [?]: 570 [0], given: 22

purple chips [#permalink]

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New post 08 Aug 2009, 09:42
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In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 88,000, how many purple chips were selected?
A)1
B)2
C)3
D)4
E)5

OA:
[Reveal] Spoiler:
B

Kudos [?]: 570 [0], given: 22

Manager
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Joined: 18 Jul 2009
Posts: 168

Kudos [?]: 113 [0], given: 37

Location: India
Schools: South Asian B-schools
Re: purple chips [#permalink]

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New post 08 Aug 2009, 19:43
OA B

we know that point system is B,G,P,R <=> 1,5,x,11 ( with 5<x<11)
thus on factorising 88000 we get 1*(2)^6*(5)^3*11...on comparing with our point chart
we can deduce that x = 2^6....but it cant be 2 as condition ...5<x<11...we can use law of indices such hat base of 2^6 will be changed to something between 5 & 11...only possible combinations for 6 = 1*6 or 2*3 thus we can have following combinations

(2^1)^6 = 2^6 (5<x<11 not satisfied as x = 2)
(2^6)^1 = 64^1 (5<x<11 not satisfied as x = 64)
(2^2)^3 = 4^3 (5<x<11 not satisfied as x = 4)
(2^3)^2 = 8^2 ( satisfied condition)


thus points are 8 and chips = 2 ...OA B
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Bhushan S.
If you like my post....Consider it for Kudos :-D

Kudos [?]: 113 [0], given: 37

Senior Manager
Senior Manager
avatar
Joined: 17 Mar 2009
Posts: 302

Kudos [?]: 570 [0], given: 22

Re: purple chips [#permalink]

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New post 08 Aug 2009, 19:55
Thanks for the solution...

Kudos [?]: 570 [0], given: 22

Re: purple chips   [#permalink] 08 Aug 2009, 19:55
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