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# purple chips

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Senior Manager
Joined: 17 Mar 2009
Posts: 299

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08 Aug 2009, 08:42
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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
Manager
Joined: 18 Jul 2009
Posts: 167
Location: India
Schools: South Asian B-schools

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08 Aug 2009, 18:43
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
_________________

Bhushan S.
If you like my post....Consider it for Kudos

Senior Manager
Joined: 17 Mar 2009
Posts: 299

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08 Aug 2009, 18:55
Thanks for the solution...
Re: purple chips   [#permalink] 08 Aug 2009, 18:55
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