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# In a certain game, a large bag is filled with blue, green

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Intern
Joined: 30 Jul 2017
Posts: 19
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

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05 Jan 2018, 10:48
Bunuel,

I have noticed that you often very kindly post links for many practice questions that belong to the same "micro-concepts" such as in this thread. Is there any way we could get our hands on the questions that are classified according to micro-concepts, I feel like practising all the "number properties" questions, I still encounter various multiple concepts that I should deal with individually.

Furthermore, is there any other way I can deal with this problem?

Thank you.

Best regards.
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Joined: 02 Sep 2009
Posts: 62289
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

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05 Jan 2018, 11:14
1
krikre wrote:
Bunuel,

I have noticed that you often very kindly post links for many practice questions that belong to the same "micro-concepts" such as in this thread. Is there any way we could get our hands on the questions that are classified according to micro-concepts, I feel like practising all the "number properties" questions, I still encounter various multiple concepts that I should deal with individually.

Furthermore, is there any other way I can deal with this problem?

Thank you.

Best regards.

Check our Special Questions Directory.
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Re: In a certain game, a large bag is filled with blue, green  [#permalink]

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19 Apr 2018, 15:10
Top Contributor
enigma123 wrote:
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

This question begs for some prime factorization.

88,000 = (2)(2)(2)(2)(2)(2)(5)(5)(5)(11)

First, we can see that there must be one (11-point) red chip.
Now, what role do these 2's play? Since there are no 2's hiding among the 5-point chips or the 11-point chips, the 2's must be associated with the x-point chips.
Since we know that each purple chip is worth 6,7,8,9 or 10 points, we know that x must equal 6, 8 or 10.

x cannot equal 6, because we don't have any 3's in the prime factorization.
If x were to equal 10, we'd need six 5's to go with our six 2's. Since we don't have six 5's in the prime factorization of 88,000, we can rule out the possibility that x equals 10.

By the process of elimination, x MUST equal 8.
Since 8 = (2)(2)(2), we can see that the six 2's can be used to create two products of 8.

Cheers,
Brent
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Re: In a certain game, a large bag is filled with blue, green  [#permalink]

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15 May 2018, 18:45
Why can't we assume purples value as 10? i.e 2*5 then the answer comes up to 3 and not 2
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Re: In a certain game, a large bag is filled with blue, green  [#permalink]

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15 May 2018, 20:20
sanjanam25 wrote:
Why can't we assume purples value as 10? i.e 2*5 then the answer comes up to 3 and not 2

$$88,000=2^6*5^3*11=2^3*(2^3*5^3)*11=2^3*(10^3)*11$$

In this case we cannot accommodate 2^3. Notice that blue, green, and red chips' values are not multiples of 2. So, 2^6 in 88,000 must be the product of the values of the purple chips drawn.
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Re: In a certain game, a large bag is filled with blue, green  [#permalink]

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02 Sep 2018, 22:48
Break the product 88000 and make it in terms of the points given
=> 88000 = 88 * 10^3
= 8*11*(5*2)^3
=8*11*5^3*2^3
=8*8*5^3*11

Since it's given that 5<x<11 hence X can only be 8 as seen from the breakdown of the product . Since two 8 are present here it means two purple chips are selected

ANS: B
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Re: In a certain game, a large bag is filled with blue, green  [#permalink]

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23 Jan 2019, 19:48
Prime factorize 880000 = 2^6 * 5^3 * 11^1
- 5 and 11 are already given points for green and red (blue need not be considered as point =1)
Now, 2^6 is a potential point for purple – this point has to be between 5 and 11 (given)
Lets see : 2^6 = 64 i.e 8^2 (and 8 does lie between 5 and 11), so 8 can be the point for purple , therefore number of purple chips selected = 2
Ans : B
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Re: In a certain game, a large bag is filled with blue, green  [#permalink]

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18 Feb 2020, 12:53
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Re: In a certain game, a large bag is filled with blue, green   [#permalink] 18 Feb 2020, 12:53

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