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

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

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03 May 2018, 17:39
ScottTargetTestPrep wrote:
jusjmkol740 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

88,000 = 88 x 1000 = 11 x 8 x 10 x 100 = 11 x 2^3 x 5 x 2 x 5^2 x 2^2 = 2^6 x 5^3 x 11^1

We see that there could be any number of blue chips since they are worth 1 point each. The prime factor 5^3 tells us that the number of green chips must be 3 since they are worth 5 points each. The prime factor 11^1 indicates that the number of red chips must be 1 since each red chip is worth 11 points. Thus, the product of the point values of purple chips must be 2^6. Since each purple chip is worth between 5 and 11 points, and the value of a purple chip must be a power of 2, each purple chip must be worth 2^3 = 8 points, since 8 is the only power of 2 between 5 and 11. Since 2^6 = 8^2, there must be 2 purple chips.

ScottTargetTestPrep & Bunuel

What if I say that 11 indicates 1 Red while 5^2 indicates ONLY 2 Greens. In this case, I'll end up having 5 x 2^6. I will say that Purple worth 10, so I'll have one purple & the remaining will be Blues. So Answer will be A. What's wrong in my approach?
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Re: In a certain game, a large bag is filled with blue, green, purple and  [#permalink]

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03 May 2018, 18:28
Hi hisho,

I think that you made a math mistake. Three of the chip values are 'fixed' (re: 1, 5 and 11); if you make the fourth value 10, then how can you get to a product of 88,000? The "2s" that you need are not there.

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

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04 May 2018, 03:32

I'm assuming here that I've the following:
1 RED => 11
2 GREEN => 5^2
32 BLUE => 32
1 PURPLE => 5 x 2 (assuming the purple = 10)

so the product will be: 11 x 5^2 x 5 x 2 x 32 = 88,000.
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Re: In a certain game, a large bag is filled with blue, green, purple and  [#permalink]

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04 May 2018, 09:11
1
Hi hisho,

Since each blue chip is worth "1" - and we're taking the PRODUCT of each of those values, we're dealing with 1^32 = 1. In your calculations, you're taking (32)(1) = 32, which is not what the prompt tells us to do.

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

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04 May 2018, 09:23
2
hisho wrote:
ScottTargetTestPrep wrote:
jusjmkol740 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

88,000 = 88 x 1000 = 11 x 8 x 10 x 100 = 11 x 2^3 x 5 x 2 x 5^2 x 2^2 = 2^6 x 5^3 x 11^1

We see that there could be any number of blue chips since they are worth 1 point each. The prime factor 5^3 tells us that the number of green chips must be 3 since they are worth 5 points each. The prime factor 11^1 indicates that the number of red chips must be 1 since each red chip is worth 11 points. Thus, the product of the point values of purple chips must be 2^6. Since each purple chip is worth between 5 and 11 points, and the value of a purple chip must be a power of 2, each purple chip must be worth 2^3 = 8 points, since 8 is the only power of 2 between 5 and 11. Since 2^6 = 8^2, there must be 2 purple chips.

ScottTargetTestPrep & Bunuel

What if I say that 11 indicates 1 Red while 5^2 indicates ONLY 2 Greens. In this case, I'll end up having 5 x 2^6. I will say that Purple worth 10, so I'll have one purple & the remaining will be Blues. So Answer will be A. What's wrong in my approach?

While your approach is certainly creative, some of the math doesn’t quite work out.

If each purple chip = 10 points, then the product 5 x 2^6 = 5 x 64 = 320.

Now, 10 x 32 = 320 or 10 x 2^5 = 320, so what happened to the factor 2^5? You said it goes to the remaining blue chips. But the blue chips are not 2 points each; the blue chips are only 1 point each. (So the product of the points from the blue chips is always 1^n = 1 for any value of n.) There is no way for the product of the points from blue chips to be 32. (You perhaps overlooked the given information in the question that the blue chips are 1 point each, not 2 points each.)
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Re: In a certain game, a large bag is filled with blue, green, purple and  [#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, purple and  [#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, purple and  [#permalink]

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24 May 2020, 23:00
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Re: In a certain game, a large bag is filled with blue, green, purple and   [#permalink] 24 May 2020, 23:00

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