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

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

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25 May 2008, 19:03
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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
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25 May 2008, 19:56
chineseburned 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

since its the product value,

88000 = 11^1 * 5 ^3 * [either 2^6 or 8^2]

since its given that The purple chips are worth more than the green chips, but less than the red chips.

x =8 and 2 purple chips are selected.

Thus B)2
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26 May 2008, 09:43
chineseburned 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

I get 2 as well..

88,000=1*5^3 * 11* (2^6) but we cant have 2^6 since we are told that purple is greater than 5..so 2^6=8^2...

8 is the value of the chip and there 2 of them..
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27 May 2008, 17:12
alpha_plus_gamma wrote:
chineseburned 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

since its the product value,

88000 = 11^1 * 5 ^3 * [either 2^6 or 8^2]

since its given that The purple chips are worth more than the green chips, but less than the red chips.

x =8 and 2 purple chips are selected.

Thus B)2

How do you know to break-down 88,000 into $$11^1 * 5^3$$ and so on?
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27 May 2008, 19:23
brokerbevo wrote:
alpha_plus_gamma wrote:
chineseburned 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

since its the product value,

88000 = 11^1 * 5 ^3 * [either 2^6 or 8^2]

since its given that The purple chips are worth more than the green chips, but less than the red chips.

x =8 and 2 purple chips are selected.

Thus B)2

How do you know to break-down 88,000 into $$11^1 * 5^3$$ and so on?

It's called getting the prime box of a number - every number can be represented as a product of prime numbers, some of which may be repeated and hence the powers in the representation.
In this case it is easy to spot that 88 is 11*8=11*2^3. Then you have to account for the 1000 remaining, which is 10^3= 2^3*5^3. Combining all those you get 11^1*5^3*2^6.
Knowing the prime factors helps you figure out the only possible value for the purple chips (which the stem says are between 6 and 10 inclusive). The only number you can get from the prime factors above in that range is 8=2^3. Therefore, purple chips are worth 8 points each.
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Re: PS: chips   [#permalink] 27 May 2008, 19:23
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