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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] New post 22 Jan 2012, 16:24
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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

[Reveal] Spoiler:
The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.
[Reveal] Spoiler: OA

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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 22 Jan 2012, 16:33
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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

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.


88,000=2^6*5^3*11, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Answer: B.
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 08 Feb 2012, 19:47
B. 2

Find the prime factors of 88000. Then you will notice that 8 can be formed 2 times.
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 09 Feb 2012, 06:25
Ans is B
given that value of 5<p<11
so now factorizing 88000 we get 5^3*2^6*11
now we split 2^6 in 8^2
so answer is B
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 09 Feb 2012, 06:35
Answer B

Basic information
G<P<R
5<x<11

What is x?

88,000 = 2^6*5^3*11
X can only be 2^6 and must be between 6 and 10, inclusive

2^6 = 64 (value)
Restriction: 2^3 * 2^3 = 8*8 --> 2 purple chips each with a value of 8
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 18 Feb 2012, 23:29
Bunuel wrote:
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

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.


88,000=2^6*5^3*11, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Answer: B.

Bunnel, thanks for the solution. I just had one confusion, we havent considered the blue chips at all
I worked out the number of purple chips as 1, considering blue chips also need to be selected.
Can you please help me clarifying this?
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 19 Feb 2012, 00:07
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raul2011 wrote:
Bunnel, thanks for the solution. I just had one confusion, we havent considered the blue chips at all
I worked out the number of purple chips as 1, considering blue chips also need to be selected.
Can you please help me clarifying this?


Sure. Since blue chips worth 1 point each then # of blue chips selected does not affect the product at all (for ANY product there can be ANY number of blue chips been selected). We are told that the product of the point values of the selected chips is 88,000. Now, # of blue chips selected can be: 0 (88,000=8^2*5^3*11), 1 (88,000=8^2*5^3*11*1), 2 (88,000=8^2*5^3*11*1^2), ..., 1,000,000 (88,000=8^2*5^3*11*1^(1,000,000)), ... basically ANY #.

Hope it's clear.

P.S. By the way, how did you even get that # of purple chips selected as 1 considering blue chips?
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 19 Mar 2012, 00:29
B->1
G->5
P->x; 5<x<11
R->11

NOW, 88000=11*8^2*5^4*1^n

hence
no of balls drawn,
B= CANT BE DETERMINED
G= 4
P= 2 (Only possible value is 8 )
R= 1
hence B
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 17 Apr 2013, 08:39
Bunuel wrote:
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

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.


88,000=2^6*5^3*11, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.
Answer: B.



Hi Bunuel. Is there a easy and fast way to factor the number? It really taking me lots of time, need help. Thanks
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 17 Apr 2013, 08:43
Expert's post
Marchikn wrote:
Bunuel wrote:
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

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.


88,000=2^6*5^3*11, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.
Answer: B.



Hi Bunuel. Is there a easy and fast way to factor the number? It really taking me lots of time, need help. Thanks


Many ways are possible, for example:

88,000 = 88*1000 = 8*11*125*8 = 2^3*11*5^3*2^3 = 2^6*5^3*11.
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 18 Apr 2013, 02:53
Bunuel wrote:
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

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.


88,000=2^6*5^3*11, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Answer: B.


Hi Bunuel.. i would appreciate it if you could answer my query.. After figuring out that the value of purple chip is 8, isnt the following a possible way of picking out chips?

I selected chips according the following table

Blue (1) - 2
Green (5) - 5
Purple (8) - 4
Red (11) - 5

or

Blue (1) - 1
Green (5) - 10
Purple (8) - 2
Red (11) - 10

or

Blue (1) - 2
Green (5) - 2
Purple (8) - 25
Red (11) - 2

There are multiple solutions to this IMO and something wrong with the question
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 18 Apr 2013, 03:10
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Transcendentalist wrote:
Bunuel wrote:
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

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.


88,000=2^6*5^3*11, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Answer: B.


Hi Bunuel.. i would appreciate it if you could answer my query.. After figuring out that the value of purple chip is 8, isnt the following a possible way of picking out chips?

I selected chips according the following table

Blue (1) - 2
Green (5) - 5
Purple (8) - 4
Red (11) - 5

or

Blue (1) - 1
Green (5) - 10
Purple (8) - 2
Red (11) - 10

or

Blue (1) - 2
Green (5) - 2
Purple (8) - 25
Red (11) - 2

There are multiple solutions to this IMO and something wrong with the question


Blue = 1 point;
Green = 5 points;
Purple = x points (5<x<11);
Red = 11 points.

None of the cases you've listed is possible:

Blue (1) - 2
Green (5) - 5
Purple (8) - 4
Red (11) - 5
Product = 5^5*8^4*11^5 not 2^6*5^3*11

Blue (1) - 1
Green (5) - 10
Purple (8) - 2
Red (11) - 10
Product = 5^10*8^2*11^10 not 2^6*5^3*11

Blue (1) - 2
Green (5) - 2
Purple (8) - 25
Red (11) - 2
Product = 5^2*8^25*11^2 not 2^6*5^3*11

Since the product is 88,000=2^6*5^3*11, then there were exactly 3 green chips and 1 red chip selected. Also, from the product it follows that 2^6=64 is the product of the (# of purple chips selected)*(value of a purple chip).

Hope it's clear.
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 19 Apr 2013, 11:43
Very Clear thanks... I just realised i was adding points rather than multiplying them :oops:
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Re: In a certain game, a large bag is filled with blue, green [#permalink] New post 28 Jul 2014, 08:30
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Bunuel wrote:
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

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.


88,000=2^6*5^3*11, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Answer: B.


Similar questions to practice:
in-a-certain-game-a-large-container-is-filled-with-red-yel-144902.html (OG)
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Hope it helps.
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Re: In a certain game, a large bag is filled with blue, green   [#permalink] 28 Jul 2014, 08:30
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