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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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22 Jan 2012, 17:24
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Question Stats:

68% (01:23) correct 32% (01:47) wrong based on 664 sessions

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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]

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22 Jan 2012, 17:33
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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.

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

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09 Feb 2012, 07:35

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]

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19 Feb 2012, 00:29
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.

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.

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

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19 Feb 2012, 01:07
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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.

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]

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19 Mar 2012, 01:29
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]

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17 Apr 2013, 09:39
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.

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]

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17 Apr 2013, 09:43
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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.

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]

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18 Apr 2013, 03:53
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.

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]

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18 Apr 2013, 04:10
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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.

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]

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28 Jul 2014, 09:30
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.

Similar questions to practice:
in-a-certain-game-a-large-container-is-filled-with-red-yel-144902.html (OG)
a-cargo-ship-carrying-four-kinds-of-items-doohickies-geega-167523.html (Veritas Prep)

Hope it helps.
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Re: In a certain game, a large bag is filled with blue, green [#permalink]

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06 Nov 2014, 12:12
Hi Bunuel,

I noticed that you went directly to 8. Why didn't you consider 6 or 10 as the possible point values for the chips?

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

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07 Nov 2014, 03:56
russ9 wrote:
Hi Bunuel,

I noticed that you went directly to 8. Why didn't you consider 6 or 10 as the possible point values for the chips?

We are told that "the purple chips are worth more than the green chips (5), but less than the red chips (11)" and it's a power of 2, so it must be 8.
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Re: In a certain game, a large bag is filled with blue, green [#permalink]

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03 Jun 2015, 02:38
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Why can't I calculate it this way:

88000 = 11 * 8 * 1000 -> 1 chips of 11 points, 1 chip of 8 points (purple), and 200 chips of 5 points (green)?

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

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03 Jun 2015, 03:04
ashishcromp2k wrote:
Why can't I calculate it this way:

88000 = 11 * 8 * 1000 -> 1 chips of 11 points (red), 1 chip of 8 points (purple), and 200 chips of 5 points (green)?

If you have 200 5-point green chips the product you will get is 5*5*...*5 = 5^200 not 5*200.
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Re: In a certain game, a large bag is filled with blue, green [#permalink]

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03 Jun 2015, 16:38
Hi All,

This question involves a bit of logical thinking and factoring skills. You have to take notes and stay organized though, if you want to answer this question correctly.

We're told:
Blue chips = 1 point each
Green chips = 5 points each
Purple chips = X points each (more than Green, less than Red, so X = 6, 7, 8, 9 or 10)
Red chips = 11 points each

We're told that taking an unknown number of chips gives us a product equal to 88,000; we need to factor 88,000 and we should look specifically for 5s, 11s and some mystery number between 6 and 10, inclusive….

88,000 =
(11)(8,000) =
(11)(5)(1600) =
(11)(5)(5)(320) =
(11)(5)(5)(5)(64)

Now, we KNOW that there's a mystery number that is between 6 and 10 (inclusive) and MUST account for that 64….

64 = (8)(8)

This gives us 2 purple chips.

[Reveal] Spoiler:
B

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

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12 Nov 2017, 08:48
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

Let’s break 88,000 into its prime factors:

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.

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Re: In a certain game, a large bag is filled with blue, green   [#permalink] 12 Nov 2017, 08:48
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