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In a certain game, a large bag is filled with blue, green, purple and 22 Jan 2012, 17:24
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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

Show 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.
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B
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In a certain game, a large bag is filled with blue, green, purple and 22 Jan 2012, 17:33
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enigma123
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.
Show more

\(88,000=2^6*5^3*11\).

Since no other chip's value is a multiple of 2, it follows that 2^6 = 64 must be the product of the values of the purple chips drawn. The value of each purple chip is some power of 2, greater than 5 but less than 11, hence it's 8 (2^3). Therefore, 64 is the product of two purple chips: 8 * 8 = 64, indicating that two purple chips were drawn.

Answer: B.
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In a certain game, a large bag is filled with blue, green, purple and 07 May 2015, 22:05
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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.

Final Answer:
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B

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In a certain game, a large bag is filled with blue, green, purple and 19 Feb 2012, 00:29
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Bunuel
enigma123
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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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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In a certain game, a large bag is filled with blue, green, purple and 19 Feb 2012, 01:07
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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?
Show more

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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In a certain game, a large bag is filled with blue, green, purple and 17 Apr 2013, 09:39
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Bunuel
enigma123
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.
Show more


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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In a certain game, a large bag is filled with blue, green, purple and 17 Apr 2013, 09:43
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Bunuel
enigma123
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
Show more

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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In a certain game, a large bag is filled with blue, green, purple and 18 Apr 2013, 03:53
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Bunuel
enigma123
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.
Show more

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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In a certain game, a large bag is filled with blue, green, purple and 18 Apr 2013, 04:10
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Bunuel
enigma123
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
Show more

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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In a certain game, a large bag is filled with blue, green, purple and 28 Jul 2014, 09:30
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Bunuel
enigma123
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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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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In a certain game, a large bag is filled with blue, green, purple and 06 Nov 2014, 12:12
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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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In a certain game, a large bag is filled with blue, green, purple and 07 Nov 2014, 03:56
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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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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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In a certain game, a large bag is filled with blue, green, purple and 15 Oct 2016, 10:29
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Hi,

I get it up to the point where 2^6 = 64 which is also 8^2 = making it 2 times of 8.

But I chose 3 time instead of 2 because I thought 8 was a factor in 5^3 = 125 in which it was (8, 15)

so I thought there was another "hidden" 8 points within 5^3

would you explain why this is wrong?

Thank you so much!
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In a certain game, a large bag is filled with blue, green, purple and 15 Oct 2016, 18:09
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Hi dorey777,

In real simple terms, 125 is an ODD number and 8 is an even number. Even numbers do NOT divide evenly into odd numbers, so there can't be a "hidden 8" inside 125.

In addition, 125 is NOT divisible by 15; (15)(8) does NOT equal 125; it equals 120.

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In a certain game, a large bag is filled with blue, green, purple and 12 Nov 2017, 08:48
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enigma123
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
Show more

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.

Answer: B
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In a certain game, a large bag is filled with blue, green, purple and 19 Apr 2018, 16:10
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enigma123
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
Show more

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.

Answer: B

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In a certain game, a large bag is filled with blue, green, purple and 03 May 2018, 18:39
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ScottTargetTestPrep
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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


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.

Answer: B
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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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In a certain game, a large bag is filled with blue, green, purple and 03 May 2018, 19:28
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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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In a certain game, a large bag is filled with blue, green, purple and 04 May 2018, 04:32
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Thanks EMPOWERgmatRichC for the reply.

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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In a certain game, a large bag is filled with blue, green, purple and 04 May 2018, 10:11
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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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