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In the game of Dubblefud, red chips, blue chips and green chips are

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In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 28 Apr 2016, 03:46
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In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5

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In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 28 Apr 2016, 03:56
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arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5


we will have to factor 16000 first..
\(16000 = 2^4*2^3*5^3\)..

now its given that blue = green
since value of ONLY green is a multiple of 5..so there are 3 of 5s or 3 of green..
so number of blue also =3


so value of blue and green chips =\(4^3*5^3 = 2^6*5^3\)..
so value of red chips = \(\frac{2^4*2^3*5^3}{2^6*5^3}=2\)
so total red chips = 2/2 =1
A

OR

\(16000 = 2^4*2^3*5^3 = 2*2*2*2*2*2*2*5*5*5\)... Now 5 points are thrice and that is why they are multiplied thrice..
so green is 3 but blue is same and therefore 3...
\(16000 = 2^4*2^3*5^3 = 2*(2*2)*(2*2)*(2*2)*5*5*5=2*4*4*4*5*5*5\)
thus there is ONLY one 2 pointer or red
ans A
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 28 Apr 2016, 04:03
arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5


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)
in-a-certain-game-a-large-bag-is-filled-with-blue-green-126425.html (MGMAT)

Hope it helps.
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 28 Apr 2016, 04:09
arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5



this is equivalent to :-

2x * 4y * 5z = 16000
y = z (given)

2x * 4y * 5y = 16000
2x * y^2 = 16000/20
2x * y^2 = 800

now from options given we will figure out which number will divide 800 and gives us a perfect square :-

which gives us x = 4 as
2* 4 * y^2 =800
y^2 = 100
y =10

Number of red chips = 4 hence D
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 26 Mar 2017, 16:55
chetan2u wrote:
arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5


we will have to factor 16000 first..
\(16000 = 2^4*2^3*5^3\)..

now its given that blue = green
since value of ONLY green is a multiple of 5..so there are 3 of 5s or 3 of green..
so number of blue also =3


so value of blue and green chips =\(4^3*5^3 = 2^6*5^3\)..
so value of red chips = \(\frac{2^4*2^3*5^3}{2^6*5^3}=2\)
so total red chips = 2/2 =1
A


4 red chips also works..

(4*2)(4*10)(5*10) = 16000
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 26 Mar 2017, 17:15
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jpmpdt wrote:
chetan2u wrote:
arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5


we will have to factor 16000 first..
\(16000 = 2^4*2^3*5^3\)..

now its given that blue = green
since value of ONLY green is a multiple of 5..so there are 3 of 5s or 3 of green..
so number of blue also =3


so value of blue and green chips =\(4^3*5^3 = 2^6*5^3\)..
so value of red chips = \(\frac{2^4*2^3*5^3}{2^6*5^3}=2\)
so total red chips = 2/2 =1
A


4 red chips also works..

(4*2)(4*10)(5*10) = 16000


Hi

4 red does not work since the method you have taken is not correct..
We are looking for PRODUCT of point value..
So if there are 4 red chips the product becomes 2*2*2*2 and not 4*2 because 4*2 is the SUM of values..

Hope it helps
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 11 Apr 2017, 17:25
arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5


My interpretation:

Step 1:
16,000 = \(5^3*2^7\)

Step 2:
R:B:G worth 2:4:5 ..therefore break the prime factors above into equivalent RBG ratios:

R = 2
B = (2*2)(2*2)(2*2) //we've used all the 2's
G = (5)(5)(5) //we've used all the 5's and B and G have the same number of groupings

Therefore after exhausting all the prime factors, we're left with one "2" for R.
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 22 May 2018, 04:51
arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5


I took a little bit of a different approach and I got to the answer pretty quick, so I thought I'd share.

R=2, B=4, G=5. We know that we have the same amount of B and G chips. So B and G have to have the same power.

BxG = 20. How many times does 20 go into 16,000?

\(\frac{16,000}{20}\)=800

\(\frac{800}{20}\)=40

\(\frac{40}{20}\)=2

So we know we have \(20^3\).

Only 2 left and we know that R=2. That means only 1 Red Chip.
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 31 Aug 2018, 00:50
2
Whenever we see numbers of variables on one side and a fixed numerical value on the other, we must go for prime factorization.
16000 = 2x2x2x2x2x2x2x5x5x5.
We know that the value of one green chip is 5 points which clearly means we have 3 green chips (5x5x5) which also means we have 3 blue chips. Product of points of 3 blue chips = 4x4x4 = (2x2)x(2x2)x(2x2).
Now, Let's see the prime factorization, 16000 = 2x(2x2)x(2x2)x(2x2)x5x5x5
We are left with only One 2 which means we have one Red chip. Answer "A".
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 31 Aug 2018, 10:08
let the no of red chips be r and b & green chips be k.
2r * 4k * 5k = 16000
40r (k^2) = 16000
r(k^2) = 400
k will be an integer only when r = 1
Ans A
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 18 Sep 2018, 05:54
chetan2u wrote:
arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5


we will have to factor 16000 first..
\(16000 = 2^4*2^3*5^3\)..

now its given that blue = green
since value of ONLY green is a multiple of 5..so there are 3 of 5s or 3 of green..
so number of blue also =3


so value of blue and green chips =\(4^3*5^3 = 2^6*5^3\)..
so value of red chips = \(\frac{2^4*2^3*5^3}{2^6*5^3}=2\)
so total red chips = 2/2 =1
A


Hey chetan2u!

I do not understand how the number of chips is equal when 4^3*5^3, can you explained it in more detail?

Thank you!!!
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 19 Sep 2018, 18:06
arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5


Breaking 16,000 into prime factors, we have:

16,000 = 16 x 1,000 = 2^4 x 10^3 = 2^4 x 2^3 x 5^3 = 2^7 x 5^3

Since there are an equal number of blue chips and green chips, there must be 3 blue chips and 3 green chips (notice that the green chips are worth 5 points each and we have 5^3 as a factor). Since the blue chips are worth 4 points each, we know that we have 4^3 blue chips, and, since 4^3 = 2^6, there must be 1 red chip so that 2^6 x 2 = 2^7.

Answer: A
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Re: In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 20 Sep 2018, 08:50
T1101 wrote:
chetan2u wrote:
arhumsid wrote:
In the game of Dubblefud, red chips, blue chips and green chips are each worth 2, 4 and 5 points respectively. In a certain selection of chips, the product of the point values of the chips is 16,000. If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. 1
B. 2
C. 3
D. 4
E. 5


we will have to factor 16000 first..
\(16000 = 2^4*2^3*5^3\)..

now its given that blue = green
since value of ONLY green is a multiple of 5..so there are 3 of 5s or 3 of green..
so number of blue also =3


so value of blue and green chips =\(4^3*5^3 = 2^6*5^3\)..
so value of red chips = \(\frac{2^4*2^3*5^3}{2^6*5^3}=2\)
so total red chips = 2/2 =1
A


Hey chetan2u!

I do not understand how the number of chips is equal when 4^3*5^3, can you explained it in more detail?

Thank you!!!


16000=2^7*5^3...
what is 16000 it is the product of the point VALUES....
since green chips are the only one product of 5 so all points of 5 are from the green chips..
since it is \(5^3\), it means there are 3 of green as they would give 5*5*5..
Now green is same as blue and blue is 4 points so \(4*4*4=4^3\)..
thus point values from blue and green is \(4^3*5^3\)..
remaining are from 2 points..
so \(\frac{2^75^3}{4^35^3}=2\)
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In the game of Dubblefud, red chips, blue chips and green chips are  [#permalink]

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New post 23 May 2019, 10:39
Imagine,

R=2=x

B=4=y

G=5=z

Here,

2^x*4*y*5*z=16000

y=z

2^x*4^y*5^y=16000

2^(x+y) * 10^y=2^4*10^3

y=3 and x+y=4

x=1

Red=1

Pick A

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In the game of Dubblefud, red chips, blue chips and green chips are   [#permalink] 23 May 2019, 10:39
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