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

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

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26 Jan 2010, 05:41
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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: OA
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26 Jan 2010, 06:11
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sudip135 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

Break it down into LCFs:
88000 --> 1000 * 88 --> 5*5*5*2*2*2*11**2*2*2
So, possible chips:
3 green (5 points)
1 red (11 points)
who cares about blue, because they are worth one.
leaving 2*2*2*2*2*2 for the purple.

We know that purple is between 5 and 11, so 2^y must be 8, y=3
2*2*2*2*2*2=8*8
So, two purple.

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26 Jan 2010, 06:22
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sudip135 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

$$88,000=2^6*5^3*11$$, as no chip's value is 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 multiple of 2, but more than 5 and less than 11, hence it's 8 (2^3). 8*8=64, two purple chips were drawn.

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02 Jul 2011, 10:22
jusjmkol740 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

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02 Jul 2011, 10:24
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Bunuel wrote:
sudip135 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

$$88,000=2^6*5^3*11$$, as no chip's value is 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 multiple of 2, but more than 5 and less than 11, hence it's 8 (2^3). 8*8=64, two purple chips were drawn.

to satisfy highlighted statement dont you think answer should be 8? which is not there, so i am totally bummed out!
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17 Aug 2011, 17:43
seems this question is a bit ambiguous, you could just draw all chips worth 5 and it'd divide up fine. It never said anything about having a random smattering of chips.
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18 Aug 2011, 02:40
fivedaysleft wrote:
Bunuel wrote:
sudip135 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

$$88,000=2^6*5^3*11$$, as no chip's value is 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 multiple of 2, but more than 5 and less than 11, hence it's 8 (2^3). 8*8=64, two purple chips were drawn.

to satisfy highlighted statement dont you think answer should be 8? which is not there, so i am totally bummed out!

Read the question again. It doesn't say "What is the value of the purple chip?" It says, "How many purple chips were selected?"
Since we have 2^6 and as you rightly figured that each purple chip has value 8 (= 2^3), there must have been 2 purple chips.
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18 Aug 2011, 08:49
VeritasPrepKarishma wrote:
pinchharmonic wrote:
seems this question is a bit ambiguous, you could just draw all chips worth 5 and it'd divide up fine. It never said anything about having a random smattering of chips.

It isn't ambiguous.
You cannot draw all 5s because then you cannot have 88000 as the product. To make 88000, you need some 2s and 11 as well.

thanks again, i stand corrected, another silly mistake i made.
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18 Aug 2011, 12:22
After looking at factors we can say that purple ball comes from 2^6.
now check the posibility because it mentioned that purple chips are worth more than the green chips, but less than the red chips ( 5 < Purple ball < 11), Thus the possible combinations are:
(2^1)^6 = 2^6 (5<x<11 not satisfied as x = 2)
(2^6)^1 = 64^1 (5<x<11 not satisfied as x = 64)
(2^2)^3 = 4^3 (5<x<11 not satisfied as x = 4)
(2^3)^2 = 8^2 ( satisfied condition)
Ans. 2
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18 Aug 2011, 21:19
88000 = 2^6 * 5^3 * 11

5<x<11 => x could be 6 or 7 or 8 or 9 or 10

x cannot be 6 , otherwise we would have got a 3 in the product
x cannot be 7, otherwise we would have seen atleast one 7.
x cannot be 9 , otherwise we would have seen a 3 in the product
x cannot be 10 , otherwise we would have seen a 5 in the product.

=> x is 8

Also 2^6 in the product cannot be from R,G,B as none of them has 2 in it.

=> 8^n = 2^6
=> there are 2 purple chips

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05 Sep 2011, 13:24
Quote:
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

B(1), G(5), P(x), R(11)
5<x<11

Prime factors of 88 000: 2,2,2,2,2,2,5,5,5,11
x=8
---> 2 purple chips.

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06 Sep 2011, 07:36
used a diff method.. but yea ans is B

88000/ 11 = 8000 (1 red chip)

8000/5 = 1600 ( 1 green chip)

1600 / 5 = 320 ( another green chip)

320 / 5 = 64 (another green chip)

since purple can be between 5 and 11, the apt number is 8 => 2 purple chips
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26 Dec 2012, 20:05
jusjmkol740 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

Given:
B = 1
G = 5
P = x
R = 11
x > 5

$$88,000 = 2*2*2*11*5*2*5*2*5*2 = 2^6*11*5^3$$

WE know x is greater than 5 so it cannot be 2 nor 4. Then, it's 8. 16 is also not possible because we have to evenly divide the number of 2s.

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

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09 Apr 2014, 02:09
The purple chips are worth more than the green chips, but less than the red chips.

Dont you guys think above statement should have been written as following:
The purple chip is worth more than the green chip, but less than the red chip.

Chips is referring to combined worth of all purple chips in the bag, a worth that is not helping any way to judge that single purple chip's worth is between Green's and Red's worth.
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Re: In a certain game, a large bag is filled with blue, green, p [#permalink]

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

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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.

[Reveal] Spoiler:
B

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Re: In a certain game, a large bag is filled with blue, green, p   [#permalink] 07 May 2015, 22:05
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