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

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.

GMAT assassins aren't born, they're made,
Rich

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.

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.

GMAT assassins aren't born, they're made,
Rich

While your approach is certainly creative, some of the math doesn’t quite work out.

If each purple chip = 10 points, then the product 5 x 2^6 = 5 x 64 = 320.

Now, 10 x 32 = 320 or 10 x 2^5 = 320, so what happened to the factor 2^5? You said it goes to the remaining blue chips. But the blue chips are not 2 points each; the blue chips are only 1 point each. (So the product of the points from the blue chips is always 1^n = 1 for any value of n.) There is no way for the product of the points from blue chips to be 32. (You perhaps overlooked the given information in the question that the blue chips are 1 point each, not 2 points each.)
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Why can't we assume purples value as 10? i.e 2*5 then the answer comes up to 3 and not 2

\(88,000=2^6*5^3*11=2^3*(2^3*5^3)*11=2^3*(10^3)*11\)

In this case we cannot accommodate 2^3. Notice that blue, green, and red chips' values are not multiples of 2. So, 2^6 in 88,000 must be the product of the values of the purple chips drawn.
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We're told a large bag is filled with blue, green, purple and red chips.

green < purple < red

Worth 1, 5, x and 11 point each.

The product of the point values of the selected chips is 88,000. The prime factorization of 88,000 = 2^6 * 5^3 * 11. We're told the purple chips weigh more than the green chips, but less than the red chips. Therefore, 5 in the prime factorization is for green chips; 11 is for purple chips. We have a 2^6 remaining, but we know that purple has to be more than 5.

2^6 = 8^2
Therefore, we have 2 purple chips. Answer is B.
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Algebraically,

The question is about powers. Let,

r = red chips, p = purple chips, g = green chips, b = blue chips (all whole numbers)

Product of the points of chips can be written as,

(11^r).(x^p).(5^g).(1^b) = 88000 (Note that 1 raised to any number stays 1)

(11^r).(x^p).(5^g) = (2^6).(5^3).(11^1) (on prime factorisation)

Simply equate the powers of the prime factors. You get,

r = 1 and g = 3

We are then left with x^p = 2^6 = 64. Given that 5<x<11, the only possible value of x can be 8. (Since 8^2 = 64, no other numbers can result in an answer of 64)

So if x is 8 and p must be a positive integer (or zero), p has to be 2.

I hope it helps!

i got to the 8x8, meaning two chips, but it doesn't satisfy the 2nd condition of the purple coin worth "The purple chips are worth more than the green chips, but less than the red chips". am i missing something?

16(worth of purple coins)>15(worth of green coins)-- correct
16(worth of purple coins)<11(worth of red coins) --- ---- this is the issue

Hi Bhanuodin007,

I think that the issue here is how you are interpreting the wording of the prompt. The intended meaning is that A (re: one) purple chip is worth than one green chip and less than one red chip. The reason we can make this particular deduction is that when we factor down 88,000 into its 'pieces', we have just 1 red chip, so neither the TOTAL of the purple chips NOR the TOTAL of the GREEN chips is less than the TOTAL of the red chips - thus, the question cannot be intending for us to deal with the sums of the individual chip colors.

Once you get to the point that you determine that a purple chip is worth 8 points - and there are two of those chips - then you've answered the question.

GMAT assassins aren't born, they're made,
Rich

I was confused between D and B since 64 is a multiple of both 2 and 4. do we take only prime factors into consideration?

Hi Jaya6,

Prime Factorization isn't actually necessary to answer this question - although you will likely need to do some type of 'division' to answer this prompt. Once you 'factor out' the possible 11s and 5s, what's left will account for the product of the value of all the purple chips (you'll find that it's 64). The prompt also tells us the value of a purple chip is greater than 5, but less than 11. I suspect that you probably know many of the standard 'squares' - so it shouldn't be too hard to determine that 64 = 8x8 - and that we have selected 2 purple chips).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com

I feel there is no unique solution for the problem stated above. I can see an alternate solution. Problem states that x must be greater than 5 but less than 11.
Prime factorization of 88000=(2)^6*(5)^3*11.
Since this prime factorization does not have a 3, x cannot be equal to 6.
But x can be equal to 8 or 10.
Considering x=10.
Blue=1*2^2 (points*number)
Green=5*5 (points*number)
Purple=10*2^2 (points*number)
Red=11*2 (points*number)
From here we can see that number of purple chips drawn can be 4.
If the problem stated that the number of chips drawn from each color should be distinct then the problem would have a unique solution with the number of purple chips drawn being 2 (of value 8).

We know that the product of chips is 88000
88000= 11*8*1000=11*2^3*2^3*5^3

B=1, G=5, P=x, R=11
x>5 and x<11
R in the above product is 1
G=3
only possible value for purple to take is 8 meaning thereby 2 chips
Therefore option B

Bunuel I understood your initial explanation but was also wondering why p = 1 cannot work:
1 Purple (1 x 8) = 8
1 Red (1 x 11) = 11
200 Green (200 x 5) = 1,000
Total product value = 88,000

Hi prateekgupta95,

The prompt tells us that we have to MULTIPLY the value of EACH of the chips together - and the end product will be 88,000.

IF.... you had 200 green chips (worth 5 points each), then the value of that piece of the calculation would be 5^200... (NOT 200 x 5).

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: Rich.C@empowergmat.com