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Since 88,000 broken into prime numbers equals 2^6 * 5^3 * 11, we know that there are three green chips worth five points each and one red chip worth eleven points. Since 2^6 equals 64 and 8^2 also equals 64, we know there were two red chips worth eight points each. The points value of a red chip has to be between 5 and 11; of the possible numbers (6, 7, 8, 9, and 10), only 8 divides evenly into 64. So we need two red chips worth eight points each and the answer is B.

I followed slightly different logic, but I got correct answer in less than 30 seconds. Please tell me any mistakes are possible if I keep this approach in mind:

First I took a number 88,000 and devided by 11 (since this is the biggest prime number of the set and it is obvious that 88, 000 devisible by 11) => I got 11*8,000.

Then: I devided 8,000 by 5 and so on till I got number 64 which is not devisible by 5. And then, since we cannot devide by 5 or 11, I just had to find number which meets condition 5<x<11.

The only possible number is 8 => 8*8=64 =>>>>> answer is 2 purple chips with value 8.

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Guys, Iam unable to understand as to how can we have a unique solution to this problem. This is how I approach -

Let, the number of Blue balls=B
Green Balls= G
Purple Balls= P
Red Balls= R

as per the problem we get,
B*5G*Px * 11R= 88000
=> BGRP x= 1600
which implies that x can be 8 or 10 as 5<x<11.
If x =8,
BGRP= 200

If x=10,
BGRP =160

Now, how can we uniquely decide the value of P? There can be multiple values for each of the variables.

Any help would be great.

Thanks,
Nikhil

Hi Svetlana,

Your method is not "wrong". Mechanically, your method is the same as how others have solved it. The key question is whether you understand what this question is asking (i.e., what are the primes of 88,000). If you were just dividing 88,000 by 11 and 5, not knowing why you were performing the division, then you may have trouble with a similar problem about prime factors but posed in a different way.

Giovanni

Never mind.

Hi Nikhil,

x, the point value for Purple, cannot be 10 because the 5 that would have to accompany a 2 is a Green ball. But, the bigger issue is with the way you approached the problem. If you divide 88,000 by 5 and 11, then use 1,600 to figure out what, between 5 and 11, evenly divides into 1,600, then you're not taking into account that there could be multiples of 5s or 11s.

Let's go one step further with your logic and let's assume that x (Purple) is 10, how many Purple balls do you have? You'd have to divide the 1,600 by 10 to tell me that, right? so, that gives us 2 Purple balls (10 * 10 * 16). So, now what do you do with 16? It's not Blue, because multiplying 1 eight times gives you 1, still. So, it must either be...

- a ball that's worth 16 points (not possible because we only have Blue, Green, Purple, and Red and you've already designated Purple to be 10), or

- 4 balls worth 2 points each (not possible either because we only have Blue, Green, Purple, and Red and you've already designated Purple to be 10).

Does this help?

Giovanni

My take is A

so why can the answer not be that 1,000 red chips were picked and one purple?

1,000 * 11 = 11,000
8 * 1 = 8

11,000 * 8 = 88,000. then the answer would be a. (1 purple chip. )

the question does not limit the number of chips drawn.

or pick two purple chips 8*8 = 64. 125 red chips is 11*125= 1,375. 64*1375 = 88,000

so the answer would be b (2 purple chips)

so are there two answers that work? what am i missing?

hi,

as "green < purple < red"=> 1<x<5...

it could be the above also... how did you conformed that x is in between 5 and 11..
Please explain..

Answer cannot be anything else other than b, i.e., 2 (64 = 8*8). Please don't have any second thoughts as this is a pretty straight forward question on prime numbers as explained earlier.

Why is the following not a possible outcome?

B, G, P, R refer to number of balls.

(11 * R) * (1 * B) * (5 * G) * (x * P) = 88,000

If the following 2 outcomes could occur..
(11 * R) * (1 * B) * (5 * G) * (x * P) = (11 * 1) * (1 * 10) * (5 * 20) * (8 * 1)

OR

(11 * R) * (B * 1) * (5 * G) * (x * P) = (11 * 1) * (1 * 8) * (5 * 20) * (10 * 1)

Purple could be 8 or 10..

Please help me understand...

Stuart : I am more confused about the following constraints: have you thought of that. Is the worth of purple chips more than green and less than the red ones:

How many Purple : 2 with 8 each = 8*2 = 16
Green : 3 with 5 each = 3*5 = 15
Red : 1 with 11 = 1*11 = 11

so 11<15<16 or R<G<P

What am I missing here?

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