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Fri Dec 03, 2010 5:56 pm
[quote="kswarna"]
Stuart Kovinsky wrote:
mmukher 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?

Options :
1
2
3
4
5

OA later.
We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.

>> IT IS NOT GIVEN ANYWHERE THAT IT NEEDS TO BE IN ORDER.
Hi,

the word "respectively" in the sentence "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. " does in fact mean that the values listed are in order.

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grant06 Just gettin' started!
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Tue Jan 18, 2011 12:24 pm
anirudhbhalotia wrote:
Stuart Kovinsky wrote:
mmukher 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?

Options :
1
2
3
4
5

OA later.
1. We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.

2. The blue chips are worth 1 point each, so we can ignore those.

3. Let's break 88000 down to primes:

4. 88 * 1000

5. 11 * 8 * 10 * 10 * 10

6. 11 * 2 * 2 * 2 * 2 * 5 * 2 * 5 * 2 * 5

7. so:

8. 2^6 * 5^3 * 11

9. Well, we're not getting any 2s out of the 1, 5 or 11, so all the 2s have to come from x.

10. Therefore, x has to be 6, 8 or 10.

11. x can't be 6, because we don't want any 3s.

12. If x were 10, it would give us 2s and 5s. So to get 6 2s we'd also have to take 6 5s, which is way more than we want.

13. Therefore, x MUST be 8.

14. To get 2^6, we need two 8s: choose (b).
I couldn't have imagined in my dreams that this is related to Prime nos.! How to make myself acquainted with such problems and how to get the knack of relating the problems to the concepts? I feel like a 6 yr old kid just starting school!

Also for the solution I got till Step 8. But after that I am not able to understand why you did what you did!

Please explain! Thanks!
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.

svetlana.gura@gmail.com Just gettin' started!
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Tue Jan 18, 2011 1:09 pm
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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nikmahes Just gettin' started!
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Wed Jan 19, 2011 8:59 am
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

giovanni.gastone Rising GMAT Star
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Sat Feb 19, 2011 8:23 pm
svetlana.gura@gmail.com wrote:
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.
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

giovanni.gastone Rising GMAT Star
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Sat Feb 19, 2011 8:50 pm
Never mind.

Last edited by giovanni.gastone on Sun Feb 20, 2011 3:32 am; edited 1 time in total

giovanni.gastone Rising GMAT Star
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Sat Feb 19, 2011 10:10 pm
nikmahes wrote:
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 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

coolly01 Just gettin' started!
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Sun Feb 27, 2011 6:36 pm
My take is A

oldguy Just gettin' started!
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Sun Mar 20, 2011 10:14 am
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?

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Stuart Kovinsky GMAT Instructor
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Mon Mar 21, 2011 1:05 am
oldguy wrote:
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,

according to the question, the product of the point values is 88000.

So, if you chose 1000 red chips, that would give you a point value of 11^1000, not 11*1000. The correct calculation would be 11*1000 if you were taking the sum of the point values of 1000 red chips.

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rajesh629 Just gettin' started!
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Wed Mar 23, 2011 6:47 am
ikaplan wrote:
88000= 88 x 1000

88= 22 x 2 x 2= 11 x 2 x 2 x 2

1000= 10 * 10 * 10= 2^3 x 5^3

so we have:

88000= 11 x 5^3 x 2^6

because (1) "green < purple < red" => 5 < purple < 11 and
because (2) we have @^6 remaining => purple=2^3=8

so there are two purple chips

My answer is B
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..

krishnakumar.ks Rising GMAT Star
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Tue Apr 12, 2011 4:43 am
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.

prashkrish Just gettin' started!
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Tue Apr 12, 2011 10:28 am
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...

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Tue Apr 12, 2011 10:40 am
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?

mmukher wrote:
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.

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### GMAT/MBA Expert

Stuart Kovinsky GMAT Instructor
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Tue Apr 12, 2011 11:07 am
maihuna wrote:
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?

mmukher wrote:
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.
You're misinterpreting the statement to read "the sum of the purple chips is greater than that of the green chips, but less than that of the red chips"; it's not the sums that are being compared, but the values of the individual chips.

As we can see from the question:

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.
"respectively" means that you take them in the order given; in other words, blue chips are worth 1 each, green chips are worth 5 each, purple chips are worth x each and red chips are worth 11 each.

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