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.

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

Let's break 88000 down to primes:

88 * 1000

11 * 8 * 10 * 10 * 10

11 * 2 * 2 * 2 * 2 * 5 * 2 * 5 * 2 * 5

so:

2^6 * 5^3 * 11

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

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

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

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.

Therefore, x MUST be 8.

To get 2^6, we need two 8s: choose (b).

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.

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

Let's break 88000 down to primes:

88 * 1000

11 * 8 * 10 * 10 * 10

11 * 2 * 2 * 2 * 2 * 5 * 2 * 5 * 2 * 5

so:

2^6 * 5^3 * 11

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

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

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

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.

Therefore, x MUST be 8.

To get 2^6, we need two 8s: choose (b).

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.

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

Let's break 88000 down to primes:

88 * 1000

11 * 8 * 10 * 10 * 10

11 * 2 * 2 * 2 * 2 * 5 * 2 * 5 * 2 * 5

so:

2^6 * 5^3 * 11

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

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

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

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.

Therefore, x MUST be 8.

To get 2^6, we need two 8s: choose (b).

kswarna 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.

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. X CAN BE 2,3,4 TOO as purple has a value in between the highest and lowest values. This can be either the specified 5 or this can be the unspecified x. So the answer should be right applied to either. now

88,000 = 11 * 8000 *1

= 11 * (20)^3 * 1

= 11 * ( 4 * 5 ) ^ 3 *1

I.E the answer is 3 CHOICE C

Nice try, but:

x is more than 5 (so it cannot equal 0, 1, 2, 3, 4 or 5)
x is less than 11 (so it cannot equal 11 or indeed 20)

The order has to match too:

You cannot make 11 by multiplying 1 * 1 * 1 * 1 etc. It is always 1 for the product of blue points.

Therefore your correct product = 11 * (4 * 5)^3 * 1 = 11 * 4^3 * 5^3 * 1 = 11 * 8^2 * 5^3 * 1
meaning that x = 8 and number of purple = 2.

I hope that helps.

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.

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

Let's break 88000 down to primes:

88 * 1000

11 * 8 * 10 * 10 * 10

11 * 2 * 2 * 2 * 2 * 5 * 2 * 5 * 2 * 5

so:

2^6 * 5^3 * 11

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

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

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

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.

Therefore, x MUST be 8.

To get 2^6, we need two 8s: choose (b).

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.

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