Problem Solving

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.

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.

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!

[email protected] 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.

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

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?

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

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.

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.

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.