Firstly,
Let us break the number 88000 into prime factors. We get,
88000 = 2^6 * 5^3 * 11
We have, blue chips as 1 point, green as 5, purple as X and red as 11.
Also, value of purple is between green and red, i.e., 6 or 7 or 8 or 9 or 10.
From the prime factors, we can deduce that number of red chips is 1. And since blue chips have 1 point each, there can be any number of blue chips.
From the factors, we know that purple must be even because green and red are odd and for the final product to be even, one number has to be even.
So, purple can be 6, 8 or 10.
6 is not possible because 6 requires a 3 which is not present in the factors.
10 is not possible because 10 (5*2) can be 1, 2 or 3 (3 being the highest power of 5 which is also the maximum number of 10's possible).
If there are 3 10's, there will be no 5's which is not possible.
If there are 1 or 2 10's, there will be 10's, 5's and 2's leading to 5 distinct values for the chips. But there are only 4 chips as per the problem statement.
Therefore, there are no 10's.
So, the purple chips valve is 8 and there are 2^6 = 8^2 => 2 purple chips.
Hence, choice b![/quote][/img][/list]
More Primes
-
Birottam Dutta
- Master | Next Rank: 500 Posts
- Posts: 342
- Joined: Wed Jul 08, 2009 8:50 am
- Thanked: 214 times
- Followed by:19 members
- GMAT Score:740
I think that the question is not easy to understand.
In my opinion, there should be small change in words of captioned question, such as :
A purple chip is worth more than a green chip but less than a red chip
So we easily have : 5< x <11. The following steps will be more simple.[/i]
When reading this statement at the first time, i supposed that the total value of purple chips shuold be greater than that of green chips but smaller than that of red chips??? If you understand in this way, you should not solve the problem.The purple chips are worth more than the green chips, but less than the red chips
In my opinion, there should be small change in words of captioned question, such as :
A purple chip is worth more than a green chip but less than a red chip
So we easily have : 5< x <11. The following steps will be more simple.[/i]
-
Shubhu@MBA
- Junior | Next Rank: 30 Posts
- Posts: 13
- Joined: Sun Jan 02, 2011 2:12 pm
- Thanked: 1 times
Purple marbles can have a value in the range
5<x<11 {6,7,8,9,10}
Now to get a multiplication factor of 88000, the most likely value for purple marble is 8(as 8*11 gives 88)
Thus, number of purple marbles selected are
88000=8*11*1000
=8*11*(8*125)
=(8*8)*(5*5*5)*11
Thus there are 2 purple marbles selected
(B) 2 is the answer
5<x<11 {6,7,8,9,10}
Now to get a multiplication factor of 88000, the most likely value for purple marble is 8(as 8*11 gives 88)
Thus, number of purple marbles selected are
88000=8*11*1000
=8*11*(8*125)
=(8*8)*(5*5*5)*11
Thus there are 2 purple marbles selected
(B) 2 is the answer
-
yogendragautam
- Newbie | Next Rank: 10 Posts
- Posts: 4
- Joined: Sun Sep 16, 2012 12:57 pm
Ok here is what I feel is easy to understand : -
As per the question : - blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. Also, P>G & P<R
product of the point values of the selected chips is 88,000
B,G,P,R
1,5,X,11 - CONDITION 1
Prime Factorizing 88000 = 11 * 8 * 1000 => 11 * (2^3) * (2^3 * 5^3) - CONDITION 2
In order to find out the value of X we need to compare and equate CONDITION 1 & CONDITION 2
11 * (2^3) * (2^3 * 5^3) = 5 * X * 11 (IGNORING Blue as anything raised to 1 is 1)
OR
11 * 8^2 * 5^3 = 11 * X * 5
as P>G & P<R means it lies between 5 & 11 so it should be 8 as per the factors shown above (2^3)*(2^3)
HENCE, 5's = 3 ; 8's=2 ; 5's=3 .... CLEARLY Purple chips are 8*8 = thats 8^2 .... so x =2 ANS (B)
As per the question : - blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. Also, P>G & P<R
product of the point values of the selected chips is 88,000
B,G,P,R
1,5,X,11 - CONDITION 1
Prime Factorizing 88000 = 11 * 8 * 1000 => 11 * (2^3) * (2^3 * 5^3) - CONDITION 2
In order to find out the value of X we need to compare and equate CONDITION 1 & CONDITION 2
11 * (2^3) * (2^3 * 5^3) = 5 * X * 11 (IGNORING Blue as anything raised to 1 is 1)
OR
11 * 8^2 * 5^3 = 11 * X * 5
as P>G & P<R means it lies between 5 & 11 so it should be 8 as per the factors shown above (2^3)*(2^3)
HENCE, 5's = 3 ; 8's=2 ; 5's=3 .... CLEARLY Purple chips are 8*8 = thats 8^2 .... so x =2 ANS (B)
-
gmat6087
- Senior | Next Rank: 100 Posts
- Posts: 53
- Joined: Sat Oct 29, 2011 3:49 am
- Thanked: 2 times
- Followed by:1 members
Hi Stuart,Stuart Kovinsky wrote:We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.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.
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).
I have one doubt, in the question " The purple chips are worth more than the green chips, but less than the red chips." does it mean that worth of each purple chip is more than that of green chip, or is it the total value of purple chips and green chips, coz if it is the later case we can't assume that purple can be between 6-10 since the question doesnt say that the chips are arranged in increasing order of the worth.
I hope I am clear.
Thanks
Satya.
OK I am sorry but I got lost at the first step itself . How did you get the 6, 7, 8, 9 or 10 points each?
Stuart Kovinsky wrote:We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.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.
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).
-
Rastis
- Master | Next Rank: 500 Posts
- Posts: 183
- Joined: Wed Sep 21, 2011 7:06 am
- Location: Washington, DC
- Thanked: 6 times
- Followed by:2 members
- GMAT Score:500
Stuart,
I got all the way to where you figure out the primes but I don't understand the very last where you say that you need to 8's and to choose B where B is 2. I understand that 2^6 equals 64 and 8x8=64 but why is it 2 and not 4 for the answer? Can you be more detailed please as to why 2 is the answer?
jess
I got all the way to where you figure out the primes but I don't understand the very last where you say that you need to 8's and to choose B where B is 2. I understand that 2^6 equals 64 and 8x8=64 but why is it 2 and not 4 for the answer? Can you be more detailed please as to why 2 is the answer?
jess
Thanks 
Stuart Kovinsky wrote:We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.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.
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).
-
rajeshsinghgmat
- Master | Next Rank: 500 Posts
- Posts: 171
- Joined: Tue Jan 08, 2013 7:24 am
- Thanked: 1 times
-
aceacharya
- Newbie | Next Rank: 10 Posts
- Posts: 8
- Joined: Mon Dec 17, 2012 5:27 pm
Hello Nikhil,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
There is a fundamental flaw in the equation that you have formed
B*5G*Px * 11R= 88000
The equation that would be formed as per the question will be more like
1^B * 5^G * x^P * 11^R = 88,000
and if you try to solve the above equation, you may find the satisfactory solution, as is explained above
Anshuman
-
vijaya priya
- Newbie | Next Rank: 10 Posts
- Posts: 2
- Joined: Sat Mar 09, 2013 10:46 am
kswarna wrote:i think it says "The purple chips are worth more than the green chips, but less than the red chips."Stuart Kovinsky wrote:We know that the purple chips are worth 6, 7, 8, 9 or 10 points each.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.
>> 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
so the value cannot equal 5 or less than 5 ! so it is surely MORE THAN 5 AND LESS THAN 11 ( NOT INCLUSIVE OF BOTH). 4 is LESS THAN 5 so cannot be the value!
