BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

More Primes

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Wed Feb 20, 2008 7:15 pm
Thanked: 6 times
Followed by:1 members

More Primes

by mmukher » Sat Apr 05, 2008 8:11 pm
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.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

Re: More Primes

by Stuart@KaplanGMAT » Sat Apr 05, 2008 10:13 pm
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).
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
Senior | Next Rank: 100 Posts
Posts: 34
Joined: Wed Feb 20, 2008 7:15 pm
Thanked: 6 times
Followed by:1 members

by mmukher » Mon Apr 07, 2008 7:30 pm
Amazing. Thanks !
Top
Junior | Next Rank: 30 Posts
Posts: 27
Joined: Thu Apr 10, 2008 1:20 pm
Thanked: 1 times

by humeixia » Thu Apr 10, 2008 2:04 pm
thanks. :P
Top
Senior | Next Rank: 100 Posts
Posts: 75
Joined: Wed Aug 27, 2008 7:19 am
Location: Orlando
Thanked: 6 times

Re: More Primes

by raajan_p » Fri Nov 28, 2008 7:27 am
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).
Thanks a lot, Stuart!!!
Top
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Sat Mar 27, 2010 7:50 am
Thanked: 9 times

by Thang Do » Sat Mar 27, 2010 8:09 am
I think the short way should be:

As in the context:

(1^a).(5^b).(x^c).(11^d)=88000

a,b,c,d is the numbers of each colour chip.

So we have to find what is c.

To find c we need find x. We will break 88000 in to 1, 5, 11 as follows:

88000 = 88.1000 = 11.8.1000 = 11. 8. 5.5.5.8 = 11.8.8.5.5.5

So

(1^a).(5^b).(x^c).(11^d)=88000 = 5.5.5.8.8.11

Because 1.1.1...1 = 1 so we dont care what is "a".

as we know that 5<x<10 so x= 8 is reasonable.

Thus

5^b = 5.5.5 --->b = 3
x^c= 8^c = 8.8=8^2 ---> c = 2 -----> answer is B
11^d= 11---> d = 1

By this way we can find a,b,c,d
Top
Legendary Member
Posts: 1404
Joined: Tue May 20, 2008 6:55 pm
Thanked: 18 times
Followed by:2 members

by tanviet » Wed Nov 03, 2010 8:06 pm
I can not understand why X can not be 10, Pleas, explain more on this
Top
User avatar
Junior | Next Rank: 30 Posts
Posts: 12
Joined: Fri Oct 02, 2009 7:40 am
Location: Mumbai, India
Thanked: 8 times
Followed by:2 members

by mvikred » Thu Nov 04, 2010 2:09 am
The answer is 2.

Can only be 8^2

Cheers !!
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 181
Joined: Fri Sep 04, 2009 12:06 pm
Thanked: 17 times
Followed by:1 members

by ikaplan » Thu Nov 04, 2010 2:25 am
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
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 286
Joined: Tue Sep 21, 2010 5:36 pm
Location: Kolkata, India
Thanked: 11 times
Followed by:5 members

by pesfunk » Thu Nov 04, 2010 4:36 am
Great question and awesome explanation...but Stuart, can this be a GMAT question...i mean the methods used....why would GMAT test this for an MBA ?
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).
Top
User avatar
Junior | Next Rank: 30 Posts
Posts: 13
Joined: Sun Jan 17, 2010 9:51 am

by paritosh_b » Thu Nov 04, 2010 8:08 am
Yes,It's 2.
Good question. :)
Top
User avatar
GMAT Instructor
Posts: 3225
Joined: Tue Jan 08, 2008 2:40 pm
Location: Toronto
Thanked: 1710 times
Followed by:614 members
GMAT Score:800

by Stuart@KaplanGMAT » Thu Nov 04, 2010 12:23 pm
pesfunk wrote:Great question and awesome explanation...but Stuart, can this be a GMAT question...i mean the methods used....why would GMAT test this for an MBA ?
Well, you could pose the same question about a lot of the topics covered by the GMAT. How often do you think an MBA grad needs to solve a quadratic equation or find the sum of a sequence?

Prime numbers (and number properties in general) are consistently tested on the GMAT, so this is definitely a possible GMAT question (and a very high level one, at that).

Here's the thing to remember: even though there's a lot of math on the GMAT, what you're really being tested on is your critical thinking and strategic problem solving skills - things every MBA applies on a daily basis. That's why you'll almost never see a question such as "what are the prime factors of 88,000?"; instead, you'll see a complicated word problem that forces you to apply that information in an unexpected context.
Image

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

Kaplan Exclusive: The Official Test Day Experience | Ready to Take a Free Practice Test? | Kaplan/Beat the GMAT Member Discount
BTG100 for $100 off a full course
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 286
Joined: Tue Sep 21, 2010 5:36 pm
Location: Kolkata, India
Thanked: 11 times
Followed by:5 members

by pesfunk » Thu Nov 04, 2010 3:59 pm
Thanks Stuart
Stuart Kovinsky wrote:
pesfunk wrote:Great question and awesome explanation...but Stuart, can this be a GMAT question...i mean the methods used....why would GMAT test this for an MBA ?
Well, you could pose the same question about a lot of the topics covered by the GMAT. How often do you think an MBA grad needs to solve a quadratic equation or find the sum of a sequence?

Prime numbers (and number properties in general) are consistently tested on the GMAT, so this is definitely a possible GMAT question (and a very high level one, at that).

Here's the thing to remember: even though there's a lot of math on the GMAT, what you're really being tested on is your critical thinking and strategic problem solving skills - things every MBA applies on a daily basis. That's why you'll almost never see a question such as "what are the prime factors of 88,000?"; instead, you'll see a complicated word problem that forces you to apply that information in an unexpected context.
Top
User avatar
Master | Next Rank: 500 Posts
Posts: 123
Joined: Tue Nov 23, 2010 7:18 pm
Location: Mumbai, India
Thanked: 5 times
Followed by:4 members

by anirudhbhalotia » Wed Dec 01, 2010 1:24 am
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!
Top
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Tue Jan 19, 2010 1:28 pm

by kswarna » Fri Dec 03, 2010 3:13 pm
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
Top
Post new topic Post Reply