GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 29 Mar 2020, 22:53

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# In a certain game, a large bag is filled with blue, green

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

22 Jan 2012, 16:24
4
1
59
00:00

Difficulty:

65% (hard)

Question Stats:

63% (02:21) correct 37% (02:33) wrong based on 731 sessions

### HideShow timer Statistics

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?

A. 1
B. 2
C. 3
D. 4
E. 5

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 62289
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

22 Jan 2012, 16:33
15
12
enigma123 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?
A)1
B)2
C)3
D)4
E)5

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.

$$88,000=2^6*5^3*11$$, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

_________________
##### General Discussion
Manager
Joined: 10 Jan 2010
Posts: 134
Location: Germany
Concentration: Strategy, General Management
Schools: IE '15 (M)
GPA: 3
WE: Consulting (Telecommunications)
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

09 Feb 2012, 06:35
2

Basic information
G<P<R
5<x<11

What is x?

88,000 = 2^6*5^3*11
X can only be 2^6 and must be between 6 and 10, inclusive

2^6 = 64 (value)
Restriction: 2^3 * 2^3 = 8*8 --> 2 purple chips each with a value of 8
Intern
Joined: 06 Dec 2011
Posts: 3
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

18 Feb 2012, 23:29
Bunuel wrote:
enigma123 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?
A)1
B)2
C)3
D)4
E)5

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.

$$88,000=2^6*5^3*11$$, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Bunnel, thanks for the solution. I just had one confusion, we havent considered the blue chips at all
I worked out the number of purple chips as 1, considering blue chips also need to be selected.
Math Expert
Joined: 02 Sep 2009
Posts: 62289
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

19 Feb 2012, 00:07
1
raul2011 wrote:
Bunnel, thanks for the solution. I just had one confusion, we havent considered the blue chips at all
I worked out the number of purple chips as 1, considering blue chips also need to be selected.

Sure. Since blue chips worth 1 point each then # of blue chips selected does not affect the product at all (for ANY product there can be ANY number of blue chips been selected). We are told that the product of the point values of the selected chips is 88,000. Now, # of blue chips selected can be: 0 (88,000=8^2*5^3*11), 1 (88,000=8^2*5^3*11*1), 2 (88,000=8^2*5^3*11*1^2), ..., 1,000,000 (88,000=8^2*5^3*11*1^(1,000,000)), ... basically ANY #.

Hope it's clear.

P.S. By the way, how did you even get that # of purple chips selected as 1 considering blue chips?
_________________
Manager
Joined: 12 Mar 2012
Posts: 181
Concentration: Operations, Strategy
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

19 Mar 2012, 00:29
B->1
G->5
P->x; 5<x<11
R->11

NOW, 88000=11*8^2*5^4*1^n

hence
no of balls drawn,
B= CANT BE DETERMINED
G= 4
P= 2 (Only possible value is 8 )
R= 1
hence B
Intern
Joined: 19 Feb 2013
Posts: 3
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

17 Apr 2013, 08:39
Bunuel wrote:
enigma123 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?
A)1
B)2
C)3
D)4
E)5

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.

$$88,000=2^6*5^3*11$$, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Hi Bunuel. Is there a easy and fast way to factor the number? It really taking me lots of time, need help. Thanks
Math Expert
Joined: 02 Sep 2009
Posts: 62289
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

17 Apr 2013, 08:43
1
Marchikn wrote:
Bunuel wrote:
enigma123 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?
A)1
B)2
C)3
D)4
E)5

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.

$$88,000=2^6*5^3*11$$, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Hi Bunuel. Is there a easy and fast way to factor the number? It really taking me lots of time, need help. Thanks

Many ways are possible, for example:

88,000 = 88*1000 = 8*11*125*8 = 2^3*11*5^3*2^3 = 2^6*5^3*11.
_________________
Manager
Joined: 24 Nov 2012
Posts: 143
Concentration: Sustainability, Entrepreneurship
GMAT 1: 770 Q50 V44
WE: Business Development (Internet and New Media)
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

18 Apr 2013, 02:53
1
Bunuel wrote:
enigma123 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?
A)1
B)2
C)3
D)4
E)5

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.

$$88,000=2^6*5^3*11$$, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Hi Bunuel.. i would appreciate it if you could answer my query.. After figuring out that the value of purple chip is 8, isnt the following a possible way of picking out chips?

I selected chips according the following table

Blue (1) - 2
Green (5) - 5
Purple (8) - 4
Red (11) - 5

or

Blue (1) - 1
Green (5) - 10
Purple (8) - 2
Red (11) - 10

or

Blue (1) - 2
Green (5) - 2
Purple (8) - 25
Red (11) - 2

There are multiple solutions to this IMO and something wrong with the question
_________________
You've been walking the ocean's edge, holding up your robes to keep them dry. You must dive naked under, and deeper under, a thousand times deeper! - Rumi

http://www.manhattangmat.com/blog/index.php/author/cbermanmanhattanprep-com/ - This is worth its weight in gold

Economist GMAT Test - 730, Q50, V41 Aug 9th, 2013
Manhattan GMAT Test - 670, Q45, V36 Aug 11th, 2013
Manhattan GMAT Test - 680, Q47, V36 Aug 17th, 2013
GmatPrep CAT 1 - 770, Q50, V44 Aug 24th, 2013
Manhattan GMAT Test - 690, Q45, V39 Aug 30th, 2013
Manhattan GMAT Test - 710, Q48, V39 Sep 13th, 2013
GmatPrep CAT 2 - 740, Q49, V41 Oct 6th, 2013

GMAT - 770, Q50, V44, Oct 7th, 2013
My Debrief - http://gmatclub.com/forum/from-the-ashes-thou-shall-rise-770-q-50-v-44-awa-5-ir-162299.html#p1284542
Math Expert
Joined: 02 Sep 2009
Posts: 62289
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

18 Apr 2013, 03:10
2
Transcendentalist wrote:
Bunuel wrote:
enigma123 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?
A)1
B)2
C)3
D)4
E)5

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.

$$88,000=2^6*5^3*11$$, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Hi Bunuel.. i would appreciate it if you could answer my query.. After figuring out that the value of purple chip is 8, isnt the following a possible way of picking out chips?

I selected chips according the following table

Blue (1) - 2
Green (5) - 5
Purple (8) - 4
Red (11) - 5

or

Blue (1) - 1
Green (5) - 10
Purple (8) - 2
Red (11) - 10

or

Blue (1) - 2
Green (5) - 2
Purple (8) - 25
Red (11) - 2

There are multiple solutions to this IMO and something wrong with the question

Blue = 1 point;
Green = 5 points;
Purple = x points (5<x<11);
Red = 11 points.

None of the cases you've listed is possible:

Blue (1) - 2
Green (5) - 5
Purple (8) - 4
Red (11) - 5
Product = 5^5*8^4*11^5 not 2^6*5^3*11

Blue (1) - 1
Green (5) - 10
Purple (8) - 2
Red (11) - 10
Product = 5^10*8^2*11^10 not 2^6*5^3*11

Blue (1) - 2
Green (5) - 2
Purple (8) - 25
Red (11) - 2
Product = 5^2*8^25*11^2 not 2^6*5^3*11

Since the product is $$88,000=2^6*5^3*11$$, then there were exactly 3 green chips and 1 red chip selected. Also, from the product it follows that 2^6=64 is the product of the (# of purple chips selected)*(value of a purple chip).

Hope it's clear.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 62289
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

28 Jul 2014, 08:30
Bunuel wrote:
enigma123 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?
A)1
B)2
C)3
D)4
E)5

The answer is B. I am struggling to understand how. But this is how I am approaching this question. Can someone please help?

Total value of chips = 88,000
Prime factors of 88,000 = 11 * 5^3 * 2^6
Also from question stem = 5<x<11.
We have to find the value of x?
Now, x cannot be 11 because as per question x<11.Now I am struggling after this.

$$88,000=2^6*5^3*11$$, as no other chip's value is a multiple of 2, hence 2^6=64 must be the product of the values of the purple chips drawn. The value of the purple chip is a some power of 2, but more than 5 and less than 11, hence it's 8 (2^3). Thus 64 is a product of 2 purple chips: 8*8=64, so two purple chips were drawn.

Similar questions to practice:
in-a-certain-game-a-large-container-is-filled-with-red-yel-144902.html (OG)
a-cargo-ship-carrying-four-kinds-of-items-doohickies-geega-167523.html (Veritas Prep)

Hope it helps.
_________________
Manager
Joined: 15 Aug 2013
Posts: 223
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

06 Nov 2014, 11:12
Hi Bunuel,

I noticed that you went directly to 8. Why didn't you consider 6 or 10 as the possible point values for the chips?
Math Expert
Joined: 02 Sep 2009
Posts: 62289
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

07 Nov 2014, 02:56
russ9 wrote:
Hi Bunuel,

I noticed that you went directly to 8. Why didn't you consider 6 or 10 as the possible point values for the chips?

We are told that "the purple chips are worth more than the green chips (5), but less than the red chips (11)" and it's a power of 2, so it must be 8.
_________________
Intern
Joined: 21 Mar 2015
Posts: 3
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

03 Jun 2015, 01:38
Why can't I calculate it this way:

88000 = 11 * 8 * 1000 -> 1 chips of 11 points, 1 chip of 8 points (purple), and 200 chips of 5 points (green)?

Math Expert
Joined: 02 Sep 2009
Posts: 62289
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

03 Jun 2015, 02:04
ashishcromp2k wrote:
Why can't I calculate it this way:

88000 = 11 * 8 * 1000 -> 1 chips of 11 points (red), 1 chip of 8 points (purple), and 200 chips of 5 points (green)?

If you have 200 5-point green chips the product you will get is 5*5*...*5 = 5^200 not 5*200.
_________________
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16319
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

03 Jun 2015, 15:38
Hi All,

This question involves a bit of logical thinking and factoring skills. You have to take notes and stay organized though, if you want to answer this question correctly.

We're told:
Blue chips = 1 point each
Green chips = 5 points each
Purple chips = X points each (more than Green, less than Red, so X = 6, 7, 8, 9 or 10)
Red chips = 11 points each

We're told that taking an unknown number of chips gives us a product equal to 88,000; we need to factor 88,000 and we should look specifically for 5s, 11s and some mystery number between 6 and 10, inclusive….

88,000 =
(11)(8,000) =
(11)(5)(1600) =
(11)(5)(5)(320) =
(11)(5)(5)(5)(64)

Now, we KNOW that there's a mystery number that is between 6 and 10 (inclusive) and MUST account for that 64….

64 = (8)(8)

This gives us 2 purple chips.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Intern
Joined: 29 Sep 2016
Posts: 16
Location: United States
Concentration: Finance, Economics
GPA: 3.01
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

15 Oct 2016, 09:29
Hi,

I get it up to the point where 2^6 = 64 which is also 8^2 = making it 2 times of 8.

But I chose 3 time instead of 2 because I thought 8 was a factor in 5^3 = 125 in which it was (8, 15)

so I thought there was another "hidden" 8 points within 5^3

would you explain why this is wrong?

Thank you so much!
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16319
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

15 Oct 2016, 17:09
Hi dorey777,

In real simple terms, 125 is an ODD number and 8 is an even number. Even numbers do NOT divide evenly into odd numbers, so there can't be a "hidden 8" inside 125.

In addition, 125 is NOT divisible by 15; (15)(8) does NOT equal 125; it equals 120.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2801
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

12 Nov 2017, 07:48
enigma123 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?

A. 1
B. 2
C. 3
D. 4
E. 5

Let’s break 88,000 into its prime factors:

88,000 = 88 x 1000 = 11 x 8 x 10 x 100 = 11 x 2^3 x 5 x 2 x 5^2 x 2^2 = 2^6 x 5^3 x 11^1

We see that there could be any number of blue chips since they are worth 1 point each. The prime factor 5^3 tells us that the number of green chips must be 3 since they are worth 5 points each. The prime factor 11^1 indicates that the number of red chips must be 1 since each red chip is worth 11 points. Thus, the product of the point values of purple chips must be 2^6. Since each purple chip is worth between 5 and 11 points, and the value of a purple chip must be a power of 2, each purple chip must be worth 2^3 = 8 points, since 8 is the only power of 2 between 5 and 11. Since 2^6 = 8^2, there must be 2 purple chips.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
197 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 16319
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: In a certain game, a large bag is filled with blue, green  [#permalink]

### Show Tags

22 Nov 2017, 17:25
1
Hi All,

This question involves a bit of logical thinking and factoring skills. You have to take notes and stay organized though, if you want to answer this question correctly.

We're told:
Blue chips = 1 point each
Green chips = 5 points each
Purple chips = X points each (more than Green, less than Red, so X = 6, 7, 8, 9 or 10)
Red chips = 11 points each

We're told that taking an unknown number of chips gives us a product equal to 88,000; we need to factor 88,000 and we should look specifically for 5s, 11s and some mystery number between 6 and 10, inclusive….

88,000 =
(11)(8,000) =
(11)(5)(1600) =
(11)(5)(5)(320) =
(11)(5)(5)(5)(64)

Now, we KNOW that there's a mystery number that is between 6 and 10 (inclusive) and MUST account for that 64….

64 = (8)(8)

This gives us 2 purple chips.

GMAT assassins aren't born, they're made,
Rich
_________________
Contact Rich at: Rich.C@empowergmat.com

The Course Used By GMAT Club Moderators To Earn 750+

souvik101990 Score: 760 Q50 V42 ★★★★★
ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★
Re: In a certain game, a large bag is filled with blue, green   [#permalink] 22 Nov 2017, 17:25

Go to page    1   2    Next  [ 28 posts ]

Display posts from previous: Sort by