In the game of Dubblefud, red chips, blue chips and green chips are each worth \(2, 4\) and \(5\) points respectively.

This topic has expert replies
Moderator
Posts: 2205
Joined: Sun Oct 15, 2017 1:50 pm
Followed by:6 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Source: Magoosh

In the game Dubblefud, red chips, blue chips and green chips are each worth in \(2, 4\) and \(5\) points respectively. In a certain selection of chips, the product of the point values is \(16,000.\) If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. \(1\)
B. \(2\)
C. \(3\)
D. \(4\)
E. \(5\)

The OA is A

Master | Next Rank: 500 Posts
Posts: 415
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times
Set the numbers of blue and green chips equal to X and the number of red chips equal to Y.

So 2^Y * 4^X*5^X = 16000, or

2^Y * 2^2X * 5^X = 2^4 * 2^3 * 5^3, or

2^(Y+2X)*5^X = 2^7 *5^3. So

X=3 and (Y+2*3)=7, so

Y=1=number of red chips

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7222
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members
BTGmoderatorLU wrote:
Sat Oct 08, 2022 5:35 pm
Source: Magoosh

In the game Dubblefud, red chips, blue chips and green chips are each worth in \(2, 4\) and \(5\) points respectively. In a certain selection of chips, the product of the point values is \(16,000.\) If the number of blue chips in this selection equals the number of green chips, how many red chips are in the selection?

A. \(1\)
B. \(2\)
C. \(3\)
D. \(4\)
E. \(5\)

The OA is A
Breaking 16,000 into prime factors, we have:

16,000 = 16 x 1,000 = 2^4 x 10^3 = 2^4 x 2^3 x 5^3 = 2^7 x 5^3

Since there are an equal number of blue chips and green chips, there must be 3 blue chips and 3 green chips (notice that the green chips are worth 5 points each and we have 5^3 as a factor). Since the blue chips are worth 4 points each, we know that we have 4^3 blue chips, and, since 4^3 = 2^6, there must be 1 red chip so that 2^6 x 2 = 2^7.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage