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

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BTGmoderatorLU: Moderator; Posts: 2554; Joined: Sun Oct 15, 2017 1:50 pmFollowed by: 6 members

by BTGmoderatorLU » Sat Oct 08, 2022 5:35 pm

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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

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Source: Beat The GMAT — Problem Solving | Sat Oct 08, 2022 5:35 pm

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

Re: In the game of Dubblefud, red chips, blue chips and green chips are each worth $2, 4$ and $5$ points respectivel

by regor60 » Wed Nov 02, 2022 9:36 am

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

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8154; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: In the game of Dubblefud, red chips, blue chips and green chips are each worth $2, 4$ and $5$ points respectivel

by Scott@TargetTestPrep » Thu Dec 01, 2022 11:06 am

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

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