There are 4 machines with the same work rate. If it took k

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Thu Mar 01, 2018 2:40 am

[GMAT math practice question]

There are 4 machines with the same work rate. If it took k hours for 3 machines to work and did k-2 hours for 4 machines when working together, what is the value of k?

A. 4
B. 5
C. 6
D. 7
E. 8

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Source: Beat The GMAT — Problem Solving | Thu Mar 01, 2018 2:40 am

mbawisdom: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Tue Dec 16, 2014 9:50 amFollowed by: 4 members; Location: London, UK; Thanked: 2 times; GMAT Score:770

by mbawisdom » Thu Mar 01, 2018 6:20 am

Max@Math Revolution wrote:[GMAT math practice question]

There are 4 machines with the same work rate. If it took k hours for 3 machines to work and did k-2 hours for 4 machines when working together, what is the value of k?

A. 4
B. 5
C. 6
D. 7
E. 8

Total machine working hours will be the same for 3 machines and 4 machines.

Total machine hours with 3 machines = 3k
Total machine hours with 4 machines = 4(k-2)

3k = 4(k-2)
3k = 4k - 8
k = 8

Answer = (E) 8

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Max@Math Revolution: Elite Legendary Member; Posts: 3991; Joined: Fri Jul 24, 2015 2:28 amFollowed by: 37 members; Location: Las Vegas, USA; Thanked: 19 times

by Max@Math Revolution » Sun Mar 04, 2018 6:17 pm

=>

Work Amount = Number of machines * Work Rate * Time
If r is the machine's work rate, we have 3rk = 4r(k-2) or 3k = 4k -8.
Thus k = 8.

Therefore, E is the answer.

Answer: E

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8196; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Mon Jun 10, 2019 6:17 pm

Max@Math Revolution wrote:[GMAT math practice question]

There are 4 machines with the same work rate. If it took k hours for 3 machines to work and did k-2 hours for 4 machines when working together, what is the value of k?

A. 4
B. 5
C. 6
D. 7
E. 8

Let the rate of each machine be r. We can create the equation:

(3r)k = (4r)(k - 2)

3k = 4k - 8

8 = k

Answer: E

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