There are 4 machines with the same work rate. If it took k hours for 3 : Problem Solving (PS)

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There are 4 machines with the same work rate. If it took k hours for 3

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Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 6390

GMAT 1: 760 Q51 V42

GPA: 3.82

There are 4 machines with the same work rate. If it took k hours for 3 [#permalink]

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01 Mar 2018, 03:50

00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:44) correct

29% (01:46) wrong

based on 74 sessions

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[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

Spoiler: OA

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Intern

Joined: 19 Feb 2018

Posts: 5

Re: There are 4 machines with the same work rate. If it took k hours for 3 [#permalink]

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01 Mar 2018, 05:33

If it takes 3 machines khours to work and 4 machine (k-2)hrs, then
1 machine will work in 3k hours which is also equivalent to 4(k-2) hours
Therefore
3k=4k-8
K=8

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Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 6390

GMAT 1: 760 Q51 V42

GPA: 3.82

Re: There are 4 machines with the same work rate. If it took k hours for 3 [#permalink]

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04 Mar 2018, 19:25

=>

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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