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Am I on the right track?

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by okigbo » Thu Oct 22, 2009 10:27 am
8) Two machine types, Type R and Type S, operate at a constant rate. R does a job in 36 hours. S does same job in 18. If we use the same number of each type to do the job in 2 hours, how many Type r machines do we need?
a. 3
b. 4
c. 6
d. 9
e. 12


R: w=36r
S: w=18r
36r=18r
Same number of each type so must be 6. For two hours for type R must be a multiple of 3; therefore 6

Is this the right way to think about the problem? Thanks.
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Re: Am I on the right track?

by Brent@GMATPrepNow » Sat Oct 24, 2009 6:43 am
okigbo wrote:8) Two machine types, Type R and Type S, operate at a constant rate. R does a job in 36 hours. S does same job in 18. If we use the same number of each type to do the job in 2 hours, how many Type r machines do we need?
a. 3
b. 4
c. 6
d. 9
e. 12

R: w=36r
S: w=18r
36r=18r
Same number of each type so must be 6. For two hours for type R must be a multiple of 3; therefore 6

Is this the right way to think about the problem? Thanks.
When it comes to questions where we must complete an entire job, I often (not always) like to know what can be accomplished in 1 unit of time (in this case, 1 hour).

Machine R can complete 1/36 of the job in 1 hour.
Machine S can complete 1/18 of the job in 1 hour.
Combined, machines R and S can complete 1/12 (1/36 + 1/18) of the job in 1 hour.

From here we can apply some logic.
If 1/12 of the job is completed in 1 hour (with 1 R machine and 1 S machine), then we could complete the entire job in 1 hour if we had 12 of each machine type.
However, the question asks us to find the # of machines required to complete the job in 2 hours. So, we need half as many machines. In other words, we need 6 of each machine.
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by Vanshika21 » Sat Mar 10, 2012 8:30 pm
Brent@GMATPrepNow wrote:
okigbo wrote:8) Two machine types, Type R and Type S, operate at a constant rate. R does a job in 36 hours. S does same job in 18. If we use the same number of each type to do the job in 2 hours, how many Type r machines do we need?
a. 3
b. 4
c. 6
d. 9
e. 12

R: w=36r
S: w=18r
36r=18r
Same number of each type so must be 6. For two hours for type R must be a multiple of 3; therefore 6

Is this the right way to think about the problem? Thanks.
When it comes to questions where we must complete an entire job, I often (not always) like to know what can be accomplished in 1 unit of time (in this case, 1 hour).

Machine R can complete 1/36 of the job in 1 hour.
Machine S can complete 1/18 of the job in 1 hour.
Combined, machines R and S can complete 1/12 (1/36 + 1/18) of the job in 1 hour.

From here we can apply some logic.
If 1/12 of the job is completed in 1 hour (with 1 R machine and 1 S machine), then we could complete the entire job in 1 hour if we had 12 of each machine type.
However, the question asks us to find the # of machines required to complete the job in 2 hours. So, we need half as many machines. In other words, we need 6 of each machine.
Is there any other approach to do this one? Thanks :)
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by GMATGuruNY » Sun Mar 11, 2012 3:53 am
I posted an alternate solution here:

https://www.beatthegmat.com/machine-r-and-s-t94824.html
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

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