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Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Word problems

by Kim9876Zey » Sat Jun 23, 2012 12:12 pm
A certain company has 18 equally qualified applicants for 4 open positions. How many different groups pf 4 applications can be chosen by the company to fill the position if the order of selection does not matter?

18
72
180
1260
3060 correct


A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hrs. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

3
4
6 Correct
9
12
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by theCEO » Sat Jun 23, 2012 5:08 pm
A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hrs. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?


For 1 R machine - rate = 1 job / 36 hrs
For y R machines - rate = 1 job / (36hrs/y) = y job / 36hrs

For 1 S machine - rate = 1 job / 18 hrs
For y R machines - rate = 1 job / (18hrs/y) = y job / 18hrs

Rate * time = number of job completed
number of job completed by R + number of job completed by S = total number of jobs completed



(y job / 36hrs)*2hrs + (y job / 18hrs)*2hrs = 1 job
(y job / 18) + (2y job /18) = 1job
(3y job / 18)= 1 job
y job / 6 = 1 job
y job = 6 job
y = 6
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by theCEO » Sat Jun 23, 2012 5:15 pm
A certain company has 18 equally qualified applicants for 4 open positions. How many different groups pf 4 applications can be chosen by the company to fill the position if the order of selection does not matter?

18*17*16*15 - fill all 4 spots (a)
4*3*2*1 - since position doesnt matter (b)
Divide (a) by (b) = 3060
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by Jim@StratusPrep » Sun Jul 08, 2012 3:46 pm
theCEO wrote:A certain company has 18 equally qualified applicants for 4 open positions. How many different groups pf 4 applications can be chosen by the company to fill the position if the order of selection does not matter?

18*17*16*15 - fill all 4 spots (a)
4*3*2*1 - since position doesnt matter (b)
Divide (a) by (b) = 3060
Spot on here. Try to reduce your work. Think if the spots and if repeats matter.
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by GMATinsight » Sun Aug 09, 2015 5:20 am
Kim9876Zey wrote:A certain company has 18 equally qualified applicants for 4 open positions. How many different groups pf 4 applications can be chosen by the company to fill the position if the order of selection does not matter?

18
72
180
1260
3060 correct

Initially There are 18 choices for first Position
Now, There are 17 choices for Second Position
Now, There are 16 choices for Third Position
Now, There are 15 choices for Forth Position

i.e. Total Ways to choose people (With arrangement) = 18*17*16*15

Since we require only the selection hence we need to exclude the arrangements of 4 selected individuals which is 4!


i.e. i.e. Total Ways to choose people (WithOUT arrangement) = (18*17*16*15)/4! = 3060

Answer: Option E
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by Brent@GMATPrepNow » Sun Aug 09, 2015 6:41 am
Kim9876Zey wrote: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 36 hrs and a machine of type S does the same job in 18 hrs. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?

3
4
6
9
12
Aside from picking numbers (e.g., letting the entire job be 36 units), we can solve the question as follows:

First, 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.
Since 1/36 + 1/18 = 1/12, we know that, combined, machines R and S can complete 1/12 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.

Answer = 6

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by Brent@GMATPrepNow » Sun Aug 09, 2015 6:43 am
Kim9876Zey wrote:A certain company has 18 equally qualified applicants for 4 open positions. How many different groups pf 4 applications can be chosen by the company to fill the position if the order of selection does not matter?

18
72
180
1260
3060
Since the order in which we select the applicants does not matter, we can use combinations.
We can select 4 people from 18 people in 18C4 ways.

18C4 = (18)(17)(16)(15)/(4)(3)(2)(1) = 3060

If anyone is interested, we have a free video on calculating combinations (like 18C4) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789
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