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
Word problems
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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
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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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
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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Spot on here. Try to reduce your work. Think if the spots and if repeats matter.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
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Initially There are 18 choices for first PositionKim9876Zey 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
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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Aside from picking numbers (e.g., letting the entire job be 36 units), we can solve the question as follows: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
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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Since the order in which we select the applicants does not matter, we can use combinations.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
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