Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Quant Quizzes are back with a Bang and with lots of Prizes. The first Quiz will be on 8th Dec, 6PM PST (7:30AM IST). The Quiz will be Live for 12 hrs. Solution can be posted anytime between 6PM-6AM PST. Please click the link for all of the details.
Join IIMU Director to gain an understanding of DEM program, its curriculum & about the career prospects through a Q&A chat session. Dec 11th at 8 PM IST and 6:30 PST
Enter The Economist GMAT Tutor’s Brightest Minds competition – it’s completely free! All you have to do is take our online GMAT simulation test and put your mind to the test. Are you ready? This competition closes on December 13th.
Attend a Veritas Prep GMAT Class for Free. With free trial classes you can work with a 99th percentile expert free of charge. Learn valuable strategies and find your new favorite instructor; click for a list of upcoming dates and teachers.
Does GMAT RC seem like an uphill battle? e-GMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days.
A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
08 Jan 2010, 14:18
5
41
00:00
A
B
C
D
E
Difficulty:
65% (hard)
Question Stats:
56% (01:38) correct 44% (01:39) wrong based on 555 sessions
HideShow timer Statistics
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
i am still not able to understand. Can you please explain in detail?
also please tell me where i went wrong.This was my logic.
No. of people office 1: 0|0|0|1|1|1|2|2|3 office 2: 1|2|3|0|1|2|0|1|0
this gives me 9 possible combination
First of all you should assign ALL 3 employees to either of the offices. You can have the following scenarios:
No. of people ***********A|B|C|D| office 1: 0|1|2|3| office 2: 3|2|1|0|
In scenario (A) and (D) there is only one way to assign three people. But in (B) and (C) there will be 3 cases in each:
Let's say there are 3 employees: Tom, Mary and Kate. In (B): Tom can be in office #1 and Mary/Kate in #2 OR Mary can be in #1 and Tom/Kate in #2 OR Kate in #1 and Tom/Mary in #2. Total 3 cases for (B). The same for (C). (A)+(B)+(C)+(D)=1+3+3+1=8.
The way I solved this was different:
Each of the three employees, Tom, Mary and Kate, has two choices office #1 or office #2. Hence total # of combinations (assignments) is 2*2*2=2^3=8.
A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
08 Jan 2010, 16:58
6
5
sagarsabnis wrote:
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices?
Re: Why D any not B? please help me out
[#permalink]
Show Tags
17 Nov 2010, 08:56
2
2
SoniaSaini wrote:
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices? A. 5 B. 6 C. 7 D. 8 E. 9
thanks in advance!!!
For each one of the 3 employees, there are two choices. He can be allotted to any one of the two offices. Hence total number ways will be 2 * 2* 2 = 8 ways
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Hi, I am kind of lost on all probability type qs :/
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices? A. 5 B. 6 C. 7 D. 8 E. 9
Think in this way: There is no restriction on the offices i.e. they can be vacant, they can accommodate all 3 employees etc. But there is a restriction on the employees i.e. each one of them must get an office.
Employee 1 can get an office in 2 ways - office A or office B Employee 2 can get an office in 2 ways - office A or office B Employee 3 can get an office in 2 ways - office A or office B All three can be allotted offices in 2*2*2 = 8 ways This takes care of all cases.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
The fastest way to solve this problem is by using the formula, 2^n, where n stands for the number of elements, or, in this case, the number of employees. This formula is derived from adding the number of combinations from
What’s important with this problem is not to treat it as a probability problem. While on the surface it may seem similar to a typical combinations problem, using the combinations formula to solve the problem is cumbersome.
Instead, use the formula, 2^n, where n stands for the number of elements, or, in this case, the number of employees.
This formula is derived from adding the number of combinations whenever you can select any number greater than zero and less than or equal to n. For instance, here we could have chosen any of three employees for the first office. So instead of using 3C0 + 3C1 + 3C2 + 3C3, we can use 2^3.
This formula becomes especially useful for larger numbers. Imagine the question were:
How many ways can 8 employees go in two offices?
(A) 8 (B) 32 (C) 48 (D) 64 (E) 120
Following the method of finding each case would take too much time. By using 2^n, we 2^8 = 64. (D)
Going back to my original point: do not think of this as a typical probability problem, but one that uses the 2^n concept. The problems, while not really a probability problem, employ the 2^n formula.
Positive integer N is the product of three distinct primes. How many factors in N?
Ans: 2^3 – 1 (zero is not a factor so hence we subtract one from 2^n).
A multiple-choice test has five possible answer choices. Any number of answers can be correct. (e.g. A-B-D is possible answer, C-D, or all five). How many different possible answers?
Ans: 2^5 – 1 = 31 You can’t leave question blank (like the empty office) so therefore -1.
By understanding the concept behind a question, instead of grouping a question under one general category, you should be able to solve problems more quickly.
_________________
Re: A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
06 Jul 2013, 17:59
1
Thank you. Then, if the company assigns employees to offices in such a way that if the offices can not be empty and more than one employee can be assigned to an office. And we have 5 employees and 3 rooms, the answer would be:
Re: A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
07 Jul 2013, 01:13
3
1
Maxirosario2012 wrote:
Thank you. Then, if the company assigns employees to offices in such a way that if the offices can not be empty and more than one employee can be assigned to an office. And we have 5 employees and 3 rooms, the answer would be:
120? I mean, 5!
No. It would be 3^5 minus restriction.
For example, for 5 employees and 2 offices it would be 2^5 - 2 ({5-0} and {0-5}).
_________________
Re: A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
07 Jul 2013, 13:35
Thank you Bunuel! I have difficulties learning combinations, this is my weakest area in the GMAT. I am planning to practice all the combinations problems in the forum. Regarding the problem that I have posted before, I think that you mean:
\(3^5\) - the combinations in which zero is an element in the set and it cannot be zero in any of the slots, with the restrictions that the 3 elements must sum up 5): {(005),(014),(023),(032),(041) ; (050)(140),(230),(320),(410) ; (500),(104),(203),(302),(401)}
243 - 15 = 228
I tried to apply combinatorics formulas to this problem (because writing that set is very time consuming) but I could not figure it out. Translating the problem: I need to find the number of combinations of three digits in which at least one of the digits is "0", the sum of those three digits is 5 and the digits range from 0 to 5 (six elements). Then, substract this number from \(3^5\)
Re: A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
31 Aug 2013, 07:47
ok, can someone tell me what's wrong with my thinking.. 1st office can have any 3 employees.. therefore 3 options, 2nd office can also have any of 3 employees hence again 3 options so it should be 3*3=9
i think the logic is similar to the way Bunuel did..the only difference is in that case we had 2 choices for each employee therefore it was 2*2*2=8.. but why is the answer different in both cases?
Re: A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
03 Sep 2013, 06:42
1
nikhil007 wrote:
ok, can someone tell me what's wrong with my thinking.. 1st office can have any 3 employees.. therefore 3 options, 2nd office can also have any of 3 employees hence again 3 options so it should be 3*3=9
i think the logic is similar to the way Bunuel did..the only difference is in that case we had 2 choices for each employee therefore it was 2*2*2=8.. but why is the answer different in both cases?
We are distributing employees to the offices not vise-versa.
_________________
Re: A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
18 Apr 2016, 12:28
1
Three people that can go in either office 1 or 2 So 2^3 =8
Important is to see that you are not distributing offices to people. That would be 3^2 instead of 2^3
_________________
Took the Gmat and got a 520 after studying for 3 weeks with a fulltime job. Now taking it again, but with 6 weeks of prep time and a part time job. Studying every day is key, try to do at least 5 exercises a day.
A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
18 Apr 2016, 15:46
with 2 offices and 3 employees, there are 3 ways to have one's own office, 3 ways to share an office with one other, and 2 ways to share an office with two others, or 8 ways total
Re: A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
05 Nov 2016, 06:26
Hi
I solved it the following way. Is my approach correct? Please comment.
4*1*2=8
we have 4 options ( 0,1,2,3 employees) for the first office and 1 for the other. Multiply by 2 as we can assign employees to 2nd office first ,in which case 1st office will have only 1 option.
Re: A certain company assigns employees to offices in such a way
[#permalink]
Show Tags
07 Nov 2016, 16:01
VeritasPrepKarishma wrote:
SoniaSaini wrote:
A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 2 different offices? A. 5 B. 6 C. 7 D. 8 E. 9
thanks in advance!!!
For each one of the 3 employees, there are two choices. He can be allotted to any one of the two offices. Hence total number ways will be 2 * 2* 2 = 8 ways
Another way to put it:
There are 3 employees in total, so the max number of people in one office is 3. And the min is 0.
Ways to distribute 3 employees (E) in 2 offices.
Office 1:
E E E E E _ E _ _ _ _ _ (empty)
Office 2: (Same as office 1.)
E E E E E _ E _ _ _ _ _ (empty)
Since there is no distinction between each employee for this particular question, there are 4 ways to have 3 employees fill an office. Since there are two offices, there are: 4 + 4 = 8 ways to assign 3 employees to 2 offices