A department manager distributed a number of books, calendars, and dia

Question

A department manager distributed a number of books, calendars, and diaries among the staff in the department, with each staff member receiving x books, y calendars, and z diaries. How many staff members were in the department?

(1) The numbers of books, calendars, and diaries that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 books, 27 calendars, and 36 diaries.

nalinnair · Answer

We do not get much from the question stem, except the fact that x, y and z have to be positive integers as they represent books, calendars, and diaries respectively.
Let us now consider the statements:
Statement 1:
This statement gives us the ratio of books, calendars, and diaries that each staff member received. This clearly is insufficient. We cannot figure out the number of staff members from this statement. It could be 10 or 1000 or even more.

So, options A and D are out.

Statement 2:
If you look at this statement, it basically provides you the same information as Statement 1. 18 books, 27 calendars, and 36 diaries distributed to all staff member means that each staff member must have received books, calendars, and diaries in the ratio 2:3:4, respectively.
However, this also gives us real numbers.
But this statement is still insufficient as the staff members could be 3 or 9.
Hence, option C is out

As mentioned above, statement 2 already contains the part of the information provided in Statement 1, there is no point looking at these statements together. Hence, even option D is out.

Option  E  is the correct answer.

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A department manager distributed a number of books, calendars, and diaries among the staff in the department, with each staff member receiving x books, y calendars, and z diaries. How many staff members were in the department?

(1) The numbers of books, calendars, and diaries that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 books, 27 calendars, and 36 diaries.

In the original condition, there are 4 variables(the number of x,y,z, staffs), which should match with the number of equations. So you need 4 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), n=1, x=18, y=27, z=36/ n=3, x=6, y=9, z=12, which is not unique and not sufficient.
Therefore, the answer is E.

 For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

shekhawat111 · Answer

I think by combining both the statements we can get a unique value i.e. 9 staff members.
Hence ( c ).

nalinnair · Answer

Hi  shekhawat111 !

Considering both the statements together can result in two solutions. One, as you correctly mentioned, 9 staff members such that each received 2 books, 3 calendars and 4 diaries (a ratio of 2:3:4). Second, 3 staff members such that each received 6 books, 9 calendars and 12 diaries (again, a ratio of 2:3:4). Therefore, both the statements even when taken together is not sufficient to find a unique solution. Hope this helps!!

Regards,
Nalin

DarleneTran · Answer

I have another approach to solve this type of DS question easier.

The question term requires "How many staff members were in the department?" which is referred to "count information". So, it needs count information as an input. 
+Statement 1: we know the ratio of each item, no count information. Insufficient data, A & D are out.
+Statement 2: after simplifying the ratio 18:27:36, we have the same ratio 2:3:4, still no count information-->Insufficient data, B is out.
As statement 1 & 2 are similar, so there's no point to combine them. C is out, then E is the right choice.

fireflyejd1 · Answer

1 - we know the ratio of the items distributed.
 2:3:4 
 We do not know how many people though. total number of items can be (2+3+4 = 9) any multiple of 9. Total number of employees can be ay multiple of 9.

2- manager distributes total of 18 books, 27 calenders and 36 diaries. 
divide everything by 9 and we get the ratio to be
 2:3:4 
this is the same information as in stem 1. And hence, for the reason mentioned above, it is not sufficient.

1+2= not sufficient because they are both providing the same information

e

deveshj21 · Answer

ScottTargetTestPrep 
As quoted above only 9(people) gives the value of total no of books books: calendars: diary as 18:27:36
the same is found by combining both the options:
option A provides the ratio as provided in option B 
option B provides the no of people
Where am i going wrong?

rsrighosh · Answer

Statement 1 :The numbers of books, calendars, and diaries that each staff member received were in the ratio 2:3:4, respectively.

Hence,  x=2m; y=3m; z=4m

Total no. of staff (n) = \frac{(Total no. of items) }{ (No. of Items received by Individual staff)}

No. of items received by individual =   x+y+z = 9m

therefore equation becomes

n = \frac{Total no. of items }{ 9m}

Total no. of items = ? 
m = ?

Insufficient

Statement 2 :The manager distributed a total of 18 books, 27 calendars, and 36 diaries.

But no. of items received by individual staff is not given.

Insufficient

Statement 1 and 2

Therefore the equation becomes

n = \frac{Total no. of items }{ 9m}

or  n = \frac{81 }{ 9m}

m can be 1 or 3 or 9

Different values of m will yield different no. of staffs (n)

Insufficient

Therefore E

lecremeglace · Answer

So when I see a wordy question like this with a lot of variables and potential ratios, my mind goes to simplifying something as quick as I can. Reading the whole question over without writing anything down yet, I notice it's a ratio question and that they are looking for a specific count ("how many staff members?"). Right away, I know that ratio information won't be enough to solve the question (more info on this can be found in this Magoosh blog post on Ratio and Proportions).

Question Stem 
The question stem doesn't provide a lot of information, so I move to statement 1.

Statement 1 
Statement 1 immediately gives me more ratio information. I can rule it out immediately because I know I need count information to solve this problem.

Statement 2 
Hmm...this looks like count information. It gives me the total number of items delivered... Off the top of my head, I don't know if there's any clever strategy I can use that is as effective as the count versus ratio information rule I used in Statement 1. I think it makes the most sense to test two cases since the numbers look pretty easy.

Test 1 
Seems like the numbers are multiples of 9, so 2 book, 3 calendars, and 4 diaries for 9 people work (maybe at this point I notice that the information provided is the same as statement 1, but if not, I move on to a simple second test)

Test 2 
I can also probably just use the same numbers that are provided, so 18 books, 27 calendars, and 36 diaries for 1 person. This also works and confirms 2 different answers. I can rule out statement 2, not sufficient.

Together, both cases I identified above still fulfill statement 1 and 2, so I can eliminate D and choose E.

Total time: 2:08 (slightly over for a harder question).

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A department manager distributed a number of books, calendars, and dia

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