subhabrata1986 wrote:
I am facing problem to understand answer of a OG12 DS question.
Question:
A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department?
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
ANSWER I DID:
BOTH statements TOGETHER are sufficient, but neither statement alone is sufficient.
As per OG12:
(1) Each of 10 staff members could have received 2 pens, 3 pencils, and 4 pads, or each of 20 staff members could have received 2 pens, 3 pencils, and 4 pads; NOT sufficient. [Agree]
(2) There could have been 1 staff member who received 18 pens, 27 pencils, and 36 pads, or 3 staff members each of whom received 6 pens, 9 pencils, and 12 pads; NOT sufficient.[Agree]
Assuming both (1) and (2), use the fact that 18:27:36 is equivalent to both 6:9:12 and 2:3:4 to obtain diff erent possibilities for the number of staff . Each of 3 staff members could have received 6 pens, 9 pencils, and 12 pads, or each of 9 staff members could have received 2 pens, 3 pencils, and 4 pads.
Now Here I defer. As per Point 1, its already shown that the ratio is ratio 2:3:4. So, we can clearly choose the staff number is 9.
Can anybody please help me to understand where I am making the mistake in this question?
Ok, look the question tells us the following:
Staff Member 1 - x pens, y pencils, z pads
Staff Member 2 - x pens, y pencils, z pads
.
.
.
Staff Member n - x pens, y pencils, z pads
Total no of pens - nx, total no of pencils - ny and total no of pads - nz
Question: What is n?
Stmnt 1: x:y:z = 2:3:4. So values of x, y and z can be 2, 3 and 4 or 4, 6 and 8 or 6, 9 and 12 or any other values in the ratio 2:3:4. They needn't necessarily be 2, 3 and 4. Just the ratio required is 2:3:4.
Of course n can be anything here. Not sufficient.
Stmnt 2: nx = 18, ny = 27 and nz = 36.
Note here that nx:ny:nz = 18:27:36 = 2:3:4 (They had 9 as a common factor)
Since n is a common factor on left side, x:y:z = 2:3:4 (Ratios are best expressed in the lowest form.)
This is a case of what we call "We already knew that." Information given in stmnt 1 is already part of stmnt 2 so it is not possible that stmnt 2 alone is not sufficient but together stmnt 1 and 2 are.
Now to your question:
Why can't we say that the number of staff members must be 9?
Because ratio of 2:3:4 is same as ratio of 6:9:12 which is same as 18:27:36 (When you multiply each number of a ratio by the same number, the ratio remains unchanged).
If 18, 27 and 36 pens, pencils and pads are distributed in the ratio 2:3:4, I could give them all to one person (18:27:36 is the same ratio as 2:3:4), to 3 people (giving them 6 pens, 9 pencils and 12 pads each. 6:9:12 is the same ratio as 2:3:4) or to 9 people (giving them 2 pens, 3 pencils and 4 pads). Hence I don't know how many staff members are there.
Karishma I agree that N is unknown, but on Right hand side when we reduced to the lowest ration, 9 is the only viable possibility. Hence N=9, May be I am missing something will need your insight.