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15 Nov 2010, 00:54
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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.
(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?
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?
15 Nov 2010, 08:00
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subhabrata1986
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?
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.
13 Dec 2012, 18:11
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I got it only by using common sense. Its not tricky if you think about it .
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
This shows you how many more pads [b]one person[b] gets compared to the number of pencils or pens he gets.
(2)The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
This can give you an idea how many gadgets are there in total to distribute, but we cannot know how many people will take them.
There can be just one person taking all the 18 pens, 27 pencils, 36 pads (in the proportion of 2:3:4 as stated in (1) )
There can be three people, each taking 6 pens, 9 pencils, 12 pads (2:3:4)
There can be 9 people, each taking 2 pens, 3 pencils, 4 pads (2:3:4)
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2:3:4, respectively.
This shows you how many more pads [b]one person[b] gets compared to the number of pencils or pens he gets.
(2)The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
This can give you an idea how many gadgets are there in total to distribute, but we cannot know how many people will take them.
There can be just one person taking all the 18 pens, 27 pencils, 36 pads (in the proportion of 2:3:4 as stated in (1) )
There can be three people, each taking 6 pens, 9 pencils, 12 pads (2:3:4)
There can be 9 people, each taking 2 pens, 3 pencils, 4 pads (2:3:4)
