At State University, the average (arithmetic mean) salary of : GMAT Data Sufficiency (DS)
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# At State University, the average (arithmetic mean) salary of

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At State University, the average (arithmetic mean) salary of [#permalink]

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21 Nov 2010, 07:19
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At State University, the average (arithmetic mean) salary of philosophy department professors is $56,000 and the average annual salary of business department professors is$74,000. If at State University there are two departments, what is the average annual salary at State University?

(1) The two departments have a total of 42 professors.
(2) There are twice as many professors in the philosophy department than in the business department.

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Can some one explain the OA to me
[Reveal] Spoiler: OA

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21 Nov 2010, 10:23
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rxs0005 wrote:
At State University, the average (arithmetic mean) salary of philosophy department professors is $56,000 and the average annual salary of business department professors is$74,000. If at State University there are two departments, what is the average annual salary at State University?

(1) The two departments have a total of 42 professors.
(2) There are twice as many professors in the philosophy department than in the business department.

(A) Statement (1) ALONE is sufficient, but statement (2) is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

Can some one explain the OA to me

Step 1 of the Kaplan Method for DS: Analyze the stem

We see that there are only two groups, and we know the average of each individual group. We're asked to find the overall average.

We think: to solve for a weighted average, we need the weighting of each group.

Step 2 of the Kaplan Method for DS: Evaluate the statements

(1) tells us the total number of professors, but not how many are in each group: insufficient, eliminate A and D.

(2) tells us that there are twice as many profs in the philosophy department; in other words, the philosophy profs make up 2/3 of all of the professors. We now know the weight of each group: sufficient, eliminate C and E; choose B!

If we actually wanted to solve (say this were a problem solving question), we'd do so as follows:

Overall average of a group = (avg group 1)(weight group 1) + (avg group 2)(weight group 2) + ... + (avg group n)(weight group n)

Overall salary average = (avg salary phil profs)(weight of phil profs) + (avg salary bus profs)(weight of bus profs)

Overall salary average = (56000)(2/3) + (74000)(1/3) = 112000/3 + 74000/3 = 186000/3 = 62000

(There are other, quicker, ways to solve using weighted averages, but applying the formula is the "textbook" approach.)

Whenever you review a question (and you should review every one you do!), you always want to finish by asking "what can I take away from this exercise?" Here are our takeaways from this question:

1) to solve for an overall average, you don't necessarily need the numbers in each group - knowing the weights of each group is sufficient;

2) the better you understand the concepts, the less math you'll need to do on test day; and

3) it's better to be a business prof than a philosophy prof!
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21 Nov 2010, 11:53
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statement 2 is sufficient . cos it gives the weightage
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04 Feb 2011, 01:54
At State University, the average (arithmetic mean) salary of philosophy department professors is $56,000 and the average annual salary of business department professors is$74,000. If at State University there are two departments, what is the average annual salary at State University?

(1) The two departments have a total of 42 professors.
(2) There are twice as many professors in the philosophy department than in the business department.
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04 Feb 2011, 03:20
Number of Philosophy Dept. professors: P
Total annual(assumed) salary of Philosophy Dept. professors: $$S_P$$

Number of Business Dept. professors: B
Total annual salary of Business Dept. professors: $$S_B$$

Total number of professors in the university: P+B
Given:
Average salary of Philopsophy Profs $$A_P=S_P/P=56000$$
Average salary of Business Profs $$A_B=S_B/B=74000$$

Q: Average annual salary of professors of State University= ?

It is a weighted average question. We need to know the strength of the professors from each department.

(1)

$$\frac{S_P+S_B}{P+B}$$
$$\frac{S_P+S_B}{42}$$
$$\frac{(P*A_P)+(B*A_B)}{42}$$
$$\frac{(P*56000)+(B*74000)}{42}$$

We don't know anything about P and B.

Not sufficient.

(2) P=2B
$$\frac{S_P+S_B}{P+B}$$
$$\frac{(2B*A_P)+(B*A_B)}{2B+B}$$
$$\frac{B(2*A_P+*A_B)}{3B}$$
$$\frac{(2*A_P+*A_B)}{3}$$

We know both A_P and A_B and thus we know the average annual salary of all professors in the State university.

Sufficient.

Ans: "B"
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28 Feb 2011, 15:39
At State University, the average (arithmetic mean) salary of philosophy department professors is $56,000 and the average annual salary of business department professors is$74,000. If at State University there are two departments, what is the average annual salary at State University?

(1) The two departments have a total of 42 professors.
(2) There are twice as many professors in the philosophy department than in the business department.
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28 Feb 2011, 18:08

Let the number of philosophy department professors = x

And the number of business department professors = y

So we have to find (56,000 * x + 74,000 * y)/(x+y)

From 1 we have :

x + y = 42, not enough

From 2 we have :

x = 2y, so by substituting the same in the above equation, x (or y) can cancel out and we can derive the value.
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28 Feb 2011, 20:25
Law of balances. It has to be B. total number is immaterial to this question. A is insuff.
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02 Mar 2011, 01:00
+1 B. Classic weighted averages problem.
Re: Average DS   [#permalink] 02 Mar 2011, 01:00
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