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29 Jan 2020, 01:43
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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Question Stats:
68% (02:15) correct
32%
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wrong
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In a certain department of ABC business school, there are either accounting or finance professors. If 2/3 of the professors are accounting professors, what is the ratio of the total number of professors that do outside consulting to the total number of professors that don't do outside consulting?
(1) 1/3 of the finance professors do outside consulting.
(2) The ratio of the number of accounting professors that do outside consulting to the number of finance professors that do outside consulting is 3:4.
(1) 1/3 of the finance professors do outside consulting.
(2) The ratio of the number of accounting professors that do outside consulting to the number of finance professors that do outside consulting is 3:4.
29 Jan 2020, 03:06
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Bunuel
Method 1:
From the statements, it should be clear that we need both statements to try and solve it. Individual statements offer too little information.
Let the total number of professors be \(3k\)
Number of accounting professors = \(2/3 * 3k = 2k\)
Number of financial professors = \(3k - 2k = k\)
Statement 1: Finance professors who do outside consulting = \(k/3\)
=> Finance professors who do not do outside consulting = Number of Finance professors - Finance professors who do outside consulting
\(= k - k/3 = 2k/3\)
Statement 2: Accounting professors who do outside consulting : Finance professors who do outside consulting = \(3 : 4\)
=> Accounting professors who do outside consulting = \(3/4\) * Finance professors who do outside consulting = \(3/4 * k/3 = k/4\)
=> Accounting professors who do not do outside consulting
= Number of Accounting professors - Accounting professors who do outside consulting
\(= 2k - k/4 = 7k/4\)
Thus, we have: ratio of the total number of professors that do outside consulting to the total number of professors that don't do outside consulting
\(= (k/3 + k/4) : (2k/3 + 7k/4)\)
= 7 : 29
Alternate approach: Using a Venn-diagram, the solution becomes kind of complicated:
According to the question, we know that:
An accounting professor doesn't teach finance and vice-versa; i.e. there is no professor who teaches both finance and accounting.
Thus, we can use a 2-Venn diagram with one representing the finance professors and the other representing the professors who participate in consulting outside.
The diagram is shown below:
Attachment:
11.JPG [ 28.53 KiB | Viewed 1847 times ]
We need to determine the ratio of the total number of professors that do outside consulting to the total number of professors that don't do outside consulting, i.e. \((q + r) : (p + s)\)
Since 2/3 of the professors are accounting professors (i.e. 1/3 of the professors are finance professors), we have:
Ratio of accounting professors to finance professors = 2 : 1
\(=> (r + s) : (p + q) = 2 : 1\) ... (i)
From Statement 1: 1/3 of the finance professors do outside consulting
\(=> q = (p + q)/3 => p = 2q\) ... (ii)
Even after using (i), we cannot determine the value of \((q + r) : (p + s)\) - Insufficient
From Statement 2: The ratio of the number of accounting professors that do outside consulting to the number of finance professors that do outside consulting is 3:4
\(=> r : q = 3 : 4\)
\(=> r = 3q/4\) ... (iii)
Even after using (i), we cannot determine the value of \((q + r) : (p + s)\) - Insufficient
Combining the statements:
From (i): \(=> (r + s) : (p + q) = 2 : 1\)
\(=> (r + s) = 2(p + q)\)
Using \(p = 2q\) and \(r = 3q/4\):
\(=> (3q/4 + s) = 2(2q + q)\)
\(=> s = 21q/4\)
Thus, we have:
\((q + r) : (p + s) = (q + 3q/4) : (2q + 21q/4) = 7 : 29\) - Sufficient
Answer C
29 Jan 2020, 07:58
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2/3 are Accounting Professors, 1/3 are Finance Professors. Using Statement 1, we know that 1/3 of those Finance Professors consult, so (1/3)(1/3) = 1/9 of all profs are Finance Professors who consult. Statement 2 tells us that the number of Accounting Professors who consult is 3/4 of the number of Finance Professors who consult, so must be (3/4)(1/9) = 1/12 of all professors. So the fraction of all professors who consult is just 1/9 + 1/12 = 7/36, and the ratio of those who do consult to those who don't is thus 7 to 29. So both statements are sufficient together, and the answer is C.
