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26 Jan 2024, 02:50
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
91% (02:31) correct
9%
(02:57)
wrong
based on 442
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Of the faculty members at a certain university, 4/9 are in the School of Liberal Arts and Sciences, 1/5 are in the School of Business, 1/6 are in the School of Education, and the remaining 51 are in the School of Nursing. If no faculty member is in more than one school, how many faculty members are there at the university?
A. 270
B. 315
C. 360
D. 405
E. 450
2024-01-26_13-46-19.png [ 52.17 KiB | Viewed 6773 times ]
A. 270
B. 315
C. 360
D. 405
E. 450
Attachment:
2024-01-26_13-46-19.png [ 52.17 KiB | Viewed 6773 times ]
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26 Jan 2024, 02:57
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guddo
- \(\frac{4}{9} + \frac{1}{5} + \frac{1}{6 }= \)
\(=\frac{40}{90} + \frac{18}{90} + \frac{15}{90 }= \)
\(=\frac{73}{90}\).
Thus, \(1-\frac{73}{90}=\frac{17}{90}\) of the faculty members constitute 51 people. Therefore, there are \(\frac{51}{(\frac{17}{90})}=\frac{51*90}{17}=3*90=270\) faculty members at the university.
Answer: A.
04 Jun 2024, 11:13
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4/9, 1/5, 1/6 of total no. of faculty.
Take LCM of the denominator i.e. LCM(9,5,6)= 90
Since, these ratios are part of total, total no. of faculty must be multiple of 90 i.e. 90k, where k is an integer k=0,1,2...
We can then eliminate option B and D.
Check options A, C and E:
A) 4/9*90k + 1/5*90k + 1/6*90k= 73k
73k+51= 270
73k=219
k=3 is an integer.
Therefore, this holds true and 270 is the answer.
C) 360
73k+ 51=360
73k=309
k is not an integer.
Take LCM of the denominator i.e. LCM(9,5,6)= 90
Since, these ratios are part of total, total no. of faculty must be multiple of 90 i.e. 90k, where k is an integer k=0,1,2...
We can then eliminate option B and D.
Check options A, C and E:
A) 4/9*90k + 1/5*90k + 1/6*90k= 73k
73k+51= 270
73k=219
k=3 is an integer.
Therefore, this holds true and 270 is the answer.
C) 360
73k+ 51=360
73k=309
k is not an integer.
