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24 Apr 2020, 02:12
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
47% (02:51) correct
53%
(02:57)
wrong
based on 96
sessions
History
Date
Time
Result
Not Attempted Yet
In Grand Oberoi hotel, 1160 guests are present currently. The hotel provides the following extra facilities: Gym, Swimming, Fun park, Food. During a regular survey the management team of Oberoi noticed something quite extraordinary about the extra facilities provided by them. They noticed that for every person who uses ‘F’ no. of facilities, there are exactly 3 persons who uses at least (F-1) no. of facilities, F = 2, 3, 4. They also found that the no. of persons who used no extra facilities is twice the no of person that used all the 4 facilities. Help the management team to find out how many persons used exactly 3 facilities.
A. 20
B. 40
C. 60
D. 80
E. 100
24 Apr 2020, 03:36
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Let the number of persons who uses exactly four facilities be ‘P’
For every person who uses 4 facilities, there are exactly three person who uses at least 3 facilities.
The number of person who uses at least 3 facilities = 3P.
---> The number of person who uses exactly 3 facilities = 3P – P = 2P
For every person who uses (any) 3 facilities, there are exactly three person who uses at least 2 facilities.
The number of person who uses at least 2 facilities = 3*3P = 9P.
For every person who uses (any) 2 facilities, there are exactly three person who uses at least 1 facility.
The number of person who uses at least 1 facility = 3*9P = 27P.
The number of person who uses NO facility = 2*P
Total persons = The number of person who uses at least 1 facility (F= 1,2,3,4) + The number of person who uses NO facility
1160 = 27P + 2P
P= 1160/29 = 40
---> The number of person who uses exactly 3 facilities = 2P =2*40 = 80
FINAL ANSWER IS (D)
Posted from my mobile device
For every person who uses 4 facilities, there are exactly three person who uses at least 3 facilities.
The number of person who uses at least 3 facilities = 3P.
---> The number of person who uses exactly 3 facilities = 3P – P = 2P
For every person who uses (any) 3 facilities, there are exactly three person who uses at least 2 facilities.
The number of person who uses at least 2 facilities = 3*3P = 9P.
For every person who uses (any) 2 facilities, there are exactly three person who uses at least 1 facility.
The number of person who uses at least 1 facility = 3*9P = 27P.
The number of person who uses NO facility = 2*P
Total persons = The number of person who uses at least 1 facility (F= 1,2,3,4) + The number of person who uses NO facility
1160 = 27P + 2P
P= 1160/29 = 40
---> The number of person who uses exactly 3 facilities = 2P =2*40 = 80
FINAL ANSWER IS (D)
Posted from my mobile device
General Discussion
24 Apr 2020, 10:10
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In Grand Oberoi hotel, 1160 guests are present currently. The hotel provides the following extra facilities: Gym, Swimming, Fun park, Food. During a regular survey the management team of Oberoi noticed something quite extraordinary about the extra facilities provided by them. They noticed that for every person who uses ‘F’ no. of facilities, there are exactly 3 persons who uses at least (F-1) no. of facilities, F = 2, 3, 4. They also found that the no. of persons who used no extra facilities is twice the no of person that used all the 4 facilities. Help the management team to find out how many persons used exactly 3 facilities.
A. 20
B. 40
C. 60
D. 80
E. 100
Basically, question is saying that if n is number of persons using 3 facilities, then \(\frac{n}{3}\) is the number of people who use 4 facilities.
Let number of people using 3 facilities,\(F_3 = n\)
Then Number of people using 2 facilities,\(F_2 = 3n\)
Number of people using 1 facility,\(F_1 = 9n\)
Number of people using 4 facilities,\(F_4 = \frac{n}{3}\)
Number of people using 0 facilities,\(F_0 = 2\frac{n}{3}\)
Hence,
\(\frac{n}{3} + n + 3n + 9n + 2\frac{n}{3} = 1160\)
n + 3n + 9n + 27n + 2n = 1160*3
42n = 1160*3
\(n = \frac{580}{7}\) ~80
IMO Answer D.
PS: The number here should be a multiple of 3, accordingly only C satisfies this condition. Also, on verifying none of the options satisfy all conditions laid by the question. Don't what am i missing?
A. 20
B. 40
C. 60
D. 80
E. 100
Basically, question is saying that if n is number of persons using 3 facilities, then \(\frac{n}{3}\) is the number of people who use 4 facilities.
Let number of people using 3 facilities,\(F_3 = n\)
Then Number of people using 2 facilities,\(F_2 = 3n\)
Number of people using 1 facility,\(F_1 = 9n\)
Number of people using 4 facilities,\(F_4 = \frac{n}{3}\)
Number of people using 0 facilities,\(F_0 = 2\frac{n}{3}\)
Hence,
\(\frac{n}{3} + n + 3n + 9n + 2\frac{n}{3} = 1160\)
n + 3n + 9n + 27n + 2n = 1160*3
42n = 1160*3
\(n = \frac{580}{7}\) ~80
IMO Answer D.
PS: The number here should be a multiple of 3, accordingly only C satisfies this condition. Also, on verifying none of the options satisfy all conditions laid by the question. Don't what am i missing?
