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A university badminton club has both students and professors as member

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Bunuel
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A university badminton club has both students and professors as member [#permalink] New post   10 Nov 2020, 10:00
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A university badminton club has both students and professors as members. Is the number of students in the club at least 45?

(1) The number of professors in the club is a multiple of 8.

(2) The number of students in the club is exactly 20% greater than the number of professors in the club.
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winterschool
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Re: A university badminton club has both students and professors as member [#permalink] New post   10 Nov 2020, 11:02
A university badminton club has both students and professors as members. Is the number of students in the club at least 45?

(1) The number of professors in the club is a multiple of 8.

(2) The number of students in the club is exactly 20% greater than the number of professors in the club.


Statement 1 : number of professors = 8n

Not Sufficient


Statement 2 : students = s, professor = p

s = 1.2p

Not sufficient

Statement 1+ Statement 2 :

n =1, p= 8 , s= 1.2*8 = 9.6 , not exactly 20% greater
n = 2, p=16, s = 1.2*16 = 19.2, not exactly 20% greater
n= 3, p = 24, s = 1.2*24 = 28.8, not exactly 20% greater
n=4, p=32, s = 32*1.2 = 38.4, not exactly 20% greater
n= 5, p=40, s= 1.2*40 = 48, exactly 20% greater

Sufficient

Answer C
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Re: A university badminton club has both students and professors as member [#permalink] New post   11 Nov 2020, 04:44
winterschool wrote:
A university badminton club has both students and professors as members. Is the number of students in the club at least 45?

(1) The number of professors in the club is a multiple of 8.

(2) The number of students in the club is exactly 20% greater than the number of professors in the club.


Statement 1 : number of professors = 8n

Not Sufficient


Statement 2 : students = s, professor = p

s = 1.2p

Not sufficient

Statement 1+ Statement 2 :

n =1, p= 8 , s= 1.2*8 = 9.6 , not exactly 20% greater
n = 2, p=16, s = 1.2*16 = 19.2, not exactly 20% greater
n= 3, p = 24, s = 1.2*24 = 28.8, not exactly 20% greater
n=4, p=32, s = 32*1.2 = 38.4, not exactly 20% greater
n= 5, p=40, s= 1.2*40 = 48, exactly 20% greater

Sufficient

Answer C


I think the answer is B. since you cannot have fraction as people count (9.6 19.2 .. 38.4) the least number of professors that matches the 20% criteria is 40 and students is 48 which is greater than 45.
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A university badminton club has both students and professors as member [#permalink] New post   11 Nov 2020, 06:12
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A university badminton club has both students and professors as members. Is the number of students in the club at least 45?


Step 1: Understanding statement 1 alone
(1) The number of professors in the club is a multiple of 8.
Professors can be 8, 16, 24,...
There is no information related to number of students.
Insufficient

Step 2: Understanding statement 2 alone
(2) The number of students in the club is exactly 20% greater than the number of professors in the club.
number of students = 120% of number of professors = 6/5 * number of professors
Number of professors is not known. Insufficient

Step 3: Combining (1) and (2)
As number of students = 6/5 * number of professors; number of professors must be divisible by 5.
Hence, smallest value possible for number of professors is 40
Therefore, number of students = 48
Sufficient

IMO C
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Re: A university badminton club has both students and professors as member [#permalink] New post   25 Feb 2022, 05:04
iamfirestar wrote:
winterschool wrote:
A university badminton club has both students and professors as members. Is the number of students in the club at least 45?

(1) The number of professors in the club is a multiple of 8.

(2) The number of students in the club is exactly 20% greater than the number of professors in the club.


Statement 1 : number of professors = 8n

Not Sufficient


Statement 2 : students = s, professor = p

s = 1.2p

Not sufficient

Statement 1+ Statement 2 :

n =1, p= 8 , s= 1.2*8 = 9.6 , not exactly 20% greater
n = 2, p=16, s = 1.2*16 = 19.2, not exactly 20% greater
n= 3, p = 24, s = 1.2*24 = 28.8, not exactly 20% greater
n=4, p=32, s = 32*1.2 = 38.4, not exactly 20% greater
n= 5, p=40, s= 1.2*40 = 48, exactly 20% greater

Sufficient

Answer C


I think the answer is B. since you cannot have fraction as people count (9.6 19.2 .. 38.4) the least number of professors that matches the 20% criteria is 40 and students is 48 which is greater than 45.


Students can also be 6 and professors 5.
So answer is C.
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Re: A university badminton club has both students and professors as member [#permalink]
25 Feb 2022, 05:04
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Bunuel
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