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A marching band of 240 musicians are to march in a rectangular formati

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A marching band of 240 musicians are to march in a rectangular formati  [#permalink]

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New post 06 Nov 2019, 06:45
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E

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Question Stats:

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A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations are possible?

A. 3
B. 4
C. 5
D. 6
E. 8


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Re: A marching band of 240 musicians are to march in a rectangular formati  [#permalink]

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New post 06 Nov 2019, 07:50
1
s*t=240= 2^4*3*5
Also 30≥t≥8

hence, we have to count the number of factors of 240 that lies in range 8-30(both inclusive)

Total possible rectangular formations= (5*2*2)- (2*6)= 8



Bunuel wrote:
A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations are possible?

A. 3
B. 4
C. 5
D. 6
E. 8


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Re: A marching band of 240 musicians are to march in a rectangular formati  [#permalink]

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New post 06 Nov 2019, 09:18
given
s*t= 240
and s & t cannot be <=8 and >=30

possible pairs ( 8,30) ( 30,8) ( 10,24) ( 24,10) ( 12,20) (20,12) ( 15,16) ( 16,15)
total 8 pairs possible
IMO E


Bunuel wrote:
A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations are possible?

A. 3
B. 4
C. 5
D. 6
E. 8


Are You Up For the Challenge: 700 Level Questions
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Re: A marching band of 240 musicians are to march in a rectangular formati  [#permalink]

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New post 07 Nov 2019, 19:58
Bunuel wrote:
A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations are possible?

A. 3
B. 4
C. 5
D. 6
E. 8


Are You Up For the Challenge: 700 Level Questions



We need to find all the factors of 240 between 8 and 30, inclusive. Since they can be 8, 10, 12, 15, 16, 20, 24, and 30, there are 8 such factors, and hence 8 different rectangular formations are possible.

Answer: E
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Re: A marching band of 240 musicians are to march in a rectangular formati   [#permalink] 07 Nov 2019, 19:58
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