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

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Bunuel
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A marching band of 240 musicians are to march in a rectangular formati [#permalink] New post   06 Nov 2019, 06:45
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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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E
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nick1816
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Re: A marching band of 240 musicians are to march in a rectangular formati [#permalink] New post   06 Nov 2019, 07:50
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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] New post   06 Nov 2019, 09:18
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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


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Re: A marching band of 240 musicians are to march in a rectangular formati [#permalink] New post   07 Nov 2019, 19:58
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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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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] New post   19 Feb 2020, 08:56
Quote:
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


8 ≤ columns must be ≤ 30
musicians = 240
f(240)=24*10=3*8*2*5=2^4*3*5
8≤factors of 240≤30 are:
two's: 8,16
two's and three's: 12,24
two's and five's: 10,20
two's three's and five's: 30
three's and five's: 15

total: 8

Ans (E)
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Re: A marching band of 240 musicians are to march in a rectangular formati [#permalink] New post   20 Sep 2023, 08:17
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Re: A marching band of 240 musicians are to march in a rectangular formati [#permalink]
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