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The flying acrobatic team is made up of 120 airplanes. The team wants

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Bunuel
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The flying acrobatic team is made up of 120 airplanes. The team wants [#permalink] New post   10 Jun 2016, 01:26
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The flying acrobatic team is made up of 120 airplanes. The team wants to form a rectangular formation with X planes in a row and Y planes in a column. If the number of airplanes in a row is no less than 4 and no more than 30, how many different combinations of rectangular shapes are possible?

A. 4.
B. 5.
C. 6.
D. 8.
E. 10.
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E
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mohshu
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Re: The flying acrobatic team is made up of 120 airplanes. The team wants [#permalink] New post   10 Jun 2016, 04:33
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firstly factors of 120 = 1,2,3,4,5,6,8,10,12,15,20,24,30,40,... etc...

the questions says each row will have airplanes not less than 4 and not more than 30,

therefore, we should be interested in the factors starting from 4 till 30 (inclusive)
4(in each row) * 30(number of columns) =120, similarly
5 * 24
6 * 20
8 * 15
10 * 12
12 * 10
15 * 8
20 * 6
24 * 5
30 * 4
total possibilities = 10
option E
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Re: The flying acrobatic team is made up of 120 airplanes. The team wants [#permalink] New post   10 Jun 2016, 04:46
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Bunuel wrote:
The flying acrobatic team is made up of 120 airplanes. The team wants to form a rectangular formation with X planes in a row and Y planes in a column. If the
number of airplanes in a row is no less than 4 and no more than 30, how many different combinations of rectangular shapes are possible?

A. 4.
B. 5.
C. 6.
D. 8.
E. 10.


\(120 = 2^3*3*5\)....
so # of factors = \((3+1)(1+1)(1+1) = 4*2*2 = 16\)......

But the row cannot have <4 and >30..
factors <4 = 1,2,3 --- 3
factors>30 = 40,60,120 - 3..
total = 6..

so possible ways = 16-6 = 10
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Re: The flying acrobatic team is made up of 120 airplanes. The team wants [#permalink] New post   02 Oct 2017, 23:48
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Bunuel wrote:
The flying acrobatic team is made up of 120 airplanes. The team wants to form a rectangular formation with X planes in a row and Y planes in a column. If the number of airplanes in a row is no less than 4 and no more than 30, how many different combinations of rectangular shapes are possible?

A. 4.
B. 5.
C. 6.
D. 8.
E. 10.


If x are the rows and Y are the colums then

Total Number of Airplanes = X*Y = 120

i.e. X*Y = 1*120
2*60
3*40
4*30
5*24
6*20
8*15
10*12

There are 5 combinations of X*Y but X and Y can be interchanged hence there are 10 possibilities for X as well as for Y

Answer: option E
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Re: The flying acrobatic team is made up of 120 airplanes. The team wants [#permalink] New post   14 Nov 2018, 13:34
There's a way that may not necessarily be used this time, but comes in handy in more complicated examples:

First let's do the prime factorization:
120|2
60 |2
30 |2
15 |3
5 |5
1

hence 120= (2^3)*(3^1)*(5^1)

This implies that 120 has in total: (3+1)(1+1)(1+1)=4*2*2=16 factors, which makes 8 pairs of factors that can form a rectangle of an area equal to 120. Since factors 1, 2 and 3 cannot be used, we are left to 8-3=5 pairs of facors. 5 pairs = 10 facors

Asnwer: E
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Re: The flying acrobatic team is made up of 120 airplanes. The team wants [#permalink] New post   20 Jul 2022, 04:59
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Re: The flying acrobatic team is made up of 120 airplanes. The team wants [#permalink]
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