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

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Math Expert
Joined: 02 Sep 2009
Posts: 47188
The flying acrobatic team is made up of 120 airplanes. The team wants  [#permalink]

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10 Jun 2016, 01:26
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5
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Difficulty:

75% (hard)

Question Stats:

60% (01:52) correct 40% (01:52) wrong based on 60 sessions

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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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Joined: 21 Mar 2016
Posts: 536
Re: The flying acrobatic team is made up of 120 airplanes. The team wants  [#permalink]

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10 Jun 2016, 04:33
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
Math Expert
Joined: 02 Aug 2009
Posts: 6286
Re: The flying acrobatic team is made up of 120 airplanes. The team wants  [#permalink]

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10 Jun 2016, 04:46
1
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]

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02 Oct 2017, 23:48
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

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Re: The flying acrobatic team is made up of 120 airplanes. The team wants &nbs [#permalink] 02 Oct 2017, 23:48
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