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10 Jun 2016, 01:26
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E
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57% (02:29) correct
43%
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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.
A. 4.
B. 5.
C. 6.
D. 8.
E. 10.
10 Jun 2016, 04:46
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Bunuel
\(120 = 2^3*3*5\)....
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
General Discussion
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
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
