The marching band is made up of 140 musicians. The band wants to form a rectangular formation with A people in a row and B people in a column. If the number of people in a row is more than 4 and less than 35, how many different combinations of rectangular shapes are possible?
Choose one
A) 3
B) 4
C) 5
D) 6
E) 7
firstly factors of 140 = 1, 2, 4, 5, 7, 10, 14, 20, 28, 35, 70, 140   the question says each row will have musicians more than 4 and less than 35,   therefore, we should be interested in the factors between 4 and 35 (noninclusive)   5(in each row) * 28(number of columns) =140, similarly   7 * 20   10 * 14   14 * 10   20 * 7   28 * 5   total possibilities = 6   option 6
<result>D</result>
The marching band is made up of 140 musicians. The band wants to form a rectangular formation with A people in a row and B people in a column. If the number of people in a row is more than 4 and less than 35, how many different combinations of rectangular shapes are possible?