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Monday, March 4, 2013

Civil Service Commission Professional or Sub-Professional Reviewer - Page 108/159

Mathematics Test V Solution - Page 108

16. If the dimensions of a square change in such a manner that the area remains constant, what must happen to the other side if one side will be increased by 1/4 of itself?

area of square remains constant

(s +  1  s) y = s (s)
        4

    5  ( s )( y )= s2
    4

                 y = s2 ( 4 )
                             5s
                 y =   4  s
                         5
                 s = -   4  s   =   1  s
                           5            5

therefore, it decreased by 1/5 of itself * Ans.

17. A man rowed 4 miles upstream for 2 hours. If the river flowed with a current of 2 miles per hour, how long did the man's return trip take?

Let x - be the rate of the boat in still water
Let 2x - be the rate of the boat upstream
Let 2 mph - be the rate of the current
Let (x + 2) - speed of the boat downstream

rateup x time = distance

(x - 2) (2) = 4
      2x - 4 = 4
            2x = 4 + 4
            2x = 8
              x = 4 miles / hr

ratedown x time = distance

(x+2) (time) = 4
(4+2) (time) = 4
       6 (time) = 4
            time = 4 / 6
            time = 2 / 3 hrs. * Ans.

18. The rectangle shown in the figure is divided into 6 equal squares. If the perimeter of the rectangle is 42 cm, what is the area of each square in cm2 ?

rectangle divided into 6 equal squares

14x = 42
    x = 42 / 14
    x = 3 cm.

Area of the squares = x2
                              = (3 cm)2
                              = 9 cm2 * Ans.

Civil Service Reviewer Post 108/159