Basic Numeracy/Quantitative Aptitude

Detailed Solution

113.

114.

115. c: The equation to solve is given by.
|-2x + 2| -3 = -3
iAdd 3 to both sides of the equation and simplify.
|-2x + 2| = 0
|-2x + 2| is equal to 0 if -2x + 2 = 0. Solve for x to obtain x = 1

116. c: The circumference of a circle is given by C = 2 pi r, where r is the radius of the circle.
Substitute C by 72 pi to obtain the equation 72 pi = 2 pi r
Simplify and solve for r to obtain r = 36

117. b: Let L and W be the length and width of the garden. The statement "the length of a rectangular garden is 2 feet longer than 3 times its width" may be formulated by L = 2 + 3 W The formula for the perimeter is given by P = 2 L + 2 W
Substitute P and L in the above equation by 100 and 2 + 3 W respectively to obtain 100 = 2(2 + 3 W) + 2 W
Solve for W and L
W = 12 and L = 2 + 3 W = 38.
Check that the perimeter of the rectangular garden is 100
P = 2 L + 2 W = 76 + 24 = 100

118. a: Let x and y be the length and width of the field. The statement "a length 10 feet more than it is width" may be formulated by x = 10 + y
The formula for the area is given by A = x y
Substitute A and x in the above equation by 264 and 10 + y respectively to obtain 264 = (10 + y) y
Write the above equation in standard form as follows y 2 + 10 y - 264 = 0
Solve the above equation for to obtain y = 12 and y = - 22
Since y is the value of a width it must be positive. The dimensions of the field are given by y = 12 and x = 10 + y = 22

119. a: Let us use profit = revenue - costs to find a formula for the profit P P = ( x 2 + 100 x ) - ( 240 x + 500 )
Substitute P in the above equation by 10,000 dollars to obtain 10000 = x 2 - 140 x - 500
Write the equation in standard form and solve for x x 2 - 140 x - 10500 = 0
Solve the above equation for x
x = 194.10 and x = -54.01
The number of units to produce must be positive, so x = 194.

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