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Civil Service Commission Past Questions and Answers


6)

In the figure below, ABCD is a parallelogram. What is the value of y – z?

The sum of the degree measures of two consecutive angles of a parallelogram is
180, so 180 = (3x – 5) + (2x – 15) = 5x – 20 ⇒ 5x = 200  ⇒ x =40. Since opposite angles of a parallelogram are equal, y = 3x – 5 = 115 and z = 2x – 15 = 65. Then y
– z = 50. The answer is (50).
7)

If the length of a rectangle is 4 times its width, and if its area is 144, what is its perimeter?
8)

If the measures of the angles of a triangle are in the ratio of 1:2:3, and if the perimeter of the triangle is 30 + 10 (3)½, what is the length of the smallest side?
9)

What is the area of Triangle ABC?

The area of Triangle CDE = 0.5(8)(15) = 60. Since the ratio of similitude for the two triangles (as calculated in solution C15) is 2.5, the area of Triangle ABC is (2.5)2 times the area of CDE: (2.5)2 × 60 = 6.25 × 60 = 375. The answer is (375).
10)

What is the perimeter of Triangle ABC?

 Solution
By the Pythagorean theorem, 82 + 152 = (CE)2 (CE)2 = 64 + 225 = 289 CE = 17. Then the perimeter of CDE = 8 + 15 + 7 = 40. Triangles ABC and CDE are similar (each has a 900 angle, and the vertical angle at C are congruent). The ratio of similitude is = 2.5, so the perimeter of ABC is 2.5 × 40 = 100. The answer is (100).


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