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May 2012

The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?

Problem
The sum and product of three distinct positive integers are 15 and 45, respectively. What is the smallest integer?

A.   1 C.   5
B.   9 D.   3

 

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Maximum stresses on a pole subjected to combined loadings

Situation
The solid pole shown in the figure is loaded with a vertical load P = 25 kN and lateral load H = 0.95 kN. The pole is 3 m high, 300 mm diameter and weighs 22 kN/m3.
 

2012-may-design-pole-under-combined-loadings.png

 

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Equivalent land area of 600 mm^2 map-area with given map-scale

Problem
The area of a park on a map is 600 mm2. If the scale of the map is 1 to 40,000 determine the true area of the park in hectares (1 hectare = 104 m2).

A.   112 C.   96
B.   84 D.   120

 

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Given the following equations: ab = 1/8, ac = 3, bc = 6. Find the value of a + b + c.

Problem
Given the following equations:

$$ab = 1/8 \qquad ac = 3 \qquad bc = 6$$

Find the value of $a + b + c$.

A.   $12$ C.   $\dfrac{4}{51}$
B.   $\dfrac{7}{16}$ D.   $12.75$

 

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