# November 2019

**Problem**

A contractor can buy a dump trucks for P800,000 each (surplus) or rent them for P1,189 per truck per day. The truck has salvage value of P100,000 at the end of its useful life of 5 years. Annual cost of maintenance is P20,000. If money is worth 14% per annum, determine the number of days per year that a truck must be used to warrant the purchase of the truck.

A. 200 | C. 198 |

B. 199 | D. 197 |

**Problem**

Mar wants to make a box with no lid from a rectangular sheet of cardboard that is 18 inches by 24 inches. The box is to be made by cutting a square of side *x* from each corner of the sheet and folding up the sides. Find the value of *x* that maximizes the volume of the box.

A. 4.3 inches | C. 10.6 inches |

B. 5.2 inches | D. 3.4 inches |

**Problem**

A box contains 5 defective and 195 non-defective cell phones. A quality control engineer selects 2 cell phones at random without replacement. What is the probability that exactly 1 is defective?

A. 0.0190 | C. 0.0390 |

B. 0.0490 | D. 0.0290 |

**Problem**

A conveyor is dispersing sands which forms into a conical pile whose height is approximately 4/3 of its base radius. Determine how fast the volume of the conical sand is changing when the radius of the base is 3 feet, if the rate of change of the radius is 3 inches per minute.

A. 2π ft/min | C. 3π ft/min |

B. 4π ft/min | D. 5π ft/min |

**Problem**

Smith and Jones, both 50% marksmen, decide to fight a duel in which they exchange alternate shots until one is hit. What are the odds in favor of the man who shoots first?

A. 1/3 | C. 2/3 |

B. 1/2 | D. 1/4 |

**Problem**

A Toyota Land Cruiser drives east from point *A* at 30 kph. Another car, Ford Expedition, starting from *B* at the same time, drives S30°W toward *A* at 60 kph. *B* is 30 km from *A*. How fast in kph is the distance between two cars changing after 30 minutes? Hint: Use the Cosine Law.

A. 70 kph | C. 55 kph |

B. 80 kph | D. 60 kph |