CE Board November 2016

Duel of Two 50% Marksmen: Odds in favor of the man who shoots first

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

 

Two Gamblers Play Until One is Bankrupt: Chance That the Better Player Wins

Problem
Player M has Php1, and Player N has Php2. Each play gives one the players Php1 from the other. Player M is enough better than player N that he wins 2/3 of the plays. They play until one is bankrupt. What is the chance that Player M wins?

A.   3/4 C.   4/7
B.   5/7 D.   2/3

 

Four Trapezia Formed by the Difference of Two Concentric Squares

Problem
ABCD is a square of side 10 cm. PQRS is a square inside ABCD. PQBA, QRCB, RSDC, and SPAD are identical trapezia, each of area 16 cm2. What is the height of each trapezium if PQ is parallel to AB and SR is parallel to DC?

A.   3 cm C.   2 cm
B.   1.8 cm D.   1.2 cm

 

2016-nov-math-trapezia_3d.jpg

Random Steps of a Drunk Man: Probability of Escaping the Cliff

Problem
From where he stands, one step toward the cliff would send the drunken man over the edge. He takes random steps, either toward or away from the cliff. At any step his probability of taking a step away is 2/3, of a step toward the cliff 1/3. What is his chance of escaping the cliff?

A.   2/27 C.   4/27
B.   107/243 D.   1/2

 

Length of Parabolic Sag Curve with Given Change in Grade Per Station

Problem
A grade of -5% is followed by a grade of 1%, the grades intersecting at the vertex (Sta. 10 + 060). The change of grade is restricted to 0.4% in 20 m. Compute the length of the vertical parabolic sag curve in meters.

A.   360 m C.   300 m
B.   320 m D.   340 m

 

Cross-Sectional Dimensions of Steel Rod to Elongate 1-mm when Subjected to 8,000 kg of Tension Force

Problem
A tensile load of 8000 kg elongates a 1-m long square rod by 1 mm. Steel modulus of elasticity is 2 × 106 kg/cm2. What is the dimension of a side of the rod?

A.   5 cm C.   2 cm
B.   1 cm D.   4 cm

Compound Curves: Finding the Stationing of PCC with Given Stationing of PC

Problems
A compound curve has the following characteristics:

I1 = 24° D1 = 6°
I2 = 36° D2 = 4°
Stationing of P.C. = km 10 + 420

Compute the stationing of P.C.C.

A.   km 10 + 560 C.   km 10 + 520
B.   km 10 + 540 D.   km 10 + 500

For Sn = 3^(2n - 1) + b; Find the Quotient a9 / a7

Problem
The sum of the first n terms of a series is 3^(2n - 1) + b. What is the quotient of the 9th and the 7th term?

A.   81 C.   83
B.   82 D.   84

 

Y-component of Vector A if Vectors A and B are Orthogonal

Problem
Compute the value of b if A and B are orthogonal.
$${\bf A} = 2{\bf i} + b{\bf j} + {\bf k}$$

$${\bf B} = 4{\bf i} - 2{\bf j} - 2{\bf k}$$

A.   6 C.   4
B.   5 D.   3

 

General Term of Arithmetic Sequence that Models the Potential Annual Salaries

Problem
A job posted at jobstreet.com offered a starting salary of \$40,000 per year and guaranteeing a raise of \$1600 per year for the rest of 5 years. Write the general term for the arithmetic sequence that models potential annual salaries.

A.   an = 38,400 + 1600n
B.   an = 33,400 + 2600n
C.   an = 36,400 + 1400n
D.   an = 34,400 +1800n

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