November 2016

Probability That Exactly 1 is Defective in Getting 2 Cell Phones

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

 

Angle Correction for Repeated Measurement

Problem
The following interior angles (in degree) of a triangular traverse were measured with the same precision.
 

Angle Value No. of Measurement
A 41 2
B 77 6
C 63 2

 

What is the most probable value of angle C, in degrees?
 

A.   62.423° C.   62.571°
B.   62.874° D.   62.745°

 

Expected Profit for the Acceptance of Estimate of an Engineering Company

Problem
An engineering company prepares an estimate for a job. The cost of preparing the estimate is Php10,000. The amount of profit over and above the Php10,000 is Php25,000 if their estimate is accepted. The probability that their estimate will be accepted 0.7 and the probability that their estimate will not be accepted is 0.3. What is the expected profit?

A.   Php12,500 C.   Php14,500
B.   Php13,500 D.   Php10,500

 

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

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