# November 2016

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

**Problem**

The sum of the first *n* terms of a series is 3^(2*n* - 1) + *b*. What is the quotient of the 9^{th} and the 7^{th} 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*= 38,400 + 1600

_{n}*n*

B.

*a*= 33,400 + 2600

_{n}*n*

C.

*a*= 36,400 + 1400

_{n}*n*

D.

*a*= 34,400 +1800

_{n}*n*

## Samuel Pepys Wrote Isaac Newton Asking Which Event is More Likely to Occur

**Problem**

Samuel Pepys wrote Isaac Newton to ask which of three events is more likely: that a person get (*a*) at least 1 six when 6 dice are rolled (*b*) at least two sixes when 12 dice are rolled, or (*c*) at least 3 sixes when 18 dice are rolled. What is the answer?

*a*) is more likely than (

*b*) and (

*c*)

B. (

*b*) is more likely than (

*a*) and (

*c*)

C. (

*c*) is more likely than (

*a*) and (

*b*)

D. (

*a*), (

*b*), and (

*c*) are equally likely

## Spinning Spherical Target: Probability for Three Marksmen to Hit on the Same Hemisphere

**Problem**

Three marksman simultaneously shoot and hit a rapidly spinning spherical target. What is the probability that the three points of impact lie on the same hemisphere?

A. 0 | C. 1 |

B. 1/2 | D. 2/3 |