## 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 |

## 08 Area Enclosed by r = a sin 3θ and r = a cos 3θ

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## 05 Area Enclosed by r = a sin 2θ and r = a cos 2θ

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## 01 Area Enclosed by r = 2a cos^2 θ

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## 07 Area Enclosed by r = 2a cos θ and r = 2a sin θ

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## 08 - Sound of Impact be Heard Before the Report of the Gun

**Problem**

A bullet is fired at a target 1,342 m away. At what point along its path would the sound of the impact of the bullet be heard 1/4 second before the report of the gun, assuming that sound travels at the rate of 335 m/sec and the bullet is 503 m/sec.

## 05 - Sum and Difference of Two Numbers Multiplied to Sum and Difference of Their Squares

**Problem**

Find two numbers such that their sum multiplied by the sum of their squares is 5500, and their difference multiplied by the difference of their squares is 352.

## 07 - A Man Covers an Unknown Distance at Different Rates

**Problem**

A man covers the distance *A* to *B* in 5 hours and 30 minutes. During the second half of the distance he traveled 1/2 kilometer less per hour than during the first half. In the return trip from *B* to *A*, by traveling 1 km/hr faster than during the first half of his trip from *A* to *B*, he consumed 3-3/4 hours. Determine the distance *AB*.

## Numbers 4, 2, 5, and 18 are Added Respectively to the First Four Terms of AP, Forming Into a GP

**Problem**

If 4, 2, 5, and 18 are added respectively to the first four terms of an arithmetic progression, the resulting series is a geometric progression. What is the common difference of the arithmetic progression?

## 06 - The Battleship Was Brought to Full Stop After 1 Hour of Voyage

**Problem**

A battleship started on a 500-mile voyage but was brought to full stop an hour after starting for military reasons, delaying it for full hour, after which it was ordered to proceed at a reduced velocity equivalent to 75% of its former rate. The ship arrived at its destination 3 hours and 3 quarters after scheduled time. If it was desired for the ship to arrive one hour and a quarter sooner, how far from the destination should the ship have been ordered stopped?