# BARC Unit Exam: Solution and Q&A

## Battalion and Messenger - Distance Covered by Messenger: Solution to Unit Exam Basic Algebra Review

A battalion, 20 miles long, advances 20 miles. During this time, a messenger on a horse travels from the rear of the battalion to the front and immediately turns around, ending up precisely at the rear of the battalion upon the completion of the 20-mile journey. How far has the messenger travelled?

## Unit Exam - Part 1

1. The number of revolutions per minute of a ball governor required to keep the balls h inches below the point of suspension varies inversely as the square root of h. If the balls are 6 inches below for 40 revolutions per minute, at what speed will they be 1-1/2 inches below?
2. Aljur owns a 24mm prime camera lens worth P10,000. He sell it to Brandon at a 10% profit based on the worth of the lens. Brandon sells the lens back to Aljur at a 10% loss. Then...
3. The price of an article is cut by 10%. To restore it to its former value the new price must be increased by:
4. Alvin can do a piece of work in 9 days. Briggs is 50% more efficient than Alvin. The number of days it takes Briggs to do the same piece of work is:/li>
5. Indicate in which one of the following equations y is neither directly nor inversely proportional to x:

## Unit Exam - Part 2

1. The largest number by which the expression $n^3 - n$ is divisible for all possible values of $n$, is:
2. When simplified and expressed with negative exponents, the expression $(x + y)^{-1}(x^{-1} + y^{-1})$ is equal to:
3. The value of $x$ in the equation $\log_{10} (x^2 - 15x) = 2$ are:

## Unit Exam - Part 3

1. The pressure P of wind on a sail varies jointly as the area A of the sail and the square of the velocity V of the wind. The pressure on a square foot is 1 lb when the velocity is 16 mph. The velocity of the wind when the pressure on a square yard is 36 lbs is:
2. The value of $10^{\log_{10} 7}$ is:
3. If $a^x = c^q = b$ and $c^y = a^z = d$, then:

## Unit Exam - Part 4

1. A merchant buys goods at 25% off the list price. He desires to mark the goods so that he can give a discount of 20% on the marked price and still clear a profit of 25% on the selling price. What per cent of the list price must he mark the goods?
2. From a group of boys and girls, 15 girls leave. There are then left two boys for each girl. After this 45 boys leave. There are then 5 girls for each boy. The number of girls in the beginning was:

## Unit Exam - Part 5

Solution Problem
Three numbers whose sum is 42 are in GP. If 1 is subtracted from the first, 3 from from the second, and 11 from the third, the remainders will be in AP. Find the smallest number.
The sum to infinity of $\dfrac{1}{7} + \dfrac{2}{7^2} + \dfrac{1}{7^3} + \dfrac{2}{7^4} + \ldots$ is:
At 2:15 o'clock, the hour and minute hands of a clock form an angle of:
Ten stones are placed in a straight line on the ground, at intervals of two feet. Ten feet beyond the end of the row is a basket from which a boy starts, picks up the stones, and carries them one at a time to the basket. How far does he run in all?
A stone is dropped into a well and the report of the stone striking the bottom is heard 7.7 seconds after it is dropped. Assume that the stone falls 16t2 feet in t seconds and that the velocity of sound is 1,120 feet per second. The depth of the well is:
A privateer discovers a merchantman 10 miles to leeward at 11:45 am and with a good breeze bears down upon her at 11 mph, while the merchant can only make 8 mph in her attempt to escape. After a two hour chase, the top sail of the privateer is carried away; she can now make only 17 miles while the merchantman makes 15. The privateer will overtake the merchantman at:

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