OAR EXAM

16 ounces

1 pound

8 pints

1 gallon

4 quarts

1 gallon

2000 lbs

1 ton

Supplemental angle

adds up to 180 degrees

Complementary angle

adds up to 90 degrees

If 3 times x exceeds 1/3 of y by 9, which of the following is the equation that shows the relationship between x and y?

3x-1/3*y=9

Questions about how fast people can do a job together?If the first painter can do the entire job in twelve hours and the second painter can do it in eight hours, then (this here is the trick!) the first guy can do 1/12 of the job per hour, and the second guy can do 1/8 per hour. How much then can they do per hour if they work together?

Take each number of hours and use 1/x amount of hours.

Example: To find out how much they can do together per hour, I add together what they can do individually per hour: 1/12 + 1/8 = 5/24.They can do 5/24 of the job per hour. Now I'll let "t" stand for how long they take to do the job together. Then they can do 1/t per hour, so 5/24 = 1/t. Flip the equation, and you get that t = 24/5 = 4.8 hours.

1/12 + 1/8 = 1/t

5/24 = 1/t

24/5 = t

=4.8 hours

One pipe can fill a pool 1.25 times faster than a second pipe. When both pipes are opened, they fill the pool in five hours. How long would it take to fill the pool if only the slower pipe is used?

hours to complete job:

fast pipe: f

slow pipe: 1.25f

together: 5

completed per hour:

fast pipe: 1/f

slow pipe: 1/1.25f

together: 1/5

adding their labor:

1/f + 1/1.25f = 1/5

multiplying through by 5f:

5 + 5/1.25 = f

5 + 4 = f = 9

Then 1.25f = 11.25, so the slower pipe takes 11.25 hours.

How much pure acid must be added to 12 ounces of a 40% acid solution in order to produce a 60% acid solution?

P1V1 + P2V2 = P3*V3

P1V1 would be X1

P2V2 is volume of firstpercentage of first

P3V3 = (X+volume of first solution)volume of final

solve for X

100x + 480 = 60(12+x), x=6

A can complete a project in 20 days and B can complete the same project in 30 days. If A and B start working on the project together and A quits 10 days before the project is completed, in how many days will the project be completed?

Therefore, A would have completed x-10/20

th of the project and B would have completed x/30

th of the project.

x-10/20+x/30=1; Solving for x, we get x = 18.

Questions about discount price

Amount of discount / Original price = % of reduction

reduction * 100 = final answer %

A businesswoman spends 1/5 of her income for rent, and 3/8 of the remainder goes towards salary. How much does she have remaining.

First take 1/5 away from 1, giving her 4/5. Multiply 4/5 * 3/8 = 12/40 = 3/10.

3/10 is the final answer

Traveling / Gas mileage / average speed question

Take the gallons of gas used * miles per gallon to get total miles traveled

Take miles traveled / average speed = hours (v = d/t)

A purchaser paid 17.16 for an article that had recently been increased in price by 4%. What was the price before the increase?

100-4=96

multiply 17.16 *.96=16.4736

A naval detachment has enough rations to feed 16 people for 10 days. If 4 more people join the detachment, for how many fewer days will the rations last?

First get the total rations, 16*10 = 160.

4 more people = 20 people. So divide 160/20 = 8 days

8 is 2 less days.

A field can be plowed by 9 machines in 5 hours. If 3 machines are broken and cannot be used, how many hours will it take to plow the field?

9*5 = 45 total machine hours to finish job

3 broken, so 6 will be used

45 / 6 = 7.5 hours

In a 3 hour examination of 320 questions, there are 40 mathematics problems. If twice as much time should be allowed for each mathematics problem as each of the other questions, how many minutes should be spent on he mathematics problems?

Let x = minutes to be spent on each problem

40x + 1/2x*280 = 180

solve for x, x = 1 minute

plug back in to initial, 40*1= 40 minutes

A tank that holds 450 gallons of water can be filled by 1 pipe in 15 minutes, and emptied by another in 30. How long would it take to fill the tank if both pipes are open?

450 / 15 = 30 gallons per minute fill rate

450 / 30 = 15 gallons per minute empty rate

30 gpm - 15 gpm = 15 gpm with both pipes open

so 450gallons/15gpm = 30 minutes

If a driver completes a trip of 120 miles at a rate of 30mph, at what rate would the driver have to travel on the return trip in order to average 40mph for the round trip?

30mph for 4 hours = 120 miles. So round trip is 240 miles.

240 miles @ 40mph would take 6 hours.

She used up 4 hours on the way there, so she has to complete the last 120 miles in 2 hours.

D=R*T, R=60mph

A bridge crosses a river that is 1520 feet wide. One bank of the river holds 1/5 of the bridge and the other holds 1/6. How long is the bridge?

(1/6)x + (1/5)x + 1520 = x

Common denominator: 5x + 6x + 45600 = 30x

Solve for x = 2,400 feet long

What is a fixed single pulley?

1 with 2 strings, i.e. a flag pole

Gear revolutions

r=D*R/d

D: number of teeth on gear A

R: revolutions of gear A

d: number of teeth on gear B

r: revolutions of gear B

hydrometer

uses floats to measure specific gravity. (weight of a liquid compared with weight of water. The liquid with the highest specific gravity will cause the float to rise higher in the glass tube.

What is a first class lever?

fulcrum is in the middle i.e. scissors or pliers

second class

fulcrum is at one end and load is in between, i.e. nutcracker, wheelbarrow fulcrum is in the wheel

third class lever?

fulcrum is at one end and effort is between i.e. tongs, tweezers, fulcrum is in part of the tool

in pulleys, which pulley will turn faster?

the small puller will turn faster than those larger than it

what kind of plane is an axe?

a wedge which is an inclined plane

can electricity flow through a circuit with a burned out bulb?

no but a voltmeter can bypass it if connected on both sides since it measures total voltage in a circut

in a 2 pulley system, how much will the movable pulley move up?

only half the distance and spin half as much as the fixed pulley, even if they are the same diameter

take number of rods on the wheel, divide that from the needed contacts per minute.

(ex. twice per second = 120 contacts per minute. 10 projection rods on wheel. 120/10=12. must rotate at 12 rpm.

RPM

cloest to the center

when driver wheel is present how will the adjacent wheels rotate

how do you increase the effort of the lever arm?

increase the length and enable a valve to blow off at a higher pressure. moving the weight further away will do this

micrometer

Sleeve section: horizontal cylindric shape; read as dollars and quarters

Thimble section: vertical cylindric shape; read as cents added to the initial money^

the first part is contributed by the main scale on the sleeve

the second part is contributed by the rotating vernier scale on the thimble (5+.5+.28=5.78mm)

Pendulums

The one with the longer string takes the longest to complete 1 swing.

The weight doesn't matter for swing time. If string length is the same, swing time is the same

if a weight hangs from a string does the length of the string matter?

no, the pull is exerted only by weight and string length doesn't matter

Buoyancy

the deeper you go with an inflated ball, the more difficult it is to hold it under water.

the deeper you go with that same ball, the more buoyant the ball is

Rate of heat exchange is faster through objects of?

greater temperature difference

water flows faster through what size area?

narrow areas than wider

4 stroke engine

intake compression combustion and exhaust

mechanical advantage

radius of axle/radius of drum (use the RADIUS NOT THE DIAMTER)

What is pressure?

pressure=force/area

what is kinetic energy?

energy in motion

what is potential energy?

stored energy in an object

electrical theory

V=I*R finds voltage drop across a circuit

I=Q/T

current=charge/time

Devices

Ammeter- measures current flow in a circuit

Voltmeter- measures voltage

Multimeter- measures both

Units

Charge= coulomb, C

Current flow= ampere, A

Power= volts*amperes

Newtons Laws

1st- object in motion will stay in motion, object at rest will stay at rest

2nd- force=mass*acceleration

3rd- for every action there is an equal and opposite reaction

weight

=mass*gravity

Heat

convection-occurs in liquids and gases y circulating currents cause by a difference in density

conduction-occurs in solids and stationary fluid depends on temp difference

Salt in to water

increases the specific gravity of solution and lowers its freezing point

Always move from

hot object to cold object

The rate of transfer is greater for the

greater temp difference

Compressing air in a closed space will

decrease the volume and raise the temp

If springs are holding u p a box

2 springs holding box attached as 1 long spring- each holding entire weight of box

2 springs holding box at different ends of the box each spring holds 1/2 weight of the box

problem

the long wolf does not support, the 2 diagonals carry it alone

aircraft will take off on a treadmill

regardless of treadmill setting

camber

curvature of the top of a wing or airfoil

aspect ratio

ratio of the distance between the wing tips of an airplane to its average wing width

high aspect ratio looks like

long and skinny wings

low aspect ratio

short and stubby wings

wing load

ratio of wing surface area to aircraft weight

compass deviation

the error of a magnetic compass due to local magnetism. it is dependent upon your heading; the difference between your desired grid or map heading and the heading you must follow due to effects of local magnetism

variation

difference between true bearing and magnetic bearing

trailing edge

aft end of airfoil where airflow traveling over its surface meets airflow from below its surface

spring tide

large ride and fall of the tide at or soon after the new or full moon

neap tide

those tides midway between spring tides that attain the least height

ebb tide

when the tide falls after high tide

troposphere

20,000 ft at poles 60000 at equator

stratosphere

120000 ft 20 miles

mesophere

300000 ft 50 miles

where is the ozone layer?

in the higher end of the stratosphere

air

78% Nitrogen, Oxygen 21%, Argon 1%, the rest is traces of Carbon Dioxide, hydrogen, and other rare gases

you typically need oxygen if you fly above 10,000 ft*****

fathometer

electronic device used in making deep sea soundings

sextant

precision instrument used in celestial navigation to me sure angles

capstan

an apparatus used for hoisting weights, consisting of a vertical spool shaped cylinder that is roared manually or by machine and around which cable is wound

4 methods of determining position

piloting, dead reckoning, celestial navigation, electronic navigation

cirrocumulus

above 18k feet

cirrus

above 18k feet

altocumulus

6k to 20k

cumulonimbus

from near the ground to above 50k feet

altocumulus

6k to 20k

altostratus

6k to 20k

stratocumulus

below 6k feet

stratus

below 6k feet

cumumlus

below 6k feet

what is the total number of degrees in the three angles of a triangle?

180

n Factorial

find the product of every number between 1 and x multiplied together, i.e. f factorial means 5x4x3x2x1

Multiplying fractions

first multiply the numerators by each other then multiply the denominators by each other

dividing fractions

to divide you have to invert the second fraction and then change the division sign to a multiplication sign and solve as mutiplying

adding & subtracting fractions

you must find the COMMON DENOMINATOR FIRST

adding and subtracting mixed numbers

you must add the WHOLE numbers first, then add the fractions and find common denominator if need be.

decimal fractions

.7=7/10 or .07 is 7/100 etc

percentages

7% is the same as 7/100 or 25% is the same as 25/100

changing a percent to a decimal

4% is .04 the rule is to drop the % and move the decimal over TWO PLACES TO THE LEFT

changing a decimal to a percentage

move the decimal two places to the RIGHT for example, .47=47% and .03=3%

finding the square root of a number that is not a perfect square

use the nearest tenth: square root of 28? well square root of 25 is 5, so you can guess that 5.2, 5.2x5.2 is 27.04 and is less than 28, we can use 5.3x5.3 which is 28.09 rounded to the nearest tenth is 28!

vertex

POINT WHERE LINES MEET IN AN ANGLE