OAR EXAM
16 ounces - answer1 pound
8 pints - answer1 gallon
4 quarts - answer1 gallon
2000 lbs - answer1 ton
Supplemental angle - answer adds up to 180 degrees
Complementary angle - answer 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? - answer3x-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? - answerTake
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? - answerhours 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? - answerP1*V1 + P2*V2 = P3*V3
P1*V1 would be X*1
P2*V2 is volume of first*percentage of first
P3*V3 = (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? - answerTherefore, 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 - answerAmount 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. - answerFirst 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 - answerTake 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? - answer100-4=96
multiply 17.16 *.96=16.4736
16 ounces - answer1 pound
8 pints - answer1 gallon
4 quarts - answer1 gallon
2000 lbs - answer1 ton
Supplemental angle - answer adds up to 180 degrees
Complementary angle - answer 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? - answer3x-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? - answerTake
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? - answerhours 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? - answerP1*V1 + P2*V2 = P3*V3
P1*V1 would be X*1
P2*V2 is volume of first*percentage of first
P3*V3 = (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? - answerTherefore, 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 - answerAmount 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. - answerFirst 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 - answerTake 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? - answer100-4=96
multiply 17.16 *.96=16.4736
