##### Algebra Basics: Place-Out Exam

We want to make sure you take classes that aren't too easy for you. This course will have new things for you to learn if you get less than 70% of this test.

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1.

What is the simplified value of

$0.625 \times 3.5 \times 2.\overline{6} \times 1.2?$

2.

Moe R. can finish cutting a lawn in $$3$$ hours. Fynn Isher can cut the same lawn in $$2$$ hours. How many minutes will it take them to mow the lawn if they work together?

3.

Two runners are running clockwise around a circular track. If they start at the same time and at the same position, after $$4.5$$ minutes, the faster runner will have covered $$1$$ more lap than the slower runner, with each having covered an integer number of laps in that time. The slower runner doesn't get passed until after he finishes a lap. The time it takes each of them to finish one lap is an integer number of seconds.

How many more seconds does it take the slower runner to finish one lap compared with the faster runner?

4.

Sam's little sister is playing a game called Counting Apples. Her rating for the game changes like this:

• Rises by $$10\%$$ from the beginning of Day $$1$$ to the end of Day $$1$$

• Falls by $$10\%$$ from the beginning of Day $$2$$ to the end of Day $$2$$

• Rises by $$10\%$$ from the beginning of Day $$3$$ to the end of Day $$3$$

• Falls by $$10\%$$ from the beginning of Day $$4$$ to the end of Day $$4$$

• Rises by $$10\%$$ from the beginning of Day $$5$$ to the end of Day $$5.$$

Overall, what is the percent change in her rating from the beginning of Day $$1$$ to the end of Day $$5,$$ rounded to the nearest whole number?

5.

Find the value of a positive number $$x$$ that makes the following true:

$x\% \text{ of } x \text{ equals } 1.$

6.

Jeremy has a pile of identical socks, each of which is either completely clean or completely dirty, and $$20\%$$ of the socks in the pile are completely clean. If he adds $$70$$ more identical dirty socks to the pile, then $$10\%$$ of the socks in the pile will be clean.

How many dirty socks were in the pile in the beginning?

7.

If $$16$$ horses eat $$5$$ stacks of hay in $$35$$ days, how many horses can eat $$4$$ stacks of hay in $$8$$ days?

8.

The number $$0.5503 \times 0.5503 \times 0.5503$$ is close to $$\frac{1}{n},$$ where $$n$$ is an integer. What is the value of $$n$$ that is closest to this number?

9.

At the soccer team pizza party, the kids who came early evenly split the cost of the pizza, which altogether cost $$\80.$$ Four late kids came, and they pitched in to share the cost of the pizza, with each of them paying $$\0.25$$ to each of the kids who were originally there, so that in the end everyone paid the same amount. How many kids were there in the beginning?

10.

What is the largest fraction which is less than (and not equal to) $$\frac{1}{2}$$ but whose numerator and denominator are positive integers less than or equal to $$100?$$