Pretest

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This pretest will not be submitted, and it will not be graded, but it will help you identify any gaps in your background knowledge and it will teach you some useful test-taking skills. We’ll release solutions to the pretest on Wednesday of Week 1.

Problem 1

Express \frac{42}{9} \cdot \frac{36}{21} as an integer without using a calculator and without long division or multiplication.

Problem 2

Choose the answer below that is closest to 412 \cdot 289, without using a calculator and without performing long multiplication.

• 40{,}000

• 80{,}000

• 120{,}000

• 160{,}000

Problem 3

Express \frac{16}{40} as a percentage without using a calculator and without long division or multiplication.

Problem 4

I just sent my friend $50 on Venmo and that used up 25% of my Venmo account balance. How much money is left in my Venmo account? Solve this problem without a calculator.

Problem 5

A bicycle shop is going out of business and has a 30% discount on all bikes. I also have a coupon for an additional 40% off any bike. As compared to the original price, what discount will I get if I use my coupon on top of the going-out-of-business discount? Solve this problem without a calculator.

Problem 6

You plan to drive to campus for your Monday, Wednesday, Friday classes and you are interested in knowing how many parking spaces are available in each of three parking structures (Gilman, Hopkins, and Pangea). We’ll assume for this problem that these are the only three parking options available. The table below shows how many unoccupied spaces there are in each parking structure at 10am on Monday, Wednesday, and Friday of Week 1.

Problem 6.1

What proportion of available spaces on Wednesday are in Gilman? Fully simplify your answer without using a calculator and without performing long division.

Problem 6.2

On average, Gilman is 80% full at 10am on Monday, Wednesday, and Friday of Week 1. What is the capacity of Gilman? Solve this problem without a calculator.

Problem 6.3

On Monday, the percentage of occupied spaces in Pangea is twice the percentage of occupied spaces in Hopkins. If Pangea has 950 parking spaces, how many parking spaces does Hopkins have? You may use a calculator for this part.

Problem 7

Every year, San Diego’s Regional Task Force on Homelessness conducts a “point-in-time” count of the number of homeless individuals in San Diego County. They send out a team of over a thousand volunteers to locate and count homeless individuals throughout the county’s shelters, streets, encampments, cars, etc. In 2023, newspapers reported that the count increased by 22% from the 2022 count. Part of that increase was explained by the fact that for the first time, volunteers were able to access and count people on Caltrans property. It was also reported that if we were to exclude the people who were counted on Caltrans property, the count would have still increased by 14%, meaning that the additional area covered could not explain all of the increase from one year’s count to the next. The 2023 point-in-time count was 10,264 individuals.

Problem 7.1

The point-in-time count is an underestimate of the true number of homeless individuals in San Diego County. Why is it always an underestimate?

Problem 7.2

How many individuals in 2023 were counted on Caltrans property? You may use a calculator.

Problem 7.3

The actual number of individuals counted on Caltrans property in 2023 was 661, which should be close to your answer to the previous question, but not exactly the same. Did the newspapers make a mistake or is there another explanation for the discrepancy?

Problem 8

At a furniture store, suppose every item has a “true value” that represents its worth. Every item in the store has a ticketed price, which is the amount that is printed on the item’s price tag that customers will pay, that is 25% higher its true value. The store wants its employees to be able to buy items at their true value. What percent discount does it need to give its employees off the ticketed price to accomplish this?

In general, if a store marks up prices by p%, what percent discount does it need to give to employees off the ticketed price so that they can buy things at the true value?

Solve this problem without a calculator.

Problem 9

One of your classes this quarter, PTS 1: Principles of Taylor Swift, has the following grading scheme:

• 20% Midterm 1
• 20% Midterm 2
• 30% Homeworks (lowest homework dropped)
• 30% Final Exam

There are 4 homework assignments, but your lowest homework score is dropped from your overall grade calculation. Each homework assignment is worth the same amount in your overall grade calculation, even though they have different numbers of available points. Your scores on all parts of the course, before the Final Exam, are as follows:

• Midterm 1: \frac{98}{100}
• Midterm 2: \frac{16}{38}
• Homework 1: \frac{3}{4}
• Homework 2: \frac{18}{25}
• Homework 3: \frac{9}{10}
• Homework 4: \frac{12}{13}

What is the minimum possible score you can earn on the Final Exam, as a percentage, to guarantee that you finish with at least a B grade (80% overall) in PTS 1? You may use a calculator (tip: you can type arithmetic expressions into Google and it will perform calculations for you!).

Problem 10

Your professor for PTS 1: Principles of Taylor Swift can grade 150 homeworks in 50 minutes. The TA can grade 150 homeworks in 75 minutes. If the professor and TA work together, how many minutes will it take them to grade 150 homeworks? Solve this problem without a calculator.

• 25 minutes

• 30 minutes

• 60 minutes

• 62.5 minutes

• 125 minutes

Problem 11

You are working in a spreadsheet editor and you highlight several consecutive rows of your spreasheet. The first highlighted row is row 543 and the last highlighted row is row 897. How many rows are highlighted?

In general, if rows n through m are highlighted, with n<m, how many rows is that?

Solve this problem without a calculator.

Problem 12

There are six different colors of M&M candies: yellow, blue, green, red, orange, and brown. You and your friend are playing a game. You will pick five M&Ms from a bag with your eyes closed. Your friend will give you a prize if none of the candies you picked are yellow, green, or blue. Unfortunately, when you play this game, you don’t win the prize. What does this say about the candies you chose? For each statement below, say whether the statement must be true, may be true, or cannot be true.

1. All five M&M’s were the same color, either yellow, blue, or green.
2. All five M&M’s were the same color, either red, orange, or brown.
3. All five M&M’s were one of the following colors: yellow, blue, green.
4. All five M&M’s were one of the following colors: red, orange, brown.
5. One or more M&M’s was yellow, blue, or green.
6. One or more M&M’s was red, orange, or brown.
7. None of the M&M’s were yellow, blue, or green.
8. None of the M&M’s were red, orange, or brown.

Once you’ve worked through the above problems, watch the following video. It summarizes key concepts covered in the pretest and discusses important test-taking strategies you should keep in mind moving forward, both in DSC 10 and your other classes.

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