ATI TEAS Math Test Practice (2025)

Answer & Explanation

The correct answer is (D) – 380.

Question Breakdown: "Asgard's Got Talent" Scoring System

Let's solve this step by step:

1. First, let's understand what we know:
   • Judges' scoring: 100 points per 2 compliments
   • Family scoring: 20 points per 36 family compliments
   • Regina got 6 compliments from judges
   • Each family member (12 people) gave her 12 compliments
2. Let's solve the judges' points first:
   • We know: 2 compliments = 100 points
   • Regina got 6 compliments
   • Think of it this way: if 2 compliments = 100 points, then:
     • 2 compliments = 100 points
     • 4 compliments = 200 points
     • 6 compliments = 300 points
   • So Regina got 300 points from judges
3. Now let's calculate family points:
   • First, calculate total family compliments:
     • 12 family members × 12 compliments each
     • = 144 total family compliments
   • We know: 36 family compliments = 20 points
   • So for 144 compliments:
     • 36 compliments = 20 points
     • 72 compliments = 40 points
     • 108 compliments = 60 points
     • 144 compliments = 80 points
   • Regina got 80 points from family
4. Total points:
   • Judges' points + Family points
   • 300 + 80 = 380 points

Therefore, Regina got 380 points total, making (D) the correct answer.

The key insight: When dealing with ratios like this, break down the problem into smaller, manageable parts. Handle one calculation at a time (judges first, then family), and use simple multiplication to scale up from the base ratio to the actual numbers you need.

The correct answer is E

Question: Mouse Trap Profit Calculation

Let's solve this step by step:

1. First, let's identify what we know:
   • Buy price (cost): $800
   • Sell price (revenue): $1,240
   • Profit per trap: $5
2. Let's find the total profit:
   • Total profit = Sell price - Buy price
   • Total profit = $1,240 - $800
   • Total profit = $440
3. Now, to find the number of traps:
   • If each trap makes $5 profit
   • And total profit is $440
   • Then: Number of traps = Total profit ÷ Profit per trap
   • Number of traps = $440 ÷ $5
   • Number of traps = 88

Therefore, 88 traps were involved, making (E) the correct answer.

The key insight: This is a two-step problem. First, you need to find the total profit by subtracting the buy price from the sell price. Then, since you know how much profit each individual trap made, you can divide the total profit by the profit per trap to find the number of traps.

Think of it like this: If each trap contributes $5 to the total profit of $440, how many $5 bills would you need to make $440? That's why we divide 440 by 5.

A helpful way to check your answer:

• 88 traps × $5 profit per trap = $440 total profit ✓

The correct answer is D.

Question #3: The Paper Filing Problem

Let's break this down step by step:

1. First, let's identify what we know:
   • Total papers: 220
   • Brad filed: 1/4 (one-quarter)
   • William filed: 1/2 (one-half)
   • We need to find: Papers remaining to be filed
2. Let's add up what's been filed:
   • To add fractions with different denominators, convert to same denominator
   • 1/2 = 2/4 (multiply both top and bottom by 2)
   • Now we can add: 1/4 + 2/4 = 3/4
   • So 3/4 of papers have been filed
3. Therefore:
   • If 3/4 are filed, then 1/4 remain
   • To find 1/4 of 220:
     • Quick method: Break 220 into 200 + 20
     • 200 ÷ 4 = 50
     • 20 ÷ 4 = 5
     • Total: 50 + 5 = 55 papers remain

The answer is (D) 55 papers.

The key insight: When working with fractions of a whole number, try breaking the number into easier parts if it's hard to divide. Also, remember that what's left is just 1 minus the fraction that's been completed.

The correct answer is (A).

Let me solve this step by step:

When dividing fractions, we multiply by the reciprocal:

• 2(2/7) ÷ 3(3/5) = 2(2/7) × (5/18)

First, let's convert the mixed numbers to improper fractions:

• 2(2/7) = (2×7 + 2)/7 = 16/7
• 3(3/5) = (3×5 + 3)/5 = 18/5

Now our problem is:

• (16/7) × (5/18)

Multiply numerators and denominators:

• (16 × 5)/(7 × 18)
• 80/126

Simplify:

• 80/126 = 40/63
• Therefore, 2(2/7) ÷ 3(3/5) = 40/63

The answer is A. 40/63

Key Insight:

When dividing fractions, remember the "KCF" rule:

• Keep the first fraction
• Change the division to multiplication
• Flip the second fraction (find its reciprocal)

Think of it this way: Just like when you divide by 2, it's the same as multiplying by 1/2, when you divide by any fraction, you multiply by its reciprocal. This is why 2 2/7 ÷ 3 3/5 becomes 16/7 × 5/18.

The correct answer is (A).
Key Concept: Remember PEMDAS

• Parentheses
• Exponents
• Multiplication/Division (left to right)
• Addition/Subtraction (left to right)

Let's solve this step by step:

1. First, solve what's inside parentheses:
   • In top: (7 - 2²)
     • First 2² = 4 (exponent)
     • Then 7 - 4 = 3
   • In bottom: (2 - 8)²
     • First 2 - 8 = -6
     • Then (-6)² = 36 (remember: negative squared = positive)
2. Now our expression looks like:
   • 5 × 3 ÷ 4 - 1
   • 3 × 36
3. Solve bottom:
   • 3 × 36 = 108
4. Solve top (left to right for multiplication/division):
   • 5 × 3 = 15
   • 15 ÷ 4 = 3.75
   • 3.75 - 1 = 2.75
5. Now we have:
   • 2.75/108
6. To get a clean fraction, multiply both top and bottom by 4:
   • (2.75 × 4)/(108 × 4)
   • 11/432

Therefore, answer (A) 11/432 is correct.

Key Insights:

1. When squaring a negative number, the result is positive
2. The order you solve operations matters - follow PEMDAS strictly
3. When multiplying both top and bottom by the same number (like 4), you're not changing the value of the fraction
4. Looking at your answer choices can help you decide if you need to convert decimals to whole numbers

Let's approach this step-by-step:

First, let's convert 0.175 liters to milliliters:
0.175 L = 0.175 × 1000 ml = 175 ml
Now, let's examine each option:

• 162 ml - This is less than 175 ml, so it's not enough. It's incorrect.
• 145 ml - This is also less than 175 ml, so it's not enough. It's incorrect.
• 172 ml - This is less than 175 ml, so it's not enough. It's incorrect.
• 198 ml - This is more than 175 ml, so it's enough. This is correct.

Regarding rounding:
In medical contexts, it's crucial to meet the requested requirements. In this case rounding down could lead to insufficient sample size, potentially affecting test results. Therefore, we always round up or choose an amount that exceeds the minimum requirement as you are required to send more than the minimum amount.

The correct answer is option D: 198 ml.

Key Insights:

1. In medical contexts, always go OVER the minimum requirement, never under
2. Converting between units (like L to mL) is crucial - remember:
   • 1 L = 1000 mL
   • Moving decimal point 3 places right when converting L to mL
3. Think practically: Having too much blood is better than too little for testing

The correct answer is (B).

To find the mean percent for ages 15-18:

1. Get the percentages for ages 15-18:
   • Age 15: 25%
   • Age 16: 47%
   • Age 17: 59%
   • Age 18: 42%
2. Calculate mean:
   • Add all numbers: 25 + 47 + 59 + 42 = 173
   • Divide by number of ages (4): 173 ÷ 4 = 43.3%

Therefore, (B) 43.3% is correct.

Key Insights:

1. When finding a mean for specific ages:
   • Only include the ages asked for (15-18)
   • Don't get distracted by other data (ages 12-14)
2. The mean isn't always a value that appears in your data
3. Mean = Total ÷ Number of items, regardless of how the numbers look
4. Round as specified (to nearest tenth in this case)

The correct answer is (C).

Let's analyze this step by step:

1. First, let's understand what the table shows:
   • Years: 1952 → 2012 (increasing by 20 years)
   • Waist sizes: 28" → 34" (steadily increasing)
2. Let's examine each choice carefully: A) "There is a negative covariance between US women's waist sizes and year"
   • FALSE - Look at the pattern:
     • As years increase, waist sizes increase
     • This is a positive relationship, not negative
     • Think of it like walking up stairs - both numbers go up together
   B) "If these two variables were graphed, waist size would go on the x axis"
   • FALSE - Remember:
     • Independent variable (what causes change) goes on x-axis
     • Time/Year is usually the independent variable
     • Year causes the changes in waist size, not vice versa
   C) "As the year increases, women's waist sizes also increase"
   • TRUE - Look at the pattern:
     • 1952: 28 inches
     • 1972: 30 inches
     • 1992: 31.5 inches
     • 2012: 34 inches
     • Clear upward trend!
   D) "If these two variables were graphed, the slope of the line between any two points would be negative"
   • FALSE - A negative slope means one variable goes up while other goes down
   • Here, both variables increase together = positive slope

Therefore, (C) is the correct answer.

Key Insights:

1. When looking at relationships between variables:
   • If both increase or both decrease = positive relationship
   • If one increases while other decreases = negative relationship
2. The independent variable (usually time) goes on x-axis
3. Slope direction tells you relationship type:
   • Upward slope = positive relationship
   • Downward slope = negative relationship

The correct answer is (D).

1. First, let's identify what we know:
   • Solution contains 150 micrograms of adrenaline
   • Solution volume is 0.3 milliliters (mL)
   • We need to find: micrograms per 1 mL
   • Final answer needs to be in milligrams (mg)
2. Let's find adrenaline concentration per 1 mL:
   • If 0.3 mL contains 150 micrograms
   • Then 1 mL contains: 150 ÷ 0.3 = 500 micrograms
3. Convert micrograms to milligrams:
   • Remember: 1 mg = 1000 micrograms
   • So: 500 micrograms = 500 ÷ 1000 = 0.5 mg

Therefore, answer (D) 0.5 mg is correct.

Key Insights:

1. When solving concentration problems:
   • First find the ratio for the amount given
   • Then convert to desired units
2. Unit conversion tips:
   • Micrograms to milligrams: divide by 1000
   • Think of moving decimal point 3 places left
3. Medical calculations require precise attention to units because wrong conversions could be dangerous

Think of it like this: If you have $150 split among 0.3 groups, each full group would get $500. Then convert that $500 to a different currency by dividing by 1000.

The correct answer is (A).
First, let's organize what we know:

• 3-year-old needs 5 mL per dose
• 5-year-old needs 7.5 mL per dose

Each child can take up to 5 doses per day
We need enough for 4 days
We need to calculate for BOTH children

Let's calculate daily needs for each child:

• 3-year-old: 5 mL × 5 doses = 25 mL per day
• 5-year-old: 7.5 mL × 5 doses = 37.5 mL per day

Total daily need: 25 mL + 37.5 mL = 62.5 mL per day for both children

Now calculate for all 4 days:

62.5 mL × 4 days = 250 mL total needed

Double-check our work:

• For 3-year-old: 5 mL × 5 doses × 4 days = 100 mL
• For 5-year-old: 7.5 mL × 5 doses × 4 days = 150 mL

Total: 100 mL + 150 mL = 250 mL

Therefore, Mary needs to buy 250 mL of liquid Tylenol.

The answer is A. 250 milliliters

Key Learning Points:

• Always organize your information first
• Break complex problems into smaller steps
• Calculate one part at a time (daily doses, then multiply by days)
• Double-check your work using a different approach
• Units matter! Keep track of milliliters (mL) throughout

The correct answer is (D)

Let me help you understand how to solve this step by step, using clear reasoning that will help you tackle similar problems in the future.

First, let's identify the outlier:

• Looking at the numbers: 6, 23, 25, 27, 27, 29, 31, 36
• Most numbers are clustered between 23-36
• 6 is much lower than the rest - it's our outlier

Let's calculate the current median (middle number):

• In order: 6, 23, 25, 27, 27, 29, 31, 36
• With 8 numbers, we average the 4th and 5th numbers
• 27 + 27) ÷ 2 = 27
• Current median = 27
• After removing the outlier (6):
• New set: 23, 25, 27, 27, 29, 31, 36
• With 7 numbers, take the 4th number
• New median = 27
• The median stays the same!

Let's check the mean:

• Current mean = (6 + 23 + 25 + 27 + 27 + 29 + 31 + 36) ÷ 8 = 25.5
• New mean (without 6) = (23 + 25 + 27 + 27 + 29 + 31 + 36) ÷ 7 = 28.3
• The mean increased because we removed a low number

Therefore, the answer is D: The median would stay the same and the mean would increase.

Key Learning Points:

An outlier is a value that's significantly different from other values

Removing a low outlier will increase the mean

The median isn't always affected by removing an outlier, especially if the outlier is on the end of the data set

With an even number of values, the median is the average of the two middle numbers

With an odd number of values, the median is the middle number

This type of question tests your understanding of how outliers affect measures of central tendency (mean and median). Remember that:

• Mean is affected by all values, including outliers
• Median is more resistant to outliers, especially those at the ends of the data set