IAAT - Iowa Algebra Aptitude Test — Questions and Answers

Question 1: A recipe for a fruit smoothie requires 3 ounces of yogurt for every 5 ounces of mixed berries. Based on this relationship, which of the following tables correctly shows the amount of yogurt and berries needed for different quantities of the smoothie? [Table A shows Yogurt(oz): 6, 9, 12 and Berries(oz): 10, 15, 20. Table B shows Yogurt(oz): 6, 8, 10 and Berries(oz): 10, 13, 16. Table C shows Yogurt(oz): 5, 10, 15 and Berries(oz): 3, 6, 9. Table D shows Yogurt(oz): 6, 9, 12 and Berries(oz): 8, 11, 14.]

Table D
Table C
Table B
Table A (Correct answer)

Correct answer: Table A

The problem states a ratio of 3 ounces of yogurt to 5 ounces of berries (3:5). We need to find the table where this ratio holds true for all entries. In Table A, the ratios are 6:10 (which simplifies to 3:5), 9:15 (simplifies to 3:5), and 12:20 (simplifies to 3:5). All pairs maintain the required 3:5 ratio. The other tables do not consistently follow this ratio.

Question 2: A student's test score is 90. To calculate their final grade, the teacher first deducts 1/3 of the points and then adds 7 bonus points. Which of the following represents the student's final grade?

60
97
77
67 (Correct answer)

Correct answer: 67

First, find 1/3 of 90, which is (1/3) * 90 = 30. Then, deduct this amount from the score: 90 - 30 = 60. Finally, add the 7 bonus points: 60 + 7 = 67. The student's final grade is 67.

Question 3: There were 46 kids in the tram, in which 26 were boys and 20 were girls. What is the ratio of the boys to the total number of girls?

14:10
13:10 (Correct answer)
12:10
15:10

Correct answer: 13:10

Explanation: The ratio of boys to the total number of girls is found by dividing the number of boys by the number of girls. In this case, there are 26 boys and 20 girls. So, the ratio of boys to girls is 26:20, which simplifies to 13:10.

Question 4: A taxi company charges $2.50 for the first mile and $0.75 for each additional mile. If 'm' represents the total number of miles traveled, which expression represents the total cost for a ride that is more than one mile?

3.25m
2.50 + 0.75m
2.50 + 0.75(m - 1) (Correct answer)
2.50m + 0.75

Correct answer: 2.50 + 0.75(m - 1)

The cost includes a flat fee of $2.50 for the first mile. The variable 'm' is the total miles. Since the first mile is already paid for by the $2.50 fee, the additional charge of $0.75 applies only to the remaining miles, which is represented by (m - 1). Thus, the total cost is 2.50 + 0.75(m - 1).

Question 5: A video game costs $350. There is a 6% sales tax. How much will the game cost including the tax?

$356
$357
$371 (Correct answer)
$365

Correct answer: $371

Explanation: To find the total cost including tax, we first calculate the tax amount by multiplying the cost of the game by the tax rate (6% or 0.06 in decimal form). Then, we add this tax amount to the original cost of the game. Tax amount = $350 * 0.06 = $21 Total cost = $350 + $21 = $371

Question 6: A middle school is tracking the number of students who participate in after-school sports. They find that the number of participants has increased by an average of 15 students per year since 2020, when there were 120 participants. If this trend continues, how many students will be participating in sports in 2026?

210 (Correct answer)
180
195
225

Correct answer: 210

First, determine the number of years that have passed from the start year (2020) to the target year (2026). This is 2026 - 2020 = 6 years. The number of participants increases by 15 students each year, so the total increase over 6 years is 6 * 15 = 90 students. To find the total number of participants in 2026, add this increase to the initial number of participants: 120 + 90 = 210 students.

Question 7: Two rival companies offer video game streaming services. Company X charges a $10 monthly fee and $3 per game downloaded. Company Y charges a flat fee of $25 per month for unlimited game downloads. For what number of games downloaded per month is the cost of both services exactly the same?

5 games (Correct answer)
4 games
3 games
6 games

Correct answer: 5 games

Let 'g' be the number of games. The cost for Company X is C = 3g + 10. The cost for Company Y is C = 25. To find when the costs are equal, set the expressions equal to each other: 3g + 10 = 25. Subtract 10 from both sides: 3g = 15. Divide by 3: g = 5. At 5 games, the cost for both services is $25.

Question 8: The table below shows the relationship between the number of hours a student spends studying (h) and the score they receive on a test (S). Which rule describes this relationship? | Hours (h) | Score (S) | |---|---| | 0 | 65 | | 1 | 72 | | 2 | 79 | | 3 | 86 |

S = 65h + 7
S = 7h + 65 (Correct answer)
S = h + 65
S = 79h - 7

Correct answer: S = 7h + 65

The score (S) starts at 65 when the hours (h) are 0. For each additional hour of studying, the score increases by 7. This can be represented by the equation S = 7h + 65. Let's test it: for h=2, S = 7(2) + 65 = 14 + 65 = 79, which matches the table.

Question 9: A group of `f` friends wins a cash prize of `P` dollars. They agree to first donate $100 to a charity and then split the remaining amount equally among themselves. Which expression represents the amount of money each friend receives?

P / (f - 100)
(P - 100) / f (Correct answer)
P/f - 100
100 - P/f

Correct answer: (P - 100) / f

The order of operations is crucial. First, the $100 donation is subtracted from the total prize money `P`, which is represented by `(P - 100)`. Then, this remaining amount is split equally among `f` friends, which means dividing by `f`. The parentheses are necessary to ensure the subtraction happens before the division.

Question 10: Evaluate the expression: 20 - 4 * (2 + 1)^2

144
-16 (Correct answer)
12
16

Correct answer: -16

Following the order of operations (PEMDAS/BODMAS): First, solve the operation inside the parentheses (2 + 1) = 3. Next, calculate the exponent 3^2 = 9. Then, perform the multiplication 4 * 9 = 36. Finally, perform the subtraction 20 - 36 = -16.

Question 11: A new mathematical operation is defined as a © b = 2a + b^2. What is the value of 4 © 5?

33 (Correct answer)
39
18
28

Correct answer: 33

This question requires substituting the given numbers into the defined operation. In this case, 'a' is 4 and 'b' is 5. The operation is a © b = 2a + b^2. So, we calculate 2 * 4 + 5^2. This simplifies to 8 + 25, which equals 33.

Question 12: Which of the following expressions represents the sum of 5 and twice x?

2x + 5
X + 5 (Correct answer)
5 + X/2
5x + 2

Correct answer: X + 5

Explanation: The sum of 5 and twice x is represented by the expression x + 5, as "twice x" is equivalent to 2x, and the sum of 5 and 2x is x + 5.

Question 13: A student is saving for a new tablet that costs $350. They already have $80 saved. They earn $15 per week for chores. Which inequality represents the number of weeks, `w`, the student must work to have at least enough money to buy the tablet?

80w + 15 ≤ 350
80 + 15w ≥ 350 (Correct answer)
80 + 15w < 350
15w - 80 ≥ 350

Correct answer: 80 + 15w ≥ 350

The student's total savings can be represented by their initial amount ($80) plus the amount they earn over time ($15 multiplied by the number of weeks, `w`), which is `80 + 15w`. The phrase 'at least' means the total must be greater than or equal to the goal of $350. Therefore, the correct inequality is `80 + 15w ≥ 350`.

Question 14: A student was asked to evaluate the expression 60 - 4² ÷ 2 × 3. Their work is shown below. Step 1: 60 - 16 ÷ 2 × 3 Step 2: 44 ÷ 2 × 3 Step 3: 22 × 3 Step 4: 66 In which step did the student make their first mistake?

Step 2 (Correct answer)
Step 4
Step 3
Step 1

Correct answer: Step 2

The student's first error occurred in Step 2. After correctly calculating the exponent in Step 1 (4² = 16), the next operations according to PEMDAS are division and multiplication from left to right. The student incorrectly performed subtraction (60 - 16) before division. The correct second step should have been to calculate 16 ÷ 2.

Question 15: A survey asked 300 middle school students to name their favorite after-school club. The results are displayed in the pie chart below. How many more students chose the Sports club than the Art club? [A pie chart titled 'Favorite After-School Club' is shown with the following percentages: Sports 40%, Music 25%, Art 20%, Drama 15%.]

20
120
60
60 (Correct answer)

Correct answer: 60

First, calculate the number of students who chose each club. Sports: 40% of 300 = 0.40 * 300 = 120 students. Art: 20% of 300 = 0.20 * 300 = 60 students. Then, find the difference between the two groups: 120 (Sports) - 60 (Art) = 60 students. Alternatively, find the difference in percentage points (40% - 20% = 20%) and then calculate that percentage of the total students (20% of 300 = 0.20 * 300 = 60).

Question 16: A video game is originally priced at $60. It is on sale for 25% off. What is the sale price of the video game?

$35
$45 (Correct answer)
$50
$15

Correct answer: $45

First, calculate the discount amount. 25% of $60 is (25/100) * 60 = 0.25 * 60 = $15. Then, subtract the discount from the original price: $60 - $15 = $45. The sale price is $45.

Question 17: What is the next number in the following geometric sequence: 80, 40, 20, 10, ___?

2
5 (Correct answer)
0
8

Correct answer: 5

This is a geometric sequence where each term is found by dividing the previous term by 2 (or multiplying by 1/2). 80 / 2 = 40, 40 / 2 = 20, and 20 / 2 = 10. Therefore, the next term in the sequence is 10 / 2 = 5.

Question 18: There are 49 boys and 28 girls in a school auditorium. Express the ratio of the number of boys to that of girls.

7:4 (Correct answer)
28:49
49:28
49:7

Correct answer: 7:4

Explanation: Given, the number of boys = 49; and the number of girls = 28. The GCF of 49 and 28 is 7. Now, to simplify, divide the two terms by their GCF which is 7. This means, (49 ÷ 7)/(28 ÷ 7) = 7/4. Therefore, the ratio of the number of boys to that of girls = 7:4.

Question 19: If 5 notebooks cost $7.50, what is the cost of 8 notebooks at the same rate?

$10.00
$11.50
$13.50
$12.00 (Correct answer)

Correct answer: $12.00

Unit cost = $7.50 ÷ 5 = $1.50 per notebook; 8 × $1.50 = $12.00.

Question 20: A company sells two products, Gadgets and Widgets. The bar chart shows the number of units sold for each product in a month, and the table shows the profit per unit. Which statement is best supported by the data? [A bar chart shows 'Units Sold'. For 'Gadgets', the bar reaches 150. For 'Widgets', the bar reaches 200.] | Product | Profit per Unit | |---|---| | Gadget | $8 | | Widget | $5 |

The profit from Gadgets and Widgets was equal.
The company sold more Gadgets than Widgets.
The total profit from Widgets was greater than the total profit from Gadgets.
The company made more profit from Gadgets than from Widgets. (Correct answer)

Correct answer: The company made more profit from Gadgets than from Widgets.

To determine the total profit for each product, multiply the units sold by the profit per unit. Profit from Gadgets: 150 units * $8/unit = $1200. Profit from Widgets: 200 units * $5/unit = $1000. Comparing the total profits, $1200 (Gadgets) is greater than $1000 (Widgets). Therefore, the company made more profit from Gadgets.

Question 21: A person has 20 coins consisting of only dimes and quarters. The total value of the coins is $3.20. Which system of equations can be used to find the number of dimes (d) and quarters (q)?

d + q = 20 AND 10d + 25q = 3.20
d + q = 20 AND 0.10d + 0.25q = 3.20 (Correct answer)
d + q = 3.20 AND 0.10d + 0.25q = 20
d + q = 5.20 AND d + q = 20

Correct answer: d + q = 20 AND 0.10d + 0.25q = 3.20

The problem can be described by two separate relationships, leading to two equations. The first is about the quantity of coins: the number of dimes (d) plus the number of quarters (q) equals 20. This gives the equation d + q = 20. The second is about the total value: the value of the dimes (0.10d) plus the value of the quarters (0.25q) equals $3.20. This gives the equation 0.10d + 0.25q = 3.20.

Question 22: How could you rewrite the problem below? 5(4y + 2x) =

5 (6xy)
20x + 10y
30yx
20y + 10x (Correct answer)

Correct answer: 20y + 10x

Explanation: To rewrite the expression 5(4y + 2x), we can distribute the 5 to each term inside the parentheses. 5(4y + 2x) = 5 4y + 5 2x Simplifying, we get: 20y + 10x

Question 23: Which of the following lists of numbers is ordered from greatest to least?

-1.5, -3/2, 0, 0.5
0.5, 0, -1.5, -3/2
0.5, 0, -3/2, -1.5 (Correct answer)
-3/2, -1.5, 0, 0.5

Correct answer: 0.5, 0, -3/2, -1.5

To compare the numbers, convert them all to the same format. -3/2 is equal to -1.5. So the numbers are -1.5, -1.5, 0, and 0.5. When ordered from greatest to least, the sequence is 0.5, 0, and then -1.5. Since -3/2 and -1.5 are equal, their order doesn't matter relative to each other. The correct list is 0.5, 0, -3/2, -1.5.

Question 24: Which proportion correctly models this problem: '3 is to 7 as n is to 35'?

3/7 = 35/n
3/35 = 7/n
7/3 = n/35
3/7 = n/35 (Correct answer)

Correct answer: 3/7 = n/35

The proportion 3/7 = n/35 keeps the same ratio structure with n corresponding to 3.

Question 25: The scatter plot below shows the relationship between the number of hours a student sleeps the night before a test and their score on the test. A line of best fit is drawn. Based on the line of best fit, what is the best prediction for the score of a student who sleeps for 8 hours? [A scatter plot shows 'Test Score vs. Hours of Sleep'. The x-axis is 'Hours of Sleep' from 4 to 10. The y-axis is 'Test Score' from 50 to 100. Data points show a positive correlation. A line of best fit passes through approximately (5, 65) and (9, 85).]

70
95
60
80 (Correct answer)

Correct answer: 80

To make a prediction using the line of best fit, locate '8 hours' on the x-axis. Move vertically up to the line of best fit, and then move horizontally to the left to read the corresponding value on the y-axis. The line passes through approximately 80 on the y-axis for an x-value of 8.

Question 26: The table below shows the cost for a plumbing service based on the number of hours worked. Which equation represents the relationship between the total cost (C) and the number of hours worked (h)? | Hours (h) | Total Cost (C) | |---|---| | 1 | $110 | | 2 | $170 | | 3 | $230 | | 4 | $290 |

C = 50h + 50
C = 110h + 60
C = 60h + 50 (Correct answer)
C = 110h

Correct answer: C = 60h + 50

First, find the hourly rate by calculating the difference in cost for each additional hour: $170 - $110 = $60; $230 - $170 = $60. This means the plumber charges $60 per hour (60h). Next, determine the fixed fee. Using the first hour: C = 60(1) + fixed fee = $110. Solving for the fixed fee gives $50. Therefore, the equation is C = 60h + 50. This can be verified with another point: for h=2, C = 60(2) + 50 = 120 + 50 = $170, which matches the table.

Question 27: John is filling up baskets with red and green apples. For every 9 red apples, he puts 4 green apples. Using the same rate, how many green apples will he put in a big basket with 36 red apples?

31
24
12
16 (Correct answer)

Correct answer: 16

Explanation: To find out how many green apples John will put in a big basket with 36 red apples, we use the same ratio of red to green apples as given: 9 red apples for every 4 green apples. So, for 36 red apples, John will put 36/9 × 4 = 16 green apples in the big basket.

Question 28: The table below shows a relationship between an input, x, and an output, y. Which equation correctly describes this relationship?

y = 4x - 1
y = 3x
y = 2x + 1
y = x² + 2 (Correct answer)

Correct answer: y = x² + 2

By testing each input value (x) in the proposed equations, only y = x² + 2 correctly produces the corresponding output value (y) for all pairs in the table. For x=1, 1²+2=3. For x=2, 2²+2=6. For x=3, 3²+2=11. For x=4, 4²+2=18.

Question 29: If 14 cups of yogurt and 4 cups of strawberry crystals are needed to make a strawberry pie, what is the ratio of yogurt and strawberry crystals that is used for the recipe?

7: 3
7: 4
7: 5
7: 2 (Correct answer)

Correct answer: 7: 2

Explanation: The ratio of yogurt to strawberry crystals used for the recipe is found by dividing the number of cups of yogurt by the number of cups of strawberry crystals. In this case, there are 14 cups of yogurt and 4 cups of strawberry crystals. So, the ratio of yogurt to strawberry crystals is 14:4, which simplifies to 7:2.

Question 30: The length of a rectangular garden is 6 feet longer than its width. If the perimeter of the garden is 60 feet, what is the area of the garden in square feet?

252 sq ft
216 sq ft (Correct answer)
225 sq ft
144 sq ft

Correct answer: 216 sq ft

Let 'w' be the width. The length 'l' is w + 6. The formula for the perimeter of a rectangle is P = 2l + 2w. Substitute the given values: 60 = 2(w + 6) + 2w. Distribute the 2: 60 = 2w + 12 + 2w. Combine like terms: 60 = 4w + 12. Subtract 12 from both sides: 48 = 4w. Divide by 4: w = 12 feet. The length is l = 12 + 6 = 18 feet. The area is A = l × w = 18 × 12 = 216 square feet.

Question 31: In a proportion, if a/b = c/d, which of the following must also be true?

a + b = c + d
a ÷ c = d ÷ b
a × d = b × c (Correct answer)
a − b = c − d

Correct answer: a × d = b × c

In any proportion a/b = c/d, the cross-products are equal: a × d = b × c.

Question 32: The table below shows a relationship between an input number, 'n', and an output number. Which rule describes this relationship? | Input (n) | Output | |---|---| | 2 | 7 | | 3 | 10 | | 4 | 13 | | 5 | 16 |

2n + 3
n + 5
3n + 1 (Correct answer)
4n - 1

Correct answer: 3n + 1

To find the correct rule, test each option with the input values. For the rule 3n + 1: when n=2, the output is 3(2)+1=7. When n=3, the output is 3(3)+1=10. When n=4, the output is 3(4)+1=13. Since this rule works for all the pairs in the table, it is the correct one. The other options fail for at least one of the pairs.

Question 33: Find the missing number in the following arithmetic sequence: 4, 10, ___, 22, 28.

16 (Correct answer)
18
17
15

Correct answer: 16

In an arithmetic sequence, the same number is added to get from one term to the next. This is called the common difference. By subtracting consecutive terms (28 - 22 = 6 and 10 - 4 = 6), we find the common difference is 6. To find the missing term, add 6 to the term before it: 10 + 6 = 16. You can verify this by adding 6 again: 16 + 6 = 22.

Question 34: A baker has 6.5 pounds of flour. A recipe for one batch of cookies requires 1.25 pounds of flour. After making two batches of cookies, how much flour does the baker have left?

3.75 pounds
4.00 pounds (Correct answer)
4.25 pounds
5.25 pounds

Correct answer: 4.00 pounds

First, calculate the total flour used for two batches: 2 * 1.25 pounds = 2.5 pounds. Then, subtract the amount used from the initial amount: 6.5 pounds - 2.5 pounds = 4.00 pounds. The baker has 4.00 pounds of flour left.

Question 35: What is the value of the expression: 3 × [20 - (2 + 4)² ÷ 9]?

12
16
48 (Correct answer)
52

Correct answer: 48

Work from the innermost grouping symbols outward. First, calculate inside the parentheses: (2 + 4) = 6. The expression becomes 3 × [20 - 6² ÷ 9]. Inside the brackets, evaluate the exponent: 6² = 36. The expression is now 3 × [20 - 36 ÷ 9]. Still inside the brackets, perform division before subtraction: 36 ÷ 9 = 4. The expression simplifies to 3 × [20 - 4]. Perform the subtraction in the brackets: 20 - 4 = 16. Finally, perform the multiplication: 3 × 16 = 48.

Question 36: The total cost (C) of a pizza is determined by a base price of $12 plus $1.50 for each topping (t). Which equation correctly represents this relationship?

C = 12 - 1.50t
C = 12t + 1.50
C = 1.50(12 + t)
C = 12 + 1.50t (Correct answer)

Correct answer: C = 12 + 1.50t

The relationship described is a fixed cost plus a variable cost. The fixed cost, or base price, is $12. This is the starting value. The variable cost depends on the number of toppings, 't', at $1.50 each, which is represented as 1.50t. The total cost is the sum of the base price and the cost of the toppings, leading to the equation C = 12 + 1.50t.

Question 37: If a laptop costs $1500 but there is a discount of 30%, what will be the new cost of the laptop?

1150
1450
1050 (Correct answer)
1000

Correct answer: 1050

Explanation: To calculate the new cost of the laptop after a 30% discount, we subtract the discount amount from the original cost. Discount amount = 30% of $1500 = 0.30 * 1500 = $450 New cost = Original cost - Discount amount = $1500 - $450 = $1050

Question 38: Consider a visual pattern made of square tiles. Figure 1 has 1 tile, Figure 2 has 4 tiles, and Figure 3 has 9 tiles, arranged in squares. If this pattern continues, how many tiles will be in Figure 6?

25
18
12
36 (Correct answer)

Correct answer: 36

The pattern shows that the number of tiles is the figure number multiplied by itself (the figure number squared). Figure 1: 1×1=1. Figure 2: 2×2=4. Figure 3: 3×3=9. Following this rule, Figure 6 will have 6×6 = 36 tiles.

Question 39: A pattern is built with square tiles. Figure 1 has 2 tiles, Figure 2 has 5 tiles, and Figure 3 has 10 tiles. Which rule can be used to find the number of tiles, T, in any Figure, n?

T = n + 1
T = n² + 1 (Correct answer)
T = 2n² - 1
T = 3n - 1

Correct answer: T = n² + 1

Let's test the rule T = n² + 1. For Figure 1 (n=1), T = 1² + 1 = 2. This is correct. For Figure 2 (n=2), T = 2² + 1 = 5. This is correct. For Figure 3 (n=3), T = 3² + 1 = 10. This is also correct. The rule holds for all given figures.

Question 40: A jacket's original price is represented by 'p'. It is on sale for 25% off. A customer has an additional coupon for $10 off the sale price. Which expression represents the final price the customer pays?

p - 0.25 - 10
p - 10.25
0.75p - 10 (Correct answer)
0.25p - 10

Correct answer: 0.75p - 10

First, calculate the sale price. A 25% discount means the customer pays 75% of the original price (100% - 25% = 75%). This is represented as 0.75p. After the discount is applied, the $10 coupon is used. This means you subtract $10 from the sale price. The final expression is 0.75p - 10.

Question 41: What is the result of -12 + (-5) - (-8)?

1
-9 (Correct answer)
-1
-25

Correct answer: -9

The expression can be rewritten as -12 - 5 + 8. First, combine the negative numbers: -12 - 5 = -17. Then, add the positive number: -17 + 8 = -9. The correct answer is -9.

Question 42: 3 + 4 (9) =

63
16
39 (Correct answer)
54

Correct answer: 39

Explanation: To solve the expression, we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). Given the expression 3 + 4 × 9: First, we perform the multiplication: 4 × 9 = 36. Then, we add 3 to the result: 3 + 36 = 39.

Question 43: Which algebraic expression correctly represents the phrase 'five less than the product of a number, `n`, and the square of another number, `m`'?

nm² - 5 (Correct answer)
5 - (n + m²)
(n + m²) - 5
5 - nm²

Correct answer: nm² - 5

'The product of a number, `n`, and the square of another number, `m`' translates to `n * m²` or `nm²`. The phrase 'five less than' indicates that 5 should be subtracted from this product. Therefore, the correct expression is `nm² - 5`.

Question 44: The line graph below shows the temperature in a city over a 12-hour period. During which two-hour interval did the temperature increase at the highest rate? [A line graph shows 'City Temperature'. The x-axis is 'Time of Day' from 6 AM to 6 PM in 2-hour increments. The y-axis is 'Temperature (°F)' from 40 to 70. The data points are: 6 AM at 45°F, 8 AM at 50°F, 10 AM at 60°F, 12 PM at 65°F, 2 PM at 68°F, 4 PM at 67°F, 6 PM at 62°F.]

8 AM to 10 AM (Correct answer)
4 PM to 6 PM
6 AM to 8 AM
12 PM to 2 PM

Correct answer: 8 AM to 10 AM

To find the highest rate of increase, look for the steepest upward slope on the graph. Calculate the temperature change for each interval: 6-8 AM: 50-45 = 5°F increase. 8-10 AM: 60-50 = 10°F increase. 12-2 PM: 68-65 = 3°F increase. 4-6 PM: 62-67 = 5°F decrease. The greatest increase was 10°F, which occurred between 8 AM and 10 AM.

Question 45: A function machine follows the rule: 'multiply the input by 4, then subtract 7'. If the output of the machine is 53, what was the input?

205
15 (Correct answer)
13.25
11

Correct answer: 15

To find the input, you must perform the inverse operations in reverse order. Start with the output, 53. The reverse of 'subtract 7' is 'add 7', so 53 + 7 = 60. The reverse of 'multiply by 4' is 'divide by 4', so 60 / 4 = 15. The input was 15.

Question 46: A coach buys `g` sports drinks for $2 each and `g` protein bars for $3 each for their team. The total cost can be represented by the expression `2g + 3g`. Which of the following expressions is NOT an equivalent way to represent the total cost?

5g² (Correct answer)
g(2 + 3)
(3 + 2)g
5g

Correct answer: 5g²

The original expression `2g + 3g` can be simplified by combining like terms to `5g`. Using the distributive property, `2g + 3g` is also equivalent to `g(2 + 3)` or `(2 + 3)g`. The expression `5g²` is not equivalent because it involves an exponent, which does not correctly model the total cost of the items.

Question 47: A cell phone plan costs $40 per month, which includes 5 GB of data. Any additional data costs $10 per GB. Which equation represents the total monthly cost (C) for a user who uses 'g' gigabytes of data, where g is greater than 5?

C = 50g
C = 40 + 10g
C = 10(g - 5)
C = 40 + 10(g - 5) (Correct answer)

Correct answer: C = 40 + 10(g - 5)

The total cost (C) is the base fee of $40 plus the cost for extra data. The amount of extra data is the total data used (g) minus the included amount (5), which is represented as (g - 5). The cost for this extra data is $10 per GB, so the extra charge is 10(g - 5). Therefore, the complete equation is C = 40 + 10(g - 5).

Question 48: James sells ice cream on weekends. If he sells cones with two scoops, he gets a bonus of 10 cents per scoop. On Saturday, he sold 12 cones with two scoops. On Sunday, he sold only 4 cones with double scoops. What was his bonus?

.10 (12 + 4)
.10 + 10 ‥ 12
.10 ‥ 12 ‥ 4
.10 ‥ 2 (12 + 4) (Correct answer)

Correct answer: .10 ‥ 2 (12 + 4)

Explanation: James gets a bonus of 10 cents per scoop. Each cone with two scoops will earn him a bonus for two scoops. On Saturday, he sold 12 cones with two scoops, and on Sunday, he sold 4 cones with two scoops. The total number of cones with two scoops sold is 12 + 4 = 16 cones. Since each cone has two scoops, the total number of scoops is 2 × (12 + 4). To calculate the total bonus: 0.10 (per scoop) × 2 × (12 + 4) = 0.10 × 2 × 16 = 0.10 × 32 = 3.20

Question 49: The ratio of red marbles to blue marbles is 2:7. If there are 63 blue marbles, how many red marbles are there?

14
16
18 (Correct answer)
21

Correct answer: 18

If 7 parts = 63, then 1 part = 9, so 2 parts (red) = 18.

Question 50: If 12 workers can complete a job in 8 days, how many days will 6 workers need to complete the same job?

12 days
16 days (Correct answer)
24 days
4 days

Correct answer: 16 days

This is inverse proportion: 12 × 8 = 6 × d, so d = 96 ÷ 6 = 16 days.

Question 51: A concert hall has 20 seats in the first row. Each subsequent row has 3 more seats than the row in front of it. How many seats are in the 8th row?

38
44
41 (Correct answer)
24

Correct answer: 41

This is an arithmetic sequence that starts at 20 with a common difference of 3. You can list the terms: Row 1=20, R2=23, R3=26, R4=29, R5=32, R6=35, R7=38, R8=41. Alternatively, the formula for the nth term is a + (n-1)d, where a=20, n=8, and d=3. This gives 20 + (8-1)*3 = 20 + 7*3 = 20 + 21 = 41.

Question 52: Which carton of yogurt is the best value?

4 oz for .49
8 oz for 1.29
6 oz for .65
16 oz for 1.60 (Correct answer)

Correct answer: 16 oz for 1.60

Explanation: 16 oz for 1.60 is the best value because it has the lowest price per ounce, making it the most cost-effective choice.

Question 53: Sophia baked cookies for her class. Every student had one cookie, including Sophia. At the end of the school day, 3 cookies were left. How many kids were in the class?

n + 3
3 - n
n - 3 (Correct answer)
3n

Correct answer: n - 3

Explanation: Let's denote the total number of cookies Sophia baked as 𝑛. Since every student, including Sophia, had one cookie, and 3 cookies were left at the end of the school day, the number of cookies eaten was n − 3. This number of cookies eaten is equal to the number of kids in the class since each student had one cookie. Therefore, the number of kids in the class is represented by the expression 𝑛 − 3.

Question 54: Which of the following verbal statements correctly represents the algebraic expression 2(n - 5)?

Two more than a number minus five.
A number decreased by five.
Twice the difference of a number and five. (Correct answer)
Five less than twice a number.

Correct answer: Twice the difference of a number and five.

The expression (n - 5) represents 'the difference of a number and five'. The number 2 outside the parentheses indicates that this entire difference is multiplied by two, or 'twice' the difference.

Question 55: Tiffany walked 1 mile from home to school. After school, she walked to her friend Joan’s house to wait for her dad to pick her up. Joan’s home is twice the distance from Tiffany’s home to school. How many miles did Tiffany walk by the time her dad picked her up?

3 miles (Correct answer)
6 miles
5 miles
2 miles

Correct answer: 3 miles

Explanation: Tiffany walked 1 mile from home to school. Joan's house is twice the distance from Tiffany's home to school, so it is 2 miles from Tiffany's home. Therefore, the distance from the school to Joan's house is also 2 miles. Adding these distances together, Tiffany walked a total of 1 mile+2 miles=3 miles.

Question 56: The perimeter of a stop sign is 48 inches. If each side is equal to one another, what is the length of each side?

n + n + n + n = 48
n + n + n + n + n + n = 48
6n = 48
8n = 48 (Correct answer)

Correct answer: 8n = 48

Explanation: A stop sign has 8 sides, and since each side is equal, the length of each side can be represented as 𝑛. The perimeter of the stop sign is the sum of the lengths of all 8 sides. Therefore, the equation to represent this is 8n = 48. Solving for 𝑛: n = 48/8 = 6 inches Thus, each side of the stop sign is 6 inches long.

Question 57: A community garden tracks the growth of a sunflower. The table below shows the height of the sunflower at the end of each week. If the pattern of growth continues, what will be the height of the sunflower at the end of Week 6? | Week (W) | Height (cm) | |---|---| | 1 | 15 | | 2 | 21 | | 3 | 27 | | 4 | 33 |

36 cm
39 cm
42 cm
45 cm (Correct answer)

Correct answer: 45 cm

By analyzing the table, we can see that the sunflower grows by 6 cm each week (21 - 15 = 6; 27 - 21 = 6). To find the height in Week 6, continue the pattern. Week 5 height would be 33 + 6 = 39 cm. Week 6 height would be 39 + 6 = 45 cm.

Question 58: Which of the following is the next number in the sequence: 2, 3, 5, 8, 12, ___?

16
15
17 (Correct answer)
18

Correct answer: 17

The pattern in this sequence is not simple addition; instead, the amount added increases by one each time. To get from 2 to 3, you add 1. From 3 to 5, you add 2. From 5 to 8, you add 3. From 8 to 12, you add 4. Therefore, to find the next number, you must add 5 to 12, which results in 17.

Question 59: A store sells 3 apples for $1.20. At this rate, how much do 10 apples cost?

$4.00 (Correct answer)
$4.20
$3.80
$3.60

Correct answer: $4.00

Unit price = $1.20 ÷ 3 = $0.40 per apple; 10 × $0.40 = $4.00.

Question 60: A pizza restaurant charges a flat fee of $3 for delivery and $11 for each pizza ordered. Which equation can be used to find the total cost (C) for any number of pizzas (p)?

C = 11p - 3
C = 14p
C = 3p + 11
C = 11p + 3 (Correct answer)

Correct answer: C = 11p + 3

The total cost (C) is the sum of the cost of the pizzas and the delivery fee. The cost of the pizzas is $11 times the number of pizzas (p), which is 11p. The delivery fee is a constant $3. Therefore, the correct equation is C = 11p + 3.

IAAT - Iowa Algebra Aptitude Test

The Iowa Algebra Aptitude Test (IAAT) is a 60-question standardized assessment that measures students' readiness for algebra coursework. It is typically administered to students in grades 7–8 and evaluates pre-algebraic skills, mathematical reasoning, and symbolic thinking across four timed sections.

Questions

40 min

Time Limit

91%

To Pass

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