IAAT - Iowa Algebra Aptitude Test — Questions and Answers

Question 1: There are 45 marbles in a box. If James picks one-third of the marbles and Lisa picks two-fifths of the remaining marbles, how many are left in the box?

3
30
12
18 (Correct answer)

Correct answer: 18

Explanation: To find out how many marbles are left in the box, we need to calculate the number of marbles picked by James and Lisa, and then subtract that from the total number of marbles. James picks one-third of the marbles, which is (1/3) * 45 = 15 marbles. The remaining marbles in the box after James picks are 45 - 15 = 30 marbles. Lisa picks two-fifths of the remaining marbles, which is (2/5) * 30 = 12 marbles. Therefore, the number of marbles left in the box is 30 - 12 = 18 marbles.

Question 2: 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: 5
7: 3
7: 4
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 3: The graph below shows the number of books read by students in a book club over four months. Which of the following statements is best supported by the information in the graph? [A bar graph shows 'Books Read by Book Club'. The x-axis is labeled 'Month' with bars for January, February, March, and April. The y-axis is labeled 'Number of Books' from 0 to 50 in increments of 10. January's bar reaches 25, February's reaches 35, March's reaches 30, and April's reaches 45.]

The average number of books read per month was 30.
The number of books read increased each month.
The greatest increase in the number of books read occurred between March and April. (Correct answer)
The book club read more books in the first two months than in the last two months.

Correct answer: The greatest increase in the number of books read occurred between March and April.

To find the correct statement, evaluate each option. A is incorrect because reading decreased from February (35) to March (30). B is incorrect because the first two months total 25+35=60 books, while the last two months total 30+45=75 books. C is correct because the increases were: Jan-Feb (35-25=10), Feb-Mar (a decrease), and Mar-Apr (45-30=15), making the March to April increase the largest. D is incorrect because the total is 25+35+30+45=135 books, and the average is 135/4 = 33.75.

Question 4: 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 5: 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 6: What is the result of -12 + (-5) - (-8)?

-9 (Correct answer)
-25
-1
1

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

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

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

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

Correct answer: $12.00

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

Question 9: 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?

11
13.25
15 (Correct answer)
205

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 10: 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
80 (Correct answer)
95
60

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 11: 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
0.75p - 10 (Correct answer)
p - 10.25
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 12: A video game costs $350. There is a 6% sales tax. How much will the game cost including the tax?

$356
$371 (Correct answer)
$357
$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 13: 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?

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

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 14: A family buys 4 adult movie tickets for $12 each and 3 child tickets for $8 each. They also buy a large popcorn for $10 and use a coupon for $5 off the entire purchase. Which expression correctly calculates their total cost?

(4 + 3) × (12 + 8) + 10 - 5
4 × 12 + 3 × 8 + 10 - 5 (Correct answer)
4 × (12 + 8) + 3 × 10 - 5
4 + 3 × 12 + 8 + 10 - 5

Correct answer: 4 × 12 + 3 × 8 + 10 - 5

To find the total cost, you must first calculate the cost of the adult tickets (4 × $12) and the child tickets (3 × $8). Then, you add the cost of the popcorn ($10) and subtract the coupon ($5). The multiplications must be performed before the addition and subtraction, representing the costs of the groups of tickets.

Question 15: The scatter plot shows the relationship between the number of hours students spent reviewing for a science exam and their exam scores. Which statement best describes the relationship shown in the data?

All students who reviewed for 4 hours got the same score.
There is no relationship between review time and exam score.
Spending more time reviewing causes exam scores to decrease.
As review time increases, the exam score tends to increase. (Correct answer)

Correct answer: As review time increases, the exam score tends to increase.

The points on the scatter plot generally trend from the lower-left to the upper-right. This pattern indicates a positive correlation, which means that as the value on the x-axis (Hours Reviewing) increases, the value on the y-axis (Exam Score) also tends to increase.

Question 16: 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 17: If y + 12 = 10 ‥ 2 What is y?

12
20
10
8 (Correct answer)

Correct answer: 8

Explanation: To solve for 𝑦, first, we simplify the expression on the right side of the equation: 10 × 2 = 20. Then, we subtract 12 from both sides of the equation to isolate y + 12 − 12 = 20 − 12. After simplification, we find that y = 8.

Question 18: 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 = 3p + 11
C = 11p - 3
C = 14p
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.

Question 19: If y is directly proportional to x, and y = 18 when x = 3, what is y when x = 7?

45
38
42 (Correct answer)
36

Correct answer: 42

Constant k = y/x = 18/3 = 6; when x = 7, y = 6 × 7 = 42.

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

-16 (Correct answer)
144
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 21: 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 (Correct answer)
n + 3
3 - n
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 22: 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 |

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

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 23: Which carton of yogurt is the best value?

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

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 24: 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 + 10 ‥ 12
.10 ‥ 12 ‥ 4
.10 ‥ 2 (12 + 4) (Correct answer)
.10 (12 + 4)

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 25: Where should parentheses be placed in the expression 5 + 3 × 8 - 2² to make its value equal to 60?

5 + 3 × (8 - 2²)
(5 + 3 × 8) - 2²
5 + (3 × 8 - 2²)
(5 + 3) × 8 - 2² (Correct answer)

Correct answer: (5 + 3) × 8 - 2²

Placing parentheses around (5 + 3) forces this addition to be performed first. The expression becomes (5 + 3) × 8 - 2², which simplifies to 8 × 8 - 2². Next, evaluate the exponent: 8 × 8 - 4. Then, perform the multiplication: 64 - 4. Finally, the subtraction gives the desired value of 60.

Question 26: A student is asked to evaluate the expression 5 - 2(9 - 4)². Their work is shown below. In which step did the student make the first mistake? Step 1: 3(9 - 4)² Step 2: 3(5)² Step 3: 3(25) Step 4: 75

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

Correct answer: Step 1

The student made a mistake in Step 1. According to the order of operations (PEMDAS), operations inside parentheses and multiplication should be performed before subtraction. Instead of evaluating (9 - 4) or handling the multiplication of 2 by the parenthetical expression, the student incorrectly performed the subtraction 5 - 2 first. The correct first step is to evaluate the expression inside the parentheses: 5 - 2(5)².

Question 27: Which of the following lists of numbers is ordered from greatest to least?

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

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 28: 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?

6 miles
3 miles (Correct answer)
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 29: In a class of 50 students, 23 are girls and the remaining are boys. Find the ratio of the number of boys to the number of girls.

17:13
27:23 (Correct answer)
25:28
35:30

Correct answer: 27:23

Explanation: Total number of students = 50; Number of girls = 23. Total number of boys = Total number of students - Total number of girls = 50 - 23 = 27 Therefore, the desired ratio is, (Number of boys: Number of girls), which is 27:23.

Question 30: 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 (Correct answer)
C = 1.50(12 + t)
C = 12t + 1.50
C = 12 - 1.50t

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 31: 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 = 3.20 AND 0.10d + 0.25q = 20
d + q = 20 AND 0.10d + 0.25q = 3.20 (Correct answer)
d + q = 20 AND 10d + 25q = 3.20
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 32: The equation 3x + 4 = 10 can be solved by which of the following methods?

Addition (Correct answer)
Multiplication
Substitution
Division

Correct answer: Addition

Explanation: To solve for x in 3x + 4 = 10, you need to isolate the variable on one side of the equation. Subtracting 4 from both sides gives you 3x = 6. Then, dividing both sides by 3 gives you x = 2. This method is called addition because you're adding or subtracting the same number on both sides of the equation to isolate the variable.

Question 33: 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 = 3n - 1
T = 2n² - 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 34: The perimeter of a rectangle is found using the formula P = 2L + 2W, where L is the length and W is the width. If the length of a rectangle is 4 units more than its width (W), which equation represents the perimeter in terms of only its width?

P = 2W + 8
P = 2L + 2(L - 4)
P = 2(W + 4) + 2W (Correct answer)
P = 6W

Correct answer: P = 2(W + 4) + 2W

The problem states that L = W + 4. To write the perimeter formula in terms of only W, we substitute (W + 4) for L in the original formula: P = 2(W + 4) + 2W.

Question 35: How could you rewrite the problem below? 5(4y + 2x) =

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

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

1050 (Correct answer)
1450
1150
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 37: Which of the following expressions represents the sum of 5 and twice x?

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

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 38: 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?

41 (Correct answer)
38
24
44

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 39: A pattern of figures is shown below. If 'n' represents the figure number, which expression can be used to find the number of squares in any figure? Figure 1: 3 squares Figure 2: 5 squares Figure 3: 7 squares

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

Correct answer: 2n + 1

The number of squares increases by 2 for each new figure. This suggests a relationship involving 2n. Let's test the expression 2n + 1. For Figure 1 (n=1), 2(1) + 1 = 3. For Figure 2 (n=2), 2(2) + 1 = 5. For Figure 3 (n=3), 2(3) + 1 = 7. The expression correctly describes the pattern.

Question 40: Which one is the best answer? 2/5 + 5/8 =

18 / 20
41/40 (Correct answer)
7 /13
10/40

Correct answer: 41/40

Explanation: To find the sum of 2/5 and 5/8, we need to find a common denominator and then add the fractions. The common denominator for 5 and 8 is 40. Converting 2/5 to have a denominator of 40, we get 16/40. Converting 5/8 to have a denominator of 40, we get 25/40. Adding the fractions, we have: 16/40 + 25/40 = 41/40

Question 41: If 9x = 54, then 8x + 1 =

49 (Correct answer)
7
37
6

Correct answer: 49

Explanation: To find the value of 8x + 1, we need to first solve the equation 9x = 54 to find the value of x. Dividing both sides of the equation by 9, we get: x = 54 / 9 Simplifying, we find: x = 6 Now we can substitute the value of x into the expression 8x + 1: 8(6) + 1 = 48 + 1 = 49 Therefore, if 9x = 54, then 8x + 1 = 49.

Question 42: 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 = 7h + 65 (Correct answer)
S = 79h - 7
S = 65h + 7
S = h + 65

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

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

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 44: 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 |

39 cm
42 cm
36 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 45: Which of the following expressions has the greatest value?

(5 + 3) × 6 (Correct answer)
5 × (6 - 3)
5 + 3 × 6
6 + 3 × 5

Correct answer: (5 + 3) × 6

To find the expression with the greatest value, we must evaluate each one correctly using the order of operations. A) 5 + 3 × 6 = 5 + 18 = 23. B) (5 + 3) × 6 = 8 × 6 = 48. C) 6 + 3 × 5 = 6 + 15 = 21. D) 5 × (6 - 3) = 5 × 3 = 15. Comparing the results (23, 48, 21, 15), the greatest value is 48.

Question 46: Which of the following ratios is equivalent to 6:9?

2:3 (Correct answer)
4:5
3:6
2:4

Correct answer: 2:3

Dividing both 6 and 9 by 3 gives 2:3, which is the simplified form.

Question 47: 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)
5g
(3 + 2)g

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 48: 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?

24
12
16 (Correct answer)
31

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 49: 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 = 40 + 10(g - 5) (Correct answer)
C = 10(g - 5)
C = 50g
C = 40 + 10g

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 50: A map has a scale of 1 inch : 50 miles. Two cities are 3.5 inches apart on the map. What is the actual distance?

150 miles
200 miles
175 miles (Correct answer)
165 miles

Correct answer: 175 miles

3.5 inches × 50 miles per inch = 175 miles.

Question 51: 3 + 4 (9) =

16
54
39 (Correct answer)
63

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

15
17 (Correct answer)
16
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 53: 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
8n = 48 (Correct answer)
6n = 48

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 54: 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?

6 games
5 games (Correct answer)
3 games
4 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 55: 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 = x² + 2 (Correct answer)
y = 2x + 1

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

2
0
8
5 (Correct answer)

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

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

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 58: A car travels 150 miles in 3 hours. At the same rate, how many miles will it travel in 5 hours?

200 miles
250 miles (Correct answer)
300 miles
225 miles

Correct answer: 250 miles

The rate is 150 ÷ 3 = 50 miles per hour; 50 × 5 = 250 miles.

Question 59: The formula for converting temperature from Celsius (C) to Fahrenheit (F) is F = (9/5)C + 32. A scientist records a temperature of 25°C. What is the equivalent temperature in Fahrenheit?

57°F
45°F
77°F (Correct answer)
102°F

Correct answer: 77°F

To solve this, substitute 25 for C in the given formula: F = (9/5) * 25 + 32. First, calculate (9/5) * 25. This simplifies to 9 * 5, which is 45. Then, add 32 to this result: F = 45 + 32. The final answer is 77°F.

Question 60: Two gears are connected. Gear A has 20 teeth and Gear B has 30 teeth. If Gear A makes 9 rotations, how many rotations does Gear B make?

4
7
5
6 (Correct answer)

Correct answer: 6

Gear ratio = 20/30 = 2/3; Gear B rotations = 9 × (20/30) = 6.

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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Exam Rules

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No feedback shown until you submit the entire exam
Unanswered questions count as wrong — answer everything
10 pretest questions are mixed in and don't affect your score
Timer auto-submits when time runs out
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These practice questions were written with AI tools. They are not real exam questions. Exam facts are checked against the official sources listed below. Not reviewed by a subject-matter expert. Editorial policy

Sources & references

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