Math (ACT) - Practice Problems

For all x = 3 (line through equality), which of the following is equivalent to the expression? 3x^2 - 7x - 6/x - 3

#17 DRILL

John has x red pencils, and three times as many red pencils as blue pencils. If he has four more yellow pencils than blue pencils, then in terms of x, how many yellow pencils does John have?

#21 DRILL

If x - z = 6 and y = 3x - 2 - 3z, then y =

#25 DRILL

In my dear Aunt Sally's math class, there are four exams. The first three exam scores are averaged, and the resulting score is averaged with the final exam score. If a, b, and c are the first three exam scores, and f is the final exam score, which of the following examples gives student't final score in the class?

#36 DRILL

In a piggy bank, there are pennies, nickels, dimes, and quarters that total $2.17 in value. If there were

#49 drill

What is the opposite reciprocal of 2?

-1/2

What is the slope of the straight line passing through the points (-2,5) and (6,4)?

-1/8

What is the reciprocal of -1/4

-4

Write 0.5 as a fraction?

1/2

What is the average of 9, 12, and 6?

All three numbers add up to 27. Since there are 3 items, 27/3= 9

Is 12 a multiple or factor of 24?

Factor

When 15% of 40 is added to 5% of 260, the resulting number is:

First 15/100=?/40 should equal 6. Then, 5/100=?/260 equals 13. 6 + 13= 19.

If a + 3b = 27 and a -3b = 9, then b =

Set up a system of equations to find a: ( a + 3b = 27) (a - 3b = 9) ______________________ 2a = 36 a = 18 <------ Use this value to find b Plug 18 into to any of the two formulas and you should get b = 3.

Is 8 one of the factors of 64?

Yes

(x⁷)²

x ¹⁴

x⁷/x²

x⁵

x⁷(x²)=

x⁹

When asked the price, in dollars, of his fancy calculator, Albert responded, " If you take the square root of the price, then add 3/8 the price, the result is 66." What is the price, in dollars, of Albert's calculator?

√x + (3/8)x = 66 . Simply find a square root number. 11 will work once trying all numbers. So, √144 + (3/8)(144) = 66

In the number 0.191919, what digit is coming next?

1

List the factors of 12.

1, 2, 3, 4, 6, 12.

List the factors of 30.

1, 2, 3, 5, 6, 10, 15, 30.

What would be a 10% discount of $18?

10/100=discount/$18, Cross multiply and dived by 100. $1.80 should be the discount.

List the four multiples of 12.

12, 24, 36, 48.

What is the only even prime number?

2

What are the single digit prime numbers?

2, 3, 5, 7

At the school cafeteria, students can choose from 3 different salads, 5 different main dishes, and 2 different desserts. If Isabel chooses one salad, one main dish, and one desert for lunch, how many different lunches could she choose?

3 x 5 x 2= 30 (Multiply all number since there is only one of each). Use slot method. _ _ _=

Write 3 as a fraction

3/1

List four multiples of 30.

30, 60, 90, 120.

What is the least common multiple of 9 and 12?

36

What is the least common multiple of 24 and 48?

48

There are 600 school children in the Lisle district. If 54 of them are high school seniors, what is the percentage of high school seniors in the Lisle district?

54/600 x 100% = 9%

In the number 0.16666, what digit is coming next?

6

What is the greatest common factor of 6 and 36

6

If $600 were deposited in a bank account for one year and earned interest of $42, what was the interest rate?

7%

How many times does 2 go into 15 evenly? How much is left over?

7, 1

Elias has to select one shirt, one pair of pants, and one pair of shoes. If he selects at random from his 8 shirts, 4 pairs of pants, and 3 pairs of shoes, and all his shirts, pants, and shoes are different colors, what is the likelihood that he will select his red shirt, black pants, and brown shoes?

8 x 4 x 3= 96. Since there is one of each, 1/96.

What is the greatest common factor of 27 and 45?

9

If 3.7 inches of rain fall in Chicago during the first 4 days of November, and the rain continues to fall at this pace for the rest of the month, approximately how many feet of rain will fall during December? (The month of December has 31 days)

Begin by calculating how many inches there are per day, that would be .925. Multiply this number by the 31 days and you should get 28.675 inches for the month of December. But, the question asks how many feet. Since there are 12 inches in a foot, divide 28.675 by 12 , you should get 2.4 ft if you round to the nearest tenth. Or you could use the part over whole formula. So, 3.7/4=?/31, then cross multiply and divide by 12 inches.

The employees of two factories, X and Y, are comparing their respective production records. Factory X has already produced 18,000 units and can produce 120 units per day. Factory Y has produced only 14,500 units but can produce 155 units per day. If d represents the number of days, which of the following equations could be solved to determine the number of days until X's total production equals Y's total production.

Find the total production of each company after d days. Factory X starts with 18,000 units and can produce 120 units per day, so its production after d days will be 18,000 + 120d. Factory Y starts with only 14,500 units, but can produce 155 units per day, so its production after d days will be 14,500 + 155d. Since you are looking for the number of days after which the total production of each factory will be equal, set the two equations equal to one another: 18,000 + 120d = 14,500 + 155d

Zach's practice bag contains 4 blue racquetballs, one red racquetballs, and 6 racquetballs. If he chooses a ball at random, which of the following is closest to the probability that the ball will NOT be green?

First there are a total of 11 balls. 5/11 are not green while 6/11 are green. So, 5/11 x 100 (part/whole) x 100 is .45% or 45%. A shortcut for this problem would be to look at the probability. 5/11 is roughly around 50%, but we know it is just under it. So, many of the choices could be eliminated right off the bat.

At a restaurant, diners enjoy an "early bird" discount of 10% off their bills. If a diner orders a meal regularly priced at $18 and leaves a tip of 15% of the discounted meal (no tax), how much does he pay in total?

First, calculate the 10% discount. Next, add on the 15% tip. You should get $18.63.

Over 9 games, a baseball team had an average of 8 runs per game. If the average number of runs for the first 7 games was 6 runs per game, and the same number of runs was scored in each of the last 2 games, how many runs did the team score during the last game?

First, find the total number of runs in the first 9 games, which should equal 72 (9 x 8= 72). Then find the total number for the first 7 games, which should equal 42 (7 x 6= 42). Now find the difference from the totals and you should get 30. Since there are 2 games left, divide 30 by 2, and you should get 15.

The starting team of a baseball club has 9 members who have an average of 12 home runs apiece for the season. The second-string team for the baseball club has 7 members who have an average of 9 home runs apiece for the season. What is the average number of home runs for the starting team and the second-string team combined?

First, we want to find the total number of runs for each team. First the first team it should equal 108 (9 x 12= 108). The second team should it equal 56 (7 x 8= 56). Add both of these totals, and you should get 164. Since there are a total of 16 members (9 + 7= 16), dived 164 by 16 and you should get 10.25.

If the ratio of 2x to 5y is 1/20, what is the ratio of x and y?

So, 2x/5=1/20. Begin by isolating x and y by cross multiplying. You should have x/y=5/40. So, this should reduce to 1/8.

Passes to the Renaissance Fair cost $9 when purchased online and $12 when purchased in person. The group sponsoring the fair would like to make at least $4,000 from sales of passes. If 240 passes were sold online, what is the minimum number of tickets that must be sold in person in order for the group to meet its goal?

The group has sold 240 passes online at $9 each. This means that they have already made (240)(9) = $2,160. In order to reach their goal, they will need $4,000 - $2,160 = $1,840. Since the question asks how many in-person tickets they will need to sell, you can approximate how many tickets will get them $1,840 by dividing: $1,840 / $12 = 153.333. Since there is no such thing as 0.333 tickets, you have to round up to get 154 tickets.

In triangle XYZ, Angle Y is a right angle and Angle Z measures less than 52 degrees. Which of the following phrases best describes the measure of angle X

The sum of all measures in a triangle are 180 degrees. Angle Y is described as a right angle, which means it is 9- degrees. The other two triangles, therefore, will have to add up to 90 degrees to complete the 180 degrees in the triangle. If angle Z measures less than 52 degrees., then Angle X must be greater than 90-52 = 38 degrees. it cannot be equal to 38 degrees because Angle Z is less than 52 degrees.

An integer, x, is subtracted from 6. That difference is then multiplied by 3. This product is 15 more than half the original integer. What is the equation of this relationship?

Translate the English in this problem into the math of the answer choices. The problem reads, "An integer, x, is subtracted from 6. That difference is then multiplied by 3." This translates into the following (6-x) x 3 or 3(6-x). The second part of the problem reads, "This product is 15 more than half the original integer." Therefore 3(6-x) will equal "15 more than half of the original integer": 15 + 1/2x or 1/2x + 15. Therefore, 3(6-x)= 1/2x + 15.

What is the least common multiple of 25, 16, and 40? a. 27 b. 32 c. 320 d. 400 e. 16,000

Use the answer choices and work backwards. Find the smallest number that divides evenly by 16, 25, and 40. This is 400: 400/16 = 25; 400/25 = 16; and 400/40 = 10. I

At the school cafeteria, 2 boys and 4 girls are forming a lunch line. If the boys must stand in the first and last places in in, how many different lines can be formed?

Use the slot method. Since we know there are 6 people, _ _ _ _ _ _. Since the boys must be at the end of the lines, 1 _ _ _ _ 2. Then, the girls can go in any order. So, 1 4 3 2 1 2= 48.

You are thrown 100 pitches and you hit 20 of them. What percent of pitches did you hit? What's the ratio of the pitches you hit to the pitches you missed?

You hit 20% of the pitches. The ratio of hits to misses is 1:4 or 1/4.