Praxis Mathematics Exam 1 — Questions and Answers

Question 1: If x= -5, then l x - 7 l =

10
-2
12 (Correct answer)

Correct answer: 12

To evaluate the expression |x - 7| when x = -5, substitute -5 for x. This gives |-5 - 7|. First, perform the subtraction inside the absolute value bars, which results in |-12|. The absolute value of a number is its distance from zero, always a non-negative value. Therefore, |-12| is 12.

Question 2: Solve and simplify: 2/3 x 3/5 x 5/10 x 6/8

0.15 (Correct answer)
0.25
0.333333333

Correct answer: 0.15

To solve this multiplication of fractions, multiply the numerators together and the denominators together. It's often easier to cancel common factors before multiplying. The expression is (2/3) * (3/5) * (5/10) * (6/8). We can cancel the '3' from the first two fractions, and the '5' from the second and third fractions, leaving (2/1) * (1/1) * (1/10) * (6/8). This simplifies to (2 * 6) / (10 * 8) = 12/80. Reducing this fraction by dividing both numerator and denominator by 4 gives 3/20, which as a decimal is 0.15.

Question 3: If Dave drives at a steady speed of 50 miles per hour, how long will it take him to drive 10 miles?

15 minutes
30 minutes
12 minutes (Correct answer)

Correct answer: 12 minutes

To find the time it takes to drive a certain distance at a steady speed, use the formula time = distance / speed. Dave drives 10 miles at 50 miles per hour. So, time = 10 miles / 50 mph = 1/5 of an hour. To convert this to minutes, multiply by 60 (since there are 60 minutes in an hour): (1/5) * 60 minutes = 12 minutes.

Question 4: John will be x in 7 years. How old was he last year?

x + 8
x - 8 (Correct answer)
7x

Correct answer: x - 8

Let John's current age be C. The problem states that John will be x years old in 7 years, so C + 7 = x. Solving for C, John's current age is x - 7. To find his age last year, subtract 1 from his current age: (x - 7) - 1. Therefore, John was x - 8 years old last year.

Question 5: Find the slope: 4x - 5y =20

5/4
4/5 (Correct answer)
4/5

Correct answer: 4/5

To find the slope of a linear equation, rewrite it in the slope-intercept form, y = mx + b, where 'm' is the slope. Starting with 4x - 5y = 20, first isolate the y term by subtracting 4x from both sides: -5y = -4x + 20. Then, divide the entire equation by -5: y = (-4x / -5) + (20 / -5). This simplifies to y = (4/5)x - 4. From this form, the slope 'm' is clearly 4/5.

Question 6: Rex is four times as old as Ted. If the sum of their ages is 30, how old is Ted?

10
6 (Correct answer)
12

Correct answer: 6

Let Ted's age be T and Rex's age be R. The problem states that Rex is four times as old as Ted, so R = 4T. It also states that the sum of their ages is 30, so R + T = 30. Substitute the first equation into the second: 4T + T = 30. This simplifies to 5T = 30. Dividing by 5, we find that Ted's age (T) is 6 years.

Question 7: On a real number line, x =-4 and y = 7. What is the length of the line XY?

11 (Correct answer)
3
- 11

Correct answer: 11

The length of a line segment on a real number line between two points x and y is found by taking the absolute difference of their coordinates. Given x = -4 and y = 7, the length is |y - x|. Calculating this, we get |7 - (-4)|, which simplifies to |7 + 4|. This equals |11|, and the absolute value of 11 is 11. Thus, the length of the line segment XY is 11 units.

Question 8: Regie has enough flour to last for days. If he increases his use of flour by 25%, however, how many day's worth of flour will he have?

30 days
28 days
32 days (Correct answer)

Correct answer: 32 days

The question is missing the initial number of days the flour would last. Assuming, based on the answer choices, that Regie initially had enough flour for 40 days, we can calculate the new duration. If he increases his use of flour by 25%, his daily consumption becomes 125% or 1.25 times the original amount. To find how many days the flour will last, divide the original number of days by the new consumption factor: 40 days / 1.25. This calculation yields 32 days.

Question 9: If x=3 and y = -1, then 3x squared + 2xy - 5 =?

18
14
16 (Correct answer)

Correct answer: 16

To evaluate the expression 3x^2 + 2xy - 5 with x=3 and y=-1, substitute these values into the expression. This gives 3(3)^2 + 2(3)(-1) - 5. Following the order of operations, first calculate the exponent: 3(9) + 2(3)(-1) - 5. Then perform the multiplications: 27 + (-6) - 5. Finally, perform the additions and subtractions from left to right: 27 - 6 - 5 = 21 - 5 = 16.

Question 10: 8.5 x 9.07 =

770.95
77.095 (Correct answer)
777.095

Correct answer: 77.095

To multiply 8.5 by 9.07, perform the multiplication as if they were whole numbers, then place the decimal point in the product. The numbers are 85 and 907. Their product is 77095. Since 8.5 has one decimal place and 9.07 has two decimal places, the total number of decimal places in the product must be 1 + 2 = 3. Counting three places from the right in 77095, the decimal point is placed to get 77.095.

Question 11: 54 is 75% of what number?

80
72 (Correct answer)
100

Correct answer: 72

To find the number of which 54 is 75%, set up the equation: Part = Percent × Whole. Here, the Part is 54, and the Percent is 75% (or 0.75 as a decimal). So, 54 = 0.75 × Whole. To find the Whole, divide 54 by 0.75: Whole = 54 / 0.75. This calculation yields 72. Therefore, 54 is 75% of 72.

Question 12: 8.26 x 76.8

63.4368
634.368 (Correct answer)
634,368

Correct answer: 634.368

To multiply 8.26 by 76.8, perform the multiplication as if they were whole numbers, then place the decimal point in the product. The numbers are 826 and 768. Their product is 634368. Since 8.26 has two decimal places and 76.8 has one decimal place, the total number of decimal places in the product must be 2 + 1 = 3. Counting three places from the right in 634368, the decimal point is placed to get 634.368.

Question 13: 3/27

1/9 (Correct answer)
1/10
1/2

Correct answer: 1/9

To simplify the fraction 3/27, find the greatest common divisor (GCD) of the numerator and the denominator. Both 3 and 27 are divisible by 3. Dividing both by 3 gives 1 in the numerator and 9 in the denominator, resulting in the simplified fraction 1/9.

Question 14: 9 / 20 =

50%
45% (Correct answer)
40%

Correct answer: 45%

To convert the fraction 9/20 to a percentage, first divide the numerator by the denominator to get a decimal. 9 divided by 20 equals 0.45. Then, multiply this decimal by 100% to express it as a percentage. Therefore, 0.45 multiplied by 100% is 45%.

Question 15: 4 2/3 - 2 ½

2 2/3
2 1/6 (Correct answer)
2 1/4

Correct answer: 2 1/6

To subtract mixed numbers, first convert them to improper fractions: 4 2/3 becomes 14/3 and 2 1/2 becomes 5/2. Find a common denominator, which is 6, so the fractions become 28/6 and 15/6. Subtracting these gives 13/6, which converts back to the mixed number 2 1/6.

Question 16: Three people divide up a large pizza. If the first person gets half and the second person gets half as much as the first person, how much is left for the third person?

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

Correct answer: 1/4

The first person gets 1/2 of the pizza. The second person gets half of what the first person got, which is (1/2) * (1/2) = 1/4 of the pizza. In total, the first two people ate 1/2 + 1/4 = 2/4 + 1/4 = 3/4 of the pizza. To find what's left for the third person, subtract the eaten portion from the whole pizza: 1 - 3/4 = 1/4.

Question 17: If John scores 20% of his team's oint in a basketball game, how many points does the team score if John scores 14 points?

72
68
70 (Correct answer)

Correct answer: 70

If John scores 20% of his team's points and that amounts to 14 points, you can set up the equation: 0.20 * Total Points = 14. To find the total points, divide John's score by his percentage contribution. So, 14 / 0.20 equals 70. The team scored 70 points in total.

Question 18: 3/8 + 1/3 + 1/8 =

5/6 (Correct answer)
3/4
1/2

Correct answer: 5/6

To add these fractions, first combine the fractions with the same denominator: 3/8 + 1/8 = 4/8, which simplifies to 1/2. Now, add 1/2 to 1/3. Find a common denominator for 2 and 3, which is 6, converting the fractions to 3/6 and 2/6. Adding these gives 3/6 + 2/6 = 5/6.

Question 19: Written in scientific notation, the number 173,000,000,000 is:

17.3 x 1010
173 x 109
1.73 x 1011 (Correct answer)

Correct answer: 1.73 x 1011

To write a number in scientific notation, place the decimal point after the first non-zero digit, creating a number between 1 and 10. For 173,000,000,000, this becomes 1.73. Then, count how many places the decimal point moved from its original position (at the end of the number) to its new position. The decimal moved 11 places to the left, so the power of 10 is 11, making the scientific notation 1.73 x 10^11.

Question 20: If a recipe for cookies calls for ¾ of a cup of sugar, and you want to quadruple the recipe, how many cups of sugar will you need?

3 cups (Correct answer)
4 cups
2 ¾ cups

Correct answer: 3 cups

To quadruple a recipe means to multiply all ingredients by 4. If the recipe calls for 3/4 of a cup of sugar, you need to calculate (3/4) * 4. Multiplying the fraction by 4 gives (3 * 4) / 4 = 12/4. This simplifies to 3 cups of sugar.

Question 21: Which of the following numbers has the greatest absolute value: 17, -9, 15.5, -20, 19?

- 20 (Correct answer)
19
15.5

Correct answer: - 20

The absolute value of a number is its distance from zero on the number line, always represented as a positive value. For the given numbers: |17|=17, |-9|=9, |15.5|=15.5, |-20|=20, and |19|=19. Comparing these absolute values, 20 is the greatest, which corresponds to the number -20.

Question 22: Randy got the following test scores in science class: 76,98,78,80 and 54. What is the median test score?

54
84
78 (Correct answer)

Correct answer: 78

To find the median of a set of numbers, first arrange them in ascending order. The scores are 54, 76, 78, 80, 98. The median is the middle value in an ordered list. Since there are five scores, the third score (78) is the middle value, representing the median.

Question 23: John's sock drawer contains 4 pairs of green socks, 7 pairs of black socks, and 7 pairs of red socks. If John reaches into the drawer at random, what are his chances of NOT selecting a pair of green socks?

1/3
7/9 (Correct answer)
2/5

Correct answer: 7/9

First, calculate the total number of sock pairs: 4 (green) + 7 (black) + 7 (red) = 18 pairs. Next, determine the number of pairs that are NOT green, which are the black and red socks: 7 + 7 = 14 pairs. The probability of not selecting a pair of green socks is the number of non-green socks divided by the total number of socks, which is 14/18. This fraction simplifies to 7/9.

Question 24: A number is multiplied by 6 and then has 4 subtracted from it. The answer is 14. Which of the following equations matches these statements?

14 = 4 - 6x
4x – 6 = 14
6x – 4 = 14 (Correct answer)

Correct answer: 6x – 4 = 14

Let 'x' represent the unknown number. The statement 'A number is multiplied by 6' translates to 6x. 'Then has 4 subtracted from it' means 6x - 4. Finally, 'The answer is 14' completes the equation as 6x - 4 = 14. This equation accurately represents the given word problem.

Question 25: Solve for x: (7x/5) +9 = 23

10 (Correct answer)
9
11

Correct answer: 10

To solve the equation (7x/5) + 9 = 23, first subtract 9 from both sides: (7x/5) = 14. Next, multiply both sides by 5 to isolate 7x: 7x = 70. Finally, divide both sides by 7 to solve for x: x = 10.

Question 26: Albert is driving at 80 miles per hour. How far will he go in 45 minutes?

60 miles (Correct answer)
45 miles
80 miles

Correct answer: 60 miles

To find the distance Albert travels, use the formula Distance = Speed × Time. His speed is 80 miles per hour. The time is 45 minutes, which needs to be converted to hours by dividing by 60: 45/60 = 0.75 hours. Therefore, Distance = 80 miles/hour × 0.75 hours = 60 miles.

Question 27: If Ted runs at 8 miles an hour,which computation would you use to determine how far Ted runs in 15 minutes?

8 x 25
8 x .15
8 x .25 (Correct answer)

Correct answer: 8 x .25

To determine the distance Ted runs, you need to multiply his speed by the time he runs. His speed is 8 miles per hour. The time is 15 minutes, which must be converted to hours by dividing by 60 minutes/hour. 15 minutes / 60 minutes/hour equals 0.25 hours. So, the computation is 8 x 0.25.

Question 28: Gerald received the following test scores in math class: 76, 86, 89, 81, and 99. What was Gerald's average test score, rounded to the nearest point?

84
87
86 (Correct answer)

Correct answer: 86

To find Gerald's average test score, first sum all his scores: 76 + 86 + 89 + 81 + 99 = 431. Then, divide the sum by the number of scores, which is 5. So, 431 / 5 = 86.2. Rounded to the nearest whole point, Gerald's average test score is 86.

Question 29: Which of the following units would be most appropriate foe measuring the length of a pen?

Micrometers
Nanometers
Centimeters (Correct answer)

Correct answer: Centimeters

Centimeters are the most appropriate unit for measuring the length of a pen. Micrometers and nanometers are far too small, used for microscopic measurements. While meters are a standard unit of length, a pen is much shorter than a meter, making centimeters a more practical and precise choice for this everyday object.

Question 30: If Todd can type 60 word a minute, how long will it take him to type a 15,000 word document?

2 hours and 45 minutes
2 hours
4 hours and 10 minutes (Correct answer)

Correct answer: 4 hours and 10 minutes

To find the total time, divide the total number of words by Todd's typing speed. 15,000 words / 60 words per minute = 250 minutes. To convert minutes to hours, divide by 60: 250 / 60 = 4 with a remainder of 10. This means it will take 4 hours and 10 minutes.

Praxis Mathematics Exam 1

If x= -5, then l x - 7 l =