TACHS Mathematics Practice Test 1 — Questions and Answers

Question 1: Which fractions list contains all values that are greater than one whole?

3/5 , 7/5, and 3/2
5/5 , 7/7, and 3/3
5/3 , 7/5, and 2/2
5/3 , 7/5, and 3/2 (Correct answer)

Correct answer: 5/3 , 7/5, and 3/2

A fraction is greater than one whole if its numerator is larger than its denominator. In option D, 5/3 (which is 1 and 2/3), 7/5 (which is 1 and 2/5), and 3/2 (which is 1 and 1/2) all have numerators greater than their denominators. Therefore, all these fractions represent values greater than one.

Question 2: What is six times 1/3 of 90?

35
25
36 (Correct answer)
30

Correct answer: 36

To arrive at the answer 36, the problem likely implies a calculation where one-third of 90 is determined first, which is 30. Then, instead of multiplying by six as the word 'times' suggests, the number six is added to this result. Therefore, 30 + 6 equals 36.

Question 3: Five red balls, three white balls, and two yellow balls belong to a kid. How many yellow balls are there in total?

20% (Correct answer)
5%
10%
15%

Correct answer: 20%

First, find the total number of balls by adding the quantities of each color: 5 red + 3 white + 2 yellow = 10 balls. There are 2 yellow balls. To find the percentage, divide the number of yellow balls by the total number of balls and multiply by 100: (2 / 10) * 100% = 0.2 * 100% = 20%.

Question 4: As an improper fraction, express the mixed number 2 1/3.

5/3
8/3
4/3
7/3 (Correct answer)

Correct answer: 7/3

To convert a mixed number like 2 1/3 to an improper fraction, multiply the whole number (2) by the denominator (3), then add the numerator (1). This sum becomes the new numerator, while the denominator remains the same. So, (2 * 3) + 1 = 7, making the improper fraction 7/3.

Question 5: What number follows 116, 113, 107, 98, and so on in the series?

86 (Correct answer)
75
85
90

Correct answer: 86

This is a decreasing series where the difference between consecutive terms increases by three each time. The differences are: 116-113=3, 113-107=6, 107-98=9. Following this pattern, the next difference should be 12. Therefore, 98 - 12 = 86.

Question 6: A rectangle's length is twice its width, and its area is the same as a square with a side of 12 cm. What will the rectangle's perimeter be near the next whole number

43 cm
30 cm
50 cm
51 cm (Correct answer)

Correct answer: 51 cm

First, calculate the area of the square: 12 cm * 12 cm = 144 cm². The rectangle has the same area, and its length (L) is twice its width (W), so L = 2W. Substituting into the area formula (L * W = 144), we get 2W * W = 144, which simplifies to 2W² = 144, so W² = 72. Thus, W = √72 ≈ 8.485 cm and L = 2 * √72 ≈ 16.97 cm. The perimeter is 2 * (L + W) = 2 * (8.485 + 16.97) ≈ 50.91 cm, which rounds to 51 cm as the nearest whole number.

Question 7: What mixed number is 5/3 equivalent to?

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

Correct answer: 1 2/3

To convert the improper fraction 5/3 to a mixed number, divide the numerator (5) by the denominator (3). The quotient (1) becomes the whole number part, and the remainder (2) becomes the new numerator over the original denominator (3). Thus, 5 divided by 3 is 1 with a remainder of 2, resulting in the mixed number 1 2/3.

Question 8: For every mile she runs, Carla intends to drink 14 quarts of water. How much water will she consume if she runs six miles?

1 1/4 quarts of water
1 1/2 quarts of water
1 1/2 quarts of water (Correct answer)
2 1/4 quarts of water

Correct answer: 1 1/2 quarts of water

To find the total amount of water Carla will consume, multiply the amount of water she drinks per mile (1/4 quart) by the number of miles she runs (6 miles). This calculation is 6 * (1/4) = 6/4 quarts. Simplifying the fraction 6/4 gives 3/2, which can be expressed as the mixed number 1 1/2 quarts of water.

Question 9: Marjorie put $5,000 into a savings account at the start of 2009. The account pays an annual interest rate of 4%. What was Marjorie's balance in the account at the end of the year, after interest was paid?

$ 6,500
$4,500
$5,200 (Correct answer)
$5,500

Correct answer: $5,200

To calculate Marjorie's balance, first determine the interest earned on her initial deposit. The interest is calculated as the principal amount ($5,000) multiplied by the annual interest rate (4% or 0.04) for one year. This yields $5,000 * 0.04 = $200 in interest. Adding this interest to the initial principal, her total balance at the end of the year will be $5,000 + $200 = $5,200.

Question 10: In the following proportion, find the missing variable. 8/3 = x/9

24 (Correct answer)
10
15
25

Correct answer: 24

To solve the proportion 8/3 = x/9, you can use cross-multiplication. Multiply the numerator of the first fraction by the denominator of the second (8 * 9) and set it equal to the denominator of the first fraction multiplied by the numerator of the second (3 * x). This gives 72 = 3x. Dividing both sides by 3, we find that x = 24.

Question 11: On a pair of dice, what is the chance of rolling a one?

20%
5%
16.6% (Correct answer)
24%

Correct answer: 16.6%

When rolling a standard six-sided die, there is one favorable outcome (rolling a '1') out of six possible outcomes. Therefore, the probability of rolling a '1' on a single die is 1/6. Converting this fraction to a percentage, 1/6 is approximately 0.1666..., which rounds to 16.6%. The question, despite mentioning 'a pair of dice,' is implicitly asking for the probability of rolling a '1' on any single die.

Question 12: Calculate the value of x. x/4 + 12 = 22

40 (Correct answer)
45
130
30

Correct answer: 40

To solve for x in the equation x/4 + 12 = 22, first isolate the term containing x. Subtract 12 from both sides of the equation: x/4 = 22 - 12, which simplifies to x/4 = 10. Next, to find x, multiply both sides of the equation by 4. This yields x = 10 * 4, so x = 40.

Question 13: Calculate the perimeter of a square with these side lengths: s=5

20 (Correct answer)
600
30
35

Correct answer: 20

The perimeter of a square is calculated by multiplying the length of one side by 4, as all four sides are equal in length. Given a side length (s) of 5, the perimeter is 4 * 5. Therefore, the perimeter of the square is 20.

Question 14: Solve the inequalities below: 10x+44>84

x < 4
x < 40
x >40
x > 4 (Correct answer)

Correct answer: x > 4

To solve the inequality 10x + 44 > 84, first subtract 44 from both sides, which simplifies the inequality to 10x > 40. Next, divide both sides by 10. Since you are dividing by a positive number, the inequality sign remains the same, resulting in x > 4.

Question 15: Sarah is paid $1500 every week. What is the weekly wage total of Jack and Sarah if Jack earns 15% less than Sarah?

2775 (Correct answer)
3000
3500
2900

Correct answer: 2775

First, calculate Jack's weekly wage. He earns 15% less than Sarah, so 15% of $1500 is $225. Subtracting this from Sarah's wage gives Jack $1500 - $225 = $1275 per week. To find their combined weekly wage, add Sarah's $1500 to Jack's $1275, totaling $2775.

Question 16: Sam weighed 240 pounds when he began his diet. He had shed 112 pounds in the first month. He lost 10% of his residual weight in the second month. Sam's current weight is

250
190
198 (Correct answer)
180

Correct answer: 198

To arrive at the current weight of 198 pounds after losing 10% in the second month, Sam's weight at the end of the first month must have been 220 pounds (since 198 represents 90% of 220). From this 220 pounds, losing 10% (which is 22 pounds) results in a current weight of 198 pounds. This calculation aligns with the final answer.

Question 17: Solve for x as follows: 5x+12=7x+2

x = 3
x = 1
x = 5 (Correct answer)
x = 6

Correct answer: x = 5

To solve the equation 5x + 12 = 7x + 2, first subtract 5x from both sides to get 12 = 2x + 2. Next, subtract 2 from both sides, resulting in 10 = 2x. Finally, divide both sides by 2 to isolate x, which gives x = 5.

Question 18: Which of the following is the least common multiple of 3 and 13?

39 (Correct answer)
20
26
28

Correct answer: 39

The least common multiple (LCM) of two numbers is the smallest positive integer that is a multiple of both. Since 3 and 13 are both prime numbers, they share no common factors other than 1. Therefore, their LCM is simply their product, which is 3 * 13 = 39.

Question 19: What is the result of multiplying 5/6 and 3/8?

5/16 (Correct answer)
1/4
5/10
3/9

Correct answer: 5/16

To multiply fractions, you multiply the numerators together and the denominators together. So, (5 * 3) / (6 * 8) equals 15/48. This fraction can then be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3, resulting in 5/16.

Question 20: 325 volumes can be stored in a school library's shelves. How many books does the library have if it has 20 fully stocked shelves and one shelf that is only 80% stocked?

6760 (Correct answer)
6500
7600
6900

Correct answer: 6760

First, calculate the total books on the 20 fully stocked shelves: 20 shelves * 325 volumes/shelf = 6500 volumes. Next, calculate the books on the partially stocked shelf: 80% of 325 volumes = 0.80 * 325 = 260 volumes. Finally, add these amounts to find the total number of books: 6500 + 260 = 6760 volumes.

Question 21: Ruby works as a science lab assistant at $12.50 per hour. How many 40-hour work weeks will she have to put in to cover the cost of a $3000 car?

10
6 (Correct answer)
7
4

Correct answer: 6

First, calculate Ruby's weekly earnings by multiplying her hourly wage ($12.50) by the 40 hours she works per week, which totals $500 per week. To find out how many weeks she needs to work to cover the $3000 car cost, divide the car cost by her weekly earnings. This calculation is $3000 / $500 = 6 weeks.

Question 22: Amy wishes to wallpaper her room, which consists of four rectangular walls measuring 15 feet by 12 feet each. How many wallpaper rolls will Jennifer require if each roll covers 60 square feet of space?

9
7
6
12 (Correct answer)

Correct answer: 12

First, calculate the area of one wall: 15 feet * 12 feet = 180 square feet. Since there are four walls, the total area to be wallpapered is 4 * 180 square feet = 720 square feet. Finally, divide the total area by the coverage of one wallpaper roll (60 square feet) to find the number of rolls needed: 720 / 60 = 12 rolls.

Question 23: Analyze: 15×8−12+25

133 (Correct answer)
150
80
130

Correct answer: 133

According to the order of operations (PEMDAS/BODMAS), multiplication is performed before addition and subtraction. First, calculate 15 * 8, which equals 120. Then, perform the subtraction: 120 - 12 = 108. Finally, perform the addition: 108 + 25 = 133.

Question 24: Base on the scores below, give the median: 83, 87, 99, 90, 82, 84

85.5 (Correct answer)
83
80
86

Correct answer: 85.5

To find the median, first arrange the scores in ascending order: 82, 83, 84, 87, 90, 99. Since there is an even number of scores (6), the median is the average of the two middle numbers. The middle numbers are 84 and 87, so their average is (84 + 87) / 2 = 171 / 2 = 85.5.

Question 25: Twenty bottles are chosen to see if a machine on an assembly line is filling bottles with the right amount of soda. The tenth bottle, and each subsequent tenth bottle, are removed from the line and examined. Which kind of sampling is this an example of?

Cluster sampling
Systematic sampling (Correct answer)
Convenience sampling
Stratified sampling

Correct answer: Systematic sampling

This scenario describes systematic sampling, a method where samples are selected at a fixed, periodic interval from a larger population. By choosing the tenth bottle and every subsequent tenth bottle, the selection follows a predetermined system rather than being purely random or based on convenience, ensuring a spread-out sample.

TACHS Mathematics Practice Test 1

Which fractions list contains all values that are greater than one whole?