the number of vacuum cleaners sold by a company per month during year 1 is listed below 18 42 29 40 24 17 29 44 19 33 46 39 which of the following is

ATI TEAS 7

TEAS Practice Math Test

1. The number of vacuum cleaners sold by a company per month during Year 1 is listed below: 18, 42, 29, 40, 24, 17, 29, 44, 19, 33, 46, 39. Which of the following is true?

A. The mean is less than the median
B. The mode is greater than the median
C. The mode is less than the mean, median, and range
D. The mode is equal to the range

Correct answer: D

Rationale: The mean number of vacuum cleaners sold per month is 31.7, the mode is 29, the median is 31, and the range is 29. The mode being equal to the range is the correct statement. Option A is incorrect because the mean (31.7) is greater than the median (31). Option B is incorrect as the mode (29) is not greater than the median (31). Option C is incorrect since the mode (29) is not less than the mean, median, or range.

2. As part of a study, a set of patients will be divided into three groups. 4/15 of the patients will be in Group Alpha, 2/5 in Group Beta, and 1/3 in Group Gamma. Order the groups from smallest to largest, according to the number of patients in each group.

A. Group Alpha, Group Beta, Group Gamma
B. Group Alpha, Group Gamma, Group Beta
C. Group Gamma, Group Alpha, Group Beta
D. Group Alpha, Group Beta, Group Gamma

Correct answer: B

Rationale: The correct order is Group Alpha, Group Gamma, Group Beta based on the common denominators of the fractions. To determine the order from smallest to largest, compare the fractions' numerators since the denominators are different. Group Alpha has 4/15 patients, Group Gamma has 1/3 patients, and Group Beta has 2/5 patients. Comparing the fractions' numerators, the order from smallest to largest is Group Alpha (4), Group Gamma (1), and Group Beta (2). Therefore, the correct order is Group Alpha, Group Gamma, Group Beta. Choice A is incorrect as it lists Group Beta before Group Gamma. Choice C is incorrect as it lists Group Gamma before Group Alpha. Choice D is incorrect as it lists Group Beta before Group Gamma, which is not in ascending order based on the number of patients.

3. Arrange the following fractions from least to greatest: 2/3, 1/2, 5/8, 7/9.

A. 7/9, 5/8, 2/3, 1/2
B. 1/2, 2/3, 5/8, 7/9
C. 1/2, 5/8, 2/3, 7/9
D. 7/9, 2/3, 5/8, 1/2

Correct answer: C

Rationale: To compare the fractions, it is beneficial to convert them to decimals or find a common denominator. When converted to decimals: 1/2 = 0.50, 5/8 = 0.625, 2/3 ≈ 0.666, and 7/9 ≈ 0.778. Therefore, the correct order from least to greatest is 1/2, 5/8, 2/3, 7/9. Choice A is incorrect because it places 7/9 first, which is the greatest fraction. Choice B is incorrect as it incorrectly lists the fractions. Choice D is incorrect as it starts with 7/9, which is the largest fraction instead of the smallest.

4. Which of the following statements is true?

A. The mean is less than the median
B. The mode is greater than the median
C. The mode is less than the mean, median, and range
D. The mode is equal to the range

Correct answer: A

Rationale: The mean is the average of a set of numbers, while the median is the middle value when the numbers are arranged in order. If a set of numbers is skewed to one side with some outliers, the mean can be influenced by these extreme values, causing it to be greater or less than the median. In cases of skewed distribution, the mean typically shifts towards the direction of the outliers, making it less than the median. Choice B is incorrect because the mode, which is the most frequent number in a dataset, may or may not be greater than the median. Choice C is incorrect because the mode can be greater than the mean or median, depending on the data. Choice D is incorrect because the mode, representing the most frequent value, has no direct relationship with the range, which is the difference between the highest and lowest values in a dataset.

5. A gift box has a length of 14 inches, a height of 8 inches, and a width of 6 inches. How many square inches of wrapping paper are needed to wrap the box?

A. 56
B. 244
C. 488
D. 672

Correct answer: C

Rationale: To find the surface area of a rectangular prism, you use the formula SA = 2lw + 2wh + 2hl, where l is the length, w is the width, and h is the height. Substituting the given dimensions, the calculation would be SA = 2(14)(6) + 2(6)(8) + 2(8)(14) = 168 + 96 + 224 = 488 square inches. Therefore, 488 square inches of wrapping paper are needed to wrap the box. Choice A (56), Choice B (244), and Choice D (672) are incorrect because they do not represent the correct surface area calculation for the given box dimensions.