# logical math

6. Distinguish between absolute and relative change. Give an example that illustrates how a relative change is calculated.

Distinguish between absolute and relative change. Choose the correct answer below.

A.

Absolute change describes the actual increase or decrease from a reference value to a new value. Relative change is the size of the absolute change in comparison to the new value and can be expressed as a percentage.

B.

Absolute change is the size of the actual increase or decrease from a reference value in comparison to the new value and can be expressed as a percentage. Relative change describes the actual increase or decrease from a reference value to a new value.

C.

Absolute change describes the actual increase or decrease from a reference value to a new value. Relative change is the size of the absolute change in comparison to the reference value and can be expressed as a percentage.

D.

Absolute change is the size of the actual increase or decrease from a reference value in comparison to the reference value and can be expressed as a percentage. Relative change describes the actual increase or decrease from a reference value to a new value.

7.Give an example of how “percent” (%) and “percentage points” can differ for the same situation. Choose the correct answer below.

A.

Consider a savings account that previously offered 2% interest and now offers 6% interest. The percent increase is 300% and the percentage point increase is 4.

B.

Consider a savings account that previously offered 2% interest and now offers 6% interest. The percent increase is 4% and the percentage point increase is 200.

C.

Consider a savings account that previously offered 2% interest and now offers 6% interest. The percent increase is 300% and the percentage point decrease is 4.

D.

If a savings account that previously offered 2% interest now offers 6% interest, then the percent increase is 200% and the percentage point increase is 4.

8Find the absolute change and the relative change in the following case.

The average sale of a house decreased from \$327000 in February 2008 to \$164000 in February 2013.

The absolute change is _______ ((Simplify your answer. Type an integer or a decimal.)

9.Find the absolute change and the relative change in the following case.

The number of commercial radio stations playing a particular genre of music decreased from 627 in 2004 to 309 in 2014.

The absolute change is _______ ((Simplify your answer. Type an integer or a decimal.)

10. Clint’s salary increased from \$23,000 to \$39,100 over a three-year period. Helen’s salary increased from \$25,000 to \$42,500 over the same period. Whose salary increased more in absolute terms? In relative terms? Explain.

Whose salary increased more in absolute terms? Select the correct choice below and fill in the answer box(es) to complete your choice.

A. Helen’s salary increased more, because her salary increased by \$_______This is more than \$______the amount that Clint’s salary increased.

B. Clint’s salary increased more, because his salary increased by \$_____This is more than \$______, the amount that Helen’s salary increased.

C. Neither person’s salary increased more, because both of their salaries increased by \$_____.

11. Complete the following sentence.

The gestation period of cattle (283 days) is _____ percent longer than the gestation period of bears (220 days).

(Round the final answer to one decimal place as needed. Round all intermediate values to three decimal places as needed.)

12.Fill in the blank.

Will is 23% taller than Wanda, so Will’s height is ____% of Wanda’s height.

13.

Fill in the blank in the following statement.

The population of city A is 31% less than the population of city B, so city A’s population is ___% of city B’s.

14.The percentage of people accessing the Internet increased from 66% in 2000 to 89% in 2012. Complete parts (a) and (b) below.

1. Describe the change as an absolute change in terms of ______ percentage points.

(Type an integer or a decimal.)

b.

15. State whether the following statement is true or false, and explain why. If the statement is false, state the true change.

If the national economy shrank at an annual rate of 9% per year for three consecutive years, then the economy shrank by 27% over the three-year period.

Choose the correct answer below and, if necessary, fill in the answer box to complete your choice.

A. The statement is false because each year there is a different reference value. The economy actually shrank by ______% over the three-year period.

(Type an integer or decimal rounded to the nearest tenth as needed.)

B.The statement is true because 3 times 9% is 27%

16. At a particular college, 70% of the undergraduates are female. If 3920 women attend the college, how many total undergraduates attend the college?

the total number of undergraduates is ______

(Round to the nearest whole number as needed.)

17.In the following statement, express the first number as a percentage of the second number.

The full-time year-round median salary for U.S. men in 2010 was \$42,100, and the full-time year-round salary for U.S. women in 2010 was \$35, 700.

The full-time year-round median salary for U.S. men in 2010 was _____% of the full-time year-round median salary for U.S. women in 2010.

(Round to the nearest tenth as needed.)

18. Complete the following sentence.

The main span of Bridge A (2700 feet) is _____ percent shorter than the main span of Bridge B (4400 feet).

(Round the final answer to one decimal place as needed.)

19. The area of a certain country is 27% more than the area of California, so the country’s area is what percent of California’s area?

The country’s area is __________% of California’s area.

(Type an integer or a decimal.)

20. Fill in the blank in the following statement.

The wholesale price of a TV is 65% less than retail price. Therefore, the wholesale price is _____ times the retail price.

21. State whether the following statement is true or false, and explain why. If the statement is false, state the true change.

If the profits in your consulting business increase by 6% one year and decrease by 2% the following year, your profits are up by 4% over two years.

Select the correct choice below and, if necessary, fill in the answer box within your choice.

A.True

B.False; If the profits in your consulting business increase by 6% one year and decrease by 2% the following year, your profits are up by _________% over two years.

(Round to two decimal places as needed.)

22. Determine whether the following claim could be true. Explain your answer.

By turning off her lights and closing her windows at night, Maria saved 124% on her monthly energy bill.

A.The claim could be true because her new monthly energy bill would be 76% of the previous monthly energy bill, which makes sense.

B.The claim could be true because her new monthly energy bill would be 24% of the previous monthly energy bill, which makes sense.

C.The claim could not be true because her new monthly energy bill would be minus24% of the previous monthly energy bill. This is impossible since the bill cannot be negative.

D.The claim could not be true because her new monthly energy bill would be minus76% of the previous monthly energy bill. This is impossible since the bill cannot be negative.

23. Answer the question about the following quote from a news source.

“The unemployment rate has risen more than a percentage point to 8.6% in February from 7.1% last November.” What is the relative change in the unemployment rate expressed as a percentage?

The unemployment rate has risen ____________%.

(Type an integer or decimal rounded to the nearest tenth as needed.)

24. The price of a four-star meal, only \$120 per couple decades ago, has since increased 300%. The current price of a four-star meal is which of the following?

A. four-star meal is \$240 because 3 x \$ 120 equals \$ 360, from which \$120 is subtracted.

B. A four-star meal is \$480 because 3 x \$ 120 equals \$ 360, which is added to \$120.

C.A four-star meal is \$960 because 3 x \$ 120 equals \$ 360, which is added to \$120 and then multiplied by 2 because the price is per couple.

D.A four-star meal is \$43 comma 200 because 3 x \$ 120 equals \$ 360, which is multiplied by 120.

E.A four-star meal is \$720 because 3 x \$ 120 equals \$ 360, which is multiplied by 2 because the price is per couple.

F.A four-star meal is \$360 because 3 x \$ 120 equals \$ 360.

25. Consider the statement “The interest rate on auto loans has increased 50% over the past decade and now stands at 15%.” What can you conclude?

A.The interest rate a decade ago was 10% because 50% of 10 is 5, and 10+ 5 =15.

B.The interest rate a decade ago was 35% because 50+ 15 =65, and 100 – 65 = 35.

C.You can’t conclude anything because the statement makes no sense.

D.The interest rate a decade ago was 10% because 50% of 10 is 5, 5 x 50 = 250 and 15 / by 150 = 0.1, or 10%.

E.You can’t conclude anything, because not enough information is given in the statement.

F.The interest rate a decade ago was 35% because 50- 15=35.

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