1. A chemist added x milliliters of pure water to 40 milliliters of a solution that was 30 percent acid, by volume, to create 40 + x milliliters of a solution that is 25 percent acid, by volume.  Which of the following equations can be used to determine the value of x?

Indicate all such equations.

a. 0.3(40) = 0.25 (40+x)

b. 0.3(40) -0.25(40) = x

c. 0.3(40)-0.25(40)=0.25x

d. 0.3(40) + x=0.25(40) + x

e. 0.3(40-x)=0.25(40)

f. 0.3(40+x) = 0.25(40+x)

2. The figure shows a circle with center D.  The measure of angle ABC is 30 degrees, and AC =BC.  What is the measure of angle ADE? (Note: The measure of an angle inscribed in a circle is equal to half the measure of the central angle that subtends the same arc.)

a. 90 degrees

b. 100 degrees

c. 120 degrees

d. 130 degrees

e. 140 degrees.

3. The sum of decimal numbers 0.qr and 0.st is 0.93 where q,r,s, and t are digits such that r + s = t and 3q=t.  what is the ratio of q to s?

Give your answer as a fraction

4.  For each value x in a list of values with mean m, the absolute deviation of x from the mean is defined as |x-m|.

What is the sum of the absolute deviations from the mean in micrograms per cubic meter, for the mean population exposures to PM2.5 air pollution in 2020 for 6 cities?

a. 1.21

b. 3.78

c. 7.24

d. 9.43

e. 14.10

5. For which of the cities was the mean population exposure to P342.5 air pollution more than 20 percent greater than that in City F

Indicate all such cities

a. A

b. B

c. C.

d. D

e. E

6.  In the circle graph, the sum of the measures of the central angles of the sectors representing agricultural sources and natural sources is closest to which of the following?

a. 28 degrees

b. 32 degrees

c. 68 degrees

d. 101 degrees

e. 129 degrees

7. A certain store sells windows in 2 sizes: small and large .  Last year the store sold each large window for $300 , sold each small window for $180, and sold 480 more small windows than large windows.    Last year, if the total of the selling prices of the windows sold was $192,000., how many large windows did the store sell?

8.  A continuous random variable R has a mean of 98 and a standard deviation of 3.  What is the value of R that is 0.5 standard deviation below the mean?

a.  92

b. 94.5

c. 95

d. 96.5

e. 97.5

9.   On Tuesday last week, a shipping company shipped boxes that were either small, medium, or large.  The ratio of the number of small boxes to the number of medium boxes to the number of large boxes was 2 to 3 to 3.  The average (arithmetic mean) weight of the small boxes was 1.8 kilograms, the average weight of the medium boxes was 5.8 kilograms, and the average weight of the large boxes as 10.5 kilograms.  the total weight of all the boxes shipped on Tuesday was 525 kilograms.  What was the total number of boxes shipped on Tuesday?

a. 88

b. 84

c. 80

d. 76

e. 72

10.  In an ice cream shop, each scoop of ice cream can be any of 8 flavors.  How many combinations of 2 scoops of ice cream of different flavors are possible at the shop?

a. 16

b. 28

c. 32

d. 56

e. 64

11.  A community theater sold a total of 360 tickets for a play.  Three types of tickets were sold: youth, adult, and senior.  The ratio of the number of adult tickets sold to the number of youth tickets sold was 4 to 1, and the ratio of the number of senior tickets sold to the number of youth tickets sold was 5 to 2.  What was the number of adult tickets sold

a. 120

b. `44

c. 150

d. 160

e. 192

12. Quantity A – The number of positive divisors of 24

Quantity B – The number of positive divisors of 243

a. quantity A is greater

b. quantity B is greater 

c. the two quantities are equal

d. the relationship cannot be determined from the information given

13.   The perimeter of a polygon is 12

Quantity A – the area of the polygon

Quantity B -10

a. Quantity A is greater

b. Quantity B is greater

c. the two quantities are equal

d. the relationship cannot be determined from the information given

14.  Each side of a hexagon X and octagon Y has length z.  The perimeters of X and Y are x and y

Quantity A – 4x

Quantity B – 3y

a. Quantity A is greater

b. Quantity B is greater

c. the two quantities are equal

d. the relationship cannot be determined from the information given

15. Set S has 17 elements, set T has 13 elements, and set S U T has 26 elements

Quantity A – the number of elements in the set S  T

Quantity B – 3

a. Quantity A is greater

b. Quantity B is greater

c. the two quantities are equal

d. the relationship cannot be determined from the information given

16 1 < a < 2

Quantity A –     a + 3

Quantity B –    3a

a. Quantity A is greater

b. Quantity B is greater

c. the two quantities are equal

d. the relationship cannot be determined from the information given

17. Data set S consists of n consecutive  even integers, and the range of the integers in S is 100

Quantity A –   n

Quantity B   – 50

a. Quantity A is greater

b. Quantity B is greater

c. the two quantities are equal

d. the relationship cannot be determined from the information given

18. x > y > 1

Quantity A –   x + 1 / y – 1 

Quantity B – y + 1/x – 1

a. Quantity A is greater

b. Quantity B is greater

c. the two quantities are equal

d. the relationship cannot be determined from the information given

19.  Quantity A – 1 percent of $20

Quantity B – 20% of $1

a. Quantity A is greater

b. Quantity B is greater

c. the two quantities are equal

d. the relationship cannot be determined from the information given