Practice Session

7/28/2019 Practice Session

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PRACTICE SESSION

1. Jerry weighed his 4 dogs in pairs. Max and Bella weighed 118 pounds, Bella and Stella weighed

120 pounds, Stella and Harpo weighed 127 pounds. How many pounds would Max and Harpo

weigh together?

a. 117b. 127

c. 115

d. 121

e. 125

2. What is the sum of the infinite geometric series 3.3+1.32+0.528+0.2112+ ... ? Round your

answer to the nearest tenth.

a. 4.5

b. 3.5

c. 8.5d. 2.5

e. 5.5

3. The numbers from 1 to 8 are separated into two non-empty sets A and B . The numbers in A

are multiplied together to get a . The numbers in B are multiplied together to get b . The larger

of the two numbers a and b is written down. What is the smallest number that can be written

down using this procedure?

a. 209

b. 208

c. 213d. 207

e. 210

4. What is the greatest number of bags that can be used to hold 528 marbles if each bag must

contain at least one marble but no two bags may contain the same number of marbles?

a. 527

b. 526

c. 528

d. 531

e. 525

5. When Maya divides her favorite number by 12, she gets a remainder of 5.What will the

remainder be if she multiplies her favorite number by 5 and then divides by 12?

a. 12

b. 1

c. 2



d. 5

e. 4

6. Compute the following sum: 1+ 12 + 12!/( 2! (12-2)!)+ ... +12!/(k! (12-k)!) + ...+ 12 +1 .

a. 8192

b. 16384

c. 512

d. 32768

e. 4096

7. Daniel and Brad are playing a game in which players are awarded either 7 points or 5 points

for a correct answer. What is the the greatest score that CANNOT be attained?

a. 30

b. 24

c. 25

d. 22

e. 23

8. According to an ancient belief, when a friend visits a sick person, 1/70 of his sickness is taken

away. What is the least amount of friends that need to visit to take away at least 77% of a

person's illness?

a. 102

b. 101

c. 103

d. 106

e. 100

9. Brian has 55 feet of fencing. He will use the fencing to enclose a play area for his puppy. What

is the maximum number of square feet he can enclose? Use an 3.14 as an approximation of Pi .

Express your answer to the nearest whole number.

a. 242

b. 243

c. 241

d. 238

e. 244

10. Mrs. Read can knit one pair of children's mittens with a ball of yarn 9 inches in diameter.

How many pairs of identical mittens can she knit with a ball of yarn 54 inches in diameter?

Assume that the balls of yarn are rolled consistently.

a. 216

b. 6

c. 36



d. 125

e. 64

11. A car that originally sold for 19000 dollars depreciates at a rate of 15% per year. What is the

number of dollars in the value of the car at the end of 4 years?Round your answer to the nearest

dollar.

a. 9918

b. 9919

c. 9920

d. 9915

e. 9921

12. In a given sample, the number of microbes doubled every second. After 7 seconds, there

were 10,000,000 microbes per cubic cm in the sample. A second sample, which also doubled

every second, started with 4 times as many microbes per cubic cm as the original sample. How

many seconds passed before the second sample had 10,000,000 microbes per cubic cm?

a. 6

b. 7

c. 2

d. 5

e. 8

13. An advertisement read, Take an additional 30% off any item which is already discounted 40%

. A clerk with MATH training said, Those two combined discounts are the same as one n%

discount. What is the value of n ?

a. 59

b. 58

c. 60

d. 55

e. 61

14. Find the sum of first 35 terms in the following of the sequence 1, 5, 6, 11, 17, 28, 45, 73, . . .

if the 35-th term is 32,039,013 and the 36-th term is 51,840,212 .

a. 83879220

b. 83879219

c. 83879218

d. 83879223

e. 83879217

15. Out of 400 fish in an aquarium 98 % are guppies. How many guppies must be removed so

that the percent of guppies in the aquarium is 92 % ?

a. 300

b. 200



c. 250

d. 350

e. 100

16. If a solution of iodine and alcohol contains 3 ounces of idoine and 16 ounces of alcohol, how

many ounces of alcohol should evaporate so that the ratio of the of iodine to the solution is 2 to

5 ? Give your answer to the nearest tenth.

a. 10.5

b. 11.5

c. 9.5

d. 14.5

e. 8.5

17. What is the sum of the elements in the following sequence -1,3,-5,7,-9,11, ...,-321 ?

a. -161

b. -159

c. -159

d. -79

e. -81

18. What is the sum of the positive whole numbers that are solutions of - 7 n + 7 > -27 ?

a. 11

b. 12

c. 7

d. 13

e. 10

19. We have 6 hippos and we weigh them in pairs. After weighing all possible pairs, we obtain

the following list of the weights of all pairs. Here is the list:

{350,360,370,370,376,380,386,390,394,396,404,406,414,424,430}

What is the sum of the weights of all the 6 hippos?

a. 1169

b. 1168

c. 1170

d. 1173

e. 1167

20. A circle of radius 3 is inscribed in a regular hexagon. What is the number of square units in

the area of the hexagon? The answer is x Sqrt[3] . Find x .

a. 19

b. 20

c. 15



d. 18

e. 21

21. Paul made a round trip between two points A and B in 8 hours. His speed going up is 3 mph .

His speed going down is 6 mph . His speed going on a level surface 4 mph . What is the distance

in miles between A and B ?

a. 16

b. 17

c. 18

d. 13

e. 19

22. A dollhouse models a real house at a scale of 1:18 . If it takes 36 cans to paint the walls of

the real house, how many cans are needed to paint the walls of the doll house? Express your

answer as a common fraction.

a. 0

b. 2/9

c. -1/9

d. 1/3

e. 1/9

23. The base 10 representation of 7^6 is 117649 . What is the base-7 representation of 117648 ?

a. 555555

b. 444444

c. 999999

d. 666666

e. 333333

24. At the grading of the Placement exams, 300 math teachers graded 100000 tests in 50 hours.

Each test had 7 problems. What is the average number of minutes it took one teacher to grade

20 problems? Express your answer to the nearest minute.

a. 27

b. 28

c. 26

d. 23

e. 29

25. What is the smallest number of 6 cm by 21 cm rectangular pieces required to form a square

with no cutting or gaps?

a. 10

b. 14

c. 6



d. 35

e. 21

26. The whole numbers 37 through 85 are arranged 7 x 7 table, with each number occurring

exactly once, and such that the sum of the entries of any row, any column, or any main diagonal

is the same. What is the common sum?

a. 427

b. 420

c. 413

d. 448

e. 406

27. What are the sum of all whole numbers 0 < y < 1000 such that y is both a perfect square and

a perfect fourth power?

a. 979

b. 978

c. 977

d. 982

e. 976

28. What is the sum of the two least, distinct positive integers each of which has exactly 2

distinct factors?

a. 6

b. 7

c. 5

d. 2

e. 8

29. Four ordered pairs listed are solutions of the same linear equation and one is not. Give the

first coordinate of the one that is not.

{(0,-8), (-2,-10), (-1,-11), (2,-6), (3,-5)}.

a. -1

b. 3

c. 2

d. -2

e. 0

30. After a price reduction of 15% an item has its price increased to its original value. What was

the percent of the of the increase? The answer is y% . Express y to the nearest hundredth.

a. 18.65

b. 17.65

c. 19.65



d. 14.65

e. 20.65

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