**8th Warm-Up**

**1. A fruit punch is made by combining 1 quart of grape juice, 3 quarts of orange juice, 2 quarts of pineapple juice, and 2 quarts of ginger ale. What percent of the final mixture is pineapple juice?**

(A) 12.5% (B) 25% (C) 33.3% (D) 37.5% (E) 50%

2. If A is the set of even integers less than 10, and B is the set of multiples of 3 less than 20, what is the union of sets A and B?

(A) {2, 4, 6, 8} (B) {3, 6, 9, 12, 15, 18} (C) {6} (D) {2, 3, 4, 6, 8, 9, 12, 15, 18} (E) {2, 4, 6, 8, 10, 12, 14, 16, 18}

3. Maggie collects marbles. She has one jar filled with 50 marbles and 4 jars each filled with 30 marbles. How many marbles does Maggie have in total?

(A) 80 (B) 150 (C) 170 (D) 230 (E) 250

4. If a and b are inversely proportional, and a = 7 when b = 6, what is

a when b is 21?

(A) 2 (B) 13 (C) 18 (D) 20 (E) 42

5. If 6a + 3b = 6, what is the value of 2a + b?

(A) 1 (B) 2 (C) 3 (D) 12 (E) 18

(A) 12.5% (B) 25% (C) 33.3% (D) 37.5% (E) 50%

2. If A is the set of even integers less than 10, and B is the set of multiples of 3 less than 20, what is the union of sets A and B?

(A) {2, 4, 6, 8} (B) {3, 6, 9, 12, 15, 18} (C) {6} (D) {2, 3, 4, 6, 8, 9, 12, 15, 18} (E) {2, 4, 6, 8, 10, 12, 14, 16, 18}

3. Maggie collects marbles. She has one jar filled with 50 marbles and 4 jars each filled with 30 marbles. How many marbles does Maggie have in total?

(A) 80 (B) 150 (C) 170 (D) 230 (E) 250

4. If a and b are inversely proportional, and a = 7 when b = 6, what is

a when b is 21?

(A) 2 (B) 13 (C) 18 (D) 20 (E) 42

5. If 6a + 3b = 6, what is the value of 2a + b?

(A) 1 (B) 2 (C) 3 (D) 12 (E) 18

**7th Warm-Up**

**1)**

**Daisy typed 3 pages in 5 minutes. At this rate, how many pages would she type in 8 hours?**

2) 4, 12, 36, 108, . . .

The first term in the sequence above is 4, and each term after the first is determined by multiplying the preceding term by What is the value of the 50th term of the sequence?

3) Set

The intersection of sets

(A) {3, 4, 9, 15, 20} (B) {1, 5, 6, 12} (C) {1, 4, 7, 9, 13, 20}

(D) {9, 14, 20} (E) {2, 4, 9, 11, 21}

4) A club is planning a trip to an upcoming concert. In order to pay the group rate, they must reserve entire rows of seats. Each row in the concert hall contains 16 seats. If there are 300 members in the group, how many rows must they reserve?

5) If purchased individually, a can of tuna costs $0.79. A multi pack of 12 cans costs $7.80. How much money would be saved by purchasing multi packs instead of 60 individual cans of tuna?

2) 4, 12, 36, 108, . . .

The first term in the sequence above is 4, and each term after the first is determined by multiplying the preceding term by What is the value of the 50th term of the sequence?

3) Set

*X*= {1, 4, 5, 6, 9, 12, 20}The intersection of sets

*X*and*Y*is {4, 9, 20}. Which of the following could be set*Y*?(A) {3, 4, 9, 15, 20} (B) {1, 5, 6, 12} (C) {1, 4, 7, 9, 13, 20}

(D) {9, 14, 20} (E) {2, 4, 9, 11, 21}

4) A club is planning a trip to an upcoming concert. In order to pay the group rate, they must reserve entire rows of seats. Each row in the concert hall contains 16 seats. If there are 300 members in the group, how many rows must they reserve?

5) If purchased individually, a can of tuna costs $0.79. A multi pack of 12 cans costs $7.80. How much money would be saved by purchasing multi packs instead of 60 individual cans of tuna?

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**6th Warm-Up**

**1) 5, 12, 33, 96, . . .**

The first term in the sequence above is 5, and each term after the first is determined by subtracting

(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

2) A team has won 50% of the 10 games it played in the first half of the season. The team would like to win 70% of the total games for the season. What percent of the remaining 10 games must it win in order to do so?

3) If 40% <

(A) 0.25 (B) 0.50 (C) 0.65 (D) 0.70 (E) 0.85

4) Harry needs to select a number that is a multiple of 2, 3, and 5. Which of the following numbers could Harry select? I. 650 II. 480 III. 1200

(A) I only (B) I and II only (C) II only (D) II and III only (E) I, II, and III

5) If 25% of

(A) 25 (B) 100 (C) 200 (D) 400 (E) 800

The first term in the sequence above is 5, and each term after the first is determined by subtracting

*a from*the preceding term and then multiplying by*b*. What is the value of*a*?(A) 1 (B) 2 (C) 3 (D) 4 (E) 5

2) A team has won 50% of the 10 games it played in the first half of the season. The team would like to win 70% of the total games for the season. What percent of the remaining 10 games must it win in order to do so?

3) If 40% <

*a*< 5/8, which of the following could be*a*?(A) 0.25 (B) 0.50 (C) 0.65 (D) 0.70 (E) 0.85

4) Harry needs to select a number that is a multiple of 2, 3, and 5. Which of the following numbers could Harry select? I. 650 II. 480 III. 1200

(A) I only (B) I and II only (C) II only (D) II and III only (E) I, II, and III

5) If 25% of

*x*is 50, what is 50% of 4*x*?(A) 25 (B) 100 (C) 200 (D) 400 (E) 800

**________________________________________________________________________________________________________**

5th Warm-Up

5th Warm-Up

**1. If**

(A) 96 (B) 144 (C) 192 (D) 288 (E) 576

2. A factory produced 10,000 trading cards in 1 hour. If 2 percent of these cards are defective, how many cards are not defective?

3. Set

What fraction of the numbers in Set

4. The same number of men and women are on a train car when it leaves the terminal station. At the first stop, 10 men get on the car and no one gets off. After this stop, there are twice as many men as women on the train car. How many people are on this train car? (A) 10 (B) 15 (C) 20 (D) 30 (E) 40

5. A number

*a*is the greatest common factor of 18 and 30, and*b*is the least common multiple of 8 and 12, what is the value of*ab*?(A) 96 (B) 144 (C) 192 (D) 288 (E) 576

2. A factory produced 10,000 trading cards in 1 hour. If 2 percent of these cards are defective, how many cards are not defective?

3. Set

*A*= {21, 29, 30, 37, 42, 47, 51, 53}.What fraction of the numbers in Set

*A*are prime?4. The same number of men and women are on a train car when it leaves the terminal station. At the first stop, 10 men get on the car and no one gets off. After this stop, there are twice as many men as women on the train car. How many people are on this train car? (A) 10 (B) 15 (C) 20 (D) 30 (E) 40

5. A number

*x*is decreased by 10%, and then this new number is increased by 20%. What is the final number, in terms of*x*? (A) 0.7*x*(B) 1.08*x*(C) 1.1*x*(D) 1.15*x*(E) 1.2*x***________________________________________________________________________________________________________**

4th Warm-Up

1. Monique sold 50 magazine subscriptions in the first week of her school fund-raiser. In the second week, she sold 30% fewer subscriptions. How many subscriptions did Monique sell in this two-week period?

(A) 20 (B) 35 (C) 70 (D) 80 (E) 85

2. The average of 7 consecutive integers is 42. What is the greatest of these integers?

3. Exactly 5 students are interested in serving as class officers. There are 3 positions open, and no student can fill more than one position. How many different assignments of positions are possible?

(A) 8 (B) 15 (C) 20 (D) 60 (E) 120

4. Several people are sitting in a row of seats in a movie theater. Starting at the right end of the row, Maureen is counted as the 9th person. Starting at the left end, she is counted as the 15th person. How many people are seated in the row?

(A) 6 (B) 7 (C) 22 (D) 23 (E) 24

5. Alfie drove to school at an average rate of 30 miles per hour and returned home later in the day at the same rate of speed. If each leg of his trip took 15 minutes, how many miles did Alfie drive in total?

(A) 7.5 (B) 15 C) 22.5 (D) 30 (E) 45

4th Warm-Up

1. Monique sold 50 magazine subscriptions in the first week of her school fund-raiser. In the second week, she sold 30% fewer subscriptions. How many subscriptions did Monique sell in this two-week period?

(A) 20 (B) 35 (C) 70 (D) 80 (E) 85

2. The average of 7 consecutive integers is 42. What is the greatest of these integers?

3. Exactly 5 students are interested in serving as class officers. There are 3 positions open, and no student can fill more than one position. How many different assignments of positions are possible?

(A) 8 (B) 15 (C) 20 (D) 60 (E) 120

4. Several people are sitting in a row of seats in a movie theater. Starting at the right end of the row, Maureen is counted as the 9th person. Starting at the left end, she is counted as the 15th person. How many people are seated in the row?

(A) 6 (B) 7 (C) 22 (D) 23 (E) 24

5. Alfie drove to school at an average rate of 30 miles per hour and returned home later in the day at the same rate of speed. If each leg of his trip took 15 minutes, how many miles did Alfie drive in total?

(A) 7.5 (B) 15 C) 22.5 (D) 30 (E) 45

**________________________________________________________________________________________________________**

3rd Warm-Up

1. At North High School, 66 students are in the band and 45 students are in the orchestra. If 24 students are in both band and orchestra, what is the ratio of the number of students who are only in the band to the number who are only in the orchestra? (A) 2:1 (B) 21:12 (C) 18:11 (D) 8:7 (E) 14:15

(A) 3 (B) 6 (C) 7 (D) 8 (E) 9

3. All of the following can be expressed as the sum of two consecutive integers EXCEPT

(A) 27 (B) 30 (C) 33 (D) 39 (E) 43

4. When

(A) 4 (B) 3 (C) 2 (D) 1 (E) 0

5. A store is offering a sale on T-shirts. If the T-shirts come in 4 different styles and 9 different colors, how many different T-shirts are on sale? (A) 5 (B) 13 (C) 36 (D) 81 (E)216

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2nd Warm-Up

3rd Warm-Up

1. At North High School, 66 students are in the band and 45 students are in the orchestra. If 24 students are in both band and orchestra, what is the ratio of the number of students who are only in the band to the number who are only in the orchestra? (A) 2:1 (B) 21:12 (C) 18:11 (D) 8:7 (E) 14:15

*2. X*= {3, 6, 9} and*Y*= {4, 8, 12}. If*a*is in*X*and*b*is in*Y,*how many different values are there for?(A) 3 (B) 6 (C) 7 (D) 8 (E) 9

3. All of the following can be expressed as the sum of two consecutive integers EXCEPT

(A) 27 (B) 30 (C) 33 (D) 39 (E) 43

4. When

*r*is divided by 5, the remainder is 3. What is the remainder when 3*r*is divided by 5?(A) 4 (B) 3 (C) 2 (D) 1 (E) 0

5. A store is offering a sale on T-shirts. If the T-shirts come in 4 different styles and 9 different colors, how many different T-shirts are on sale? (A) 5 (B) 13 (C) 36 (D) 81 (E)216

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2nd Warm-Up

**1. The blocks in a certain toy chest are either red or blue. If the ratio of the number of red blocks to the number of blue blocks is 1/3 , each of the following could be the number of blocks in the chest EXCEPT**

(A) 12 (B) 16 (C) 20 (D) 30 (E) 36

2. If it is now Thursday, what day will it be 200 days from now?

(A) Sunday (B) Monday (C) Wednesday (D) Thursday (E) Saturday

3. A store sells its merchandise at 20% above the wholesale price. If the store sells an item for $30.00, what is its wholesale price?

(A) $6.00 (B) $24.00 (C) $25.00 (D) $27.00 (E) $36.00

4. Greg bought 6 bottles of water from a vendor. He paid with a ten dollar bill and got back two dollars in change. He realized that he had received too much change and gave one dollar back to the vendor. What was the price of each bottle of water?

(A) $1.00 (B) $1.15 (C) $1.25 (D) $1.50 (E) $2.00

5. If Maia can read 20 pages in 18 minutes, how long will it take her to read 150 pages?

(A) 1 hour and 6 minutes (B) 1 hour and 35 minutes (C) 2 hours and 15 minutes

(D) 2 hours and 46 minutes (E) 3 hours and 18 minutes

(A) 12 (B) 16 (C) 20 (D) 30 (E) 36

2. If it is now Thursday, what day will it be 200 days from now?

(A) Sunday (B) Monday (C) Wednesday (D) Thursday (E) Saturday

3. A store sells its merchandise at 20% above the wholesale price. If the store sells an item for $30.00, what is its wholesale price?

(A) $6.00 (B) $24.00 (C) $25.00 (D) $27.00 (E) $36.00

4. Greg bought 6 bottles of water from a vendor. He paid with a ten dollar bill and got back two dollars in change. He realized that he had received too much change and gave one dollar back to the vendor. What was the price of each bottle of water?

(A) $1.00 (B) $1.15 (C) $1.25 (D) $1.50 (E) $2.00

5. If Maia can read 20 pages in 18 minutes, how long will it take her to read 150 pages?

(A) 1 hour and 6 minutes (B) 1 hour and 35 minutes (C) 2 hours and 15 minutes

(D) 2 hours and 46 minutes (E) 3 hours and 18 minutes

**_________________________________________________________________________________________________________________________________________________**

1st Warm-Up

1. Martha is dividing cookies into packages. If she puts 5 cookies in each package, she will make 33 packages with no cookies left over. If instead she puts 3 cookies in each package, how many packages can she make?

2. The weight of 80 screws in a jar of identical screws is 2 ounces. What is the weight, in ounces, of 4 screws?

3. All numbers that are divisible by both 3 and 5 are also divisible by 10. Which of the following numbers can be used to show that the statement above is FALSE? (A) 20 (B) 25 (C) 30 (D) 40 (E) 45

4. Gabo bought three chicken dinners for $6.95 each and one hamburger meal for $5.75. He and three friends decide to divide the cost of the meals equally. How much money does Gabo receive in total from his three friends?

5. What is the least positive integer divisible by the numbers 2, 4, and 7?

1st Warm-Up

1. Martha is dividing cookies into packages. If she puts 5 cookies in each package, she will make 33 packages with no cookies left over. If instead she puts 3 cookies in each package, how many packages can she make?

2. The weight of 80 screws in a jar of identical screws is 2 ounces. What is the weight, in ounces, of 4 screws?

3. All numbers that are divisible by both 3 and 5 are also divisible by 10. Which of the following numbers can be used to show that the statement above is FALSE? (A) 20 (B) 25 (C) 30 (D) 40 (E) 45

4. Gabo bought three chicken dinners for $6.95 each and one hamburger meal for $5.75. He and three friends decide to divide the cost of the meals equally. How much money does Gabo receive in total from his three friends?

5. What is the least positive integer divisible by the numbers 2, 4, and 7?