If a:b = 2:3, and c:b = 5:7, then what is a:c? 10:21 B) 7:10 C) 14:15 D) 10:7 E) 15:14

1. If a:b = 2:3, and c:b = 5:7, then what is a:c? • 10:21 B) 7:10 C) 14:15 D) 10:7 E) 15:14 • Hint: use fractions

2. If a:b = 2:3, and c:b = 5:7, then what is a:c? • 10:21 B) 7:10 C) 14:15 D) 10:7 E) 15:14 • Treat as fractions: a/b = 2/3 and b/c = 7/5 (note it’s flipped) • (a/b)(b/c) = (a/c) = (2/3)(7/5) = 14/15 (c) • Happy Birthday Andrew!

3. If Maria can read 10 pages in 8 minutes, then how long will it take her to read 90 pages? • 18 minutes • 1 hr and 8 minutes • 1 hr and 12 minutes • 1 hr and 20 minutes • 1 hr and 30 minutes

4. If Maria can read 10 pages in 8 minutes, then how long will it take her to read 90 pages? • 18 minutes • 1 hr and 8 minutes • 1 hr and 12 minutes • 1 hr and 20 minutes • 1 hr and 30 minutes • 9 times longer, or 9(8) = 72 minutes = 1 hr and 12 minutes

5. Thought for the Day If a turtle loses its shell, is it naked or homeless?

6. If this figure is made of identical squares, and the area of the entire figure is 125, then what is the perimeter?

7. If this figure is made of identical squares, and the area of the entire figure is 125, then what is the perimeter? Five identical squares means the area of each one is 125 / 5 = 25 Since Area = s2, then the side will be √25 = 5 There are twelve exterior sides, so the perimeter will be 12 ∙ 5 = 60

8. What is the numerator of (1/2 + 1/6) – (1/12 + 1/3) in simplest terms?

9. What is the numerator of (1/2 + 1/6) – (1/12 + 1/3) in simplest terms? (1/2 + 1/6) = (6/12 + 2/12) = 8/12 1/12 + 1/3 =1/12 + 4/12 = 5/12 8/12 – 5/12 = 3/12 = ¼ Answer: 1

10. How many odd integers are between 10/3 and 83/4? A) 8 B) 9 C) 10 D) 18 E) 19

11. How many odd integers are between 10/3 and 83/4? • 8 B) 9 C) 10 D) 18 E) 19 • 10/3 = 3.33 • 83/4 = 20.75 • Thus, between them: 5 , 7 , 9 , 11 , 13 , 15 , 17 , 19

12. The pom-pons in the Cheer Shop are either blue or white. If the ratio of the number of blue pom-pons to the number of white pom-pons is 1:3, each of the following could be the total number of pom-pons EXCEPT: A) 12 B) 16 C) 20 D) 30 E) 36

13. The pom-pons in the Cheer Shop are either blue or white. If the ratio of the number of blue pom-pons to the number of white pom-pons is 1:3, each of the following could be the total number of pom-pons EXCEPT: • 12 B) 16 C) 20 D) 30 E) 36 • For every blue, there are 3 white, thus 4 in a “group.” • The total number must be a multiple of 4. D) 30 is not.

14. The number n is a multiple of 3 and a factor of 48. Grid a possible value for n.

15. The number n is a multiple of 3 and a factor of 48. Grid a possible value for n. Factors of 48: (1 ,48),(2 , 24),(3 , 16),(4 , 12),(6 , 0) You can grid any of these that are multiples of 3: 3 , 6 , 12 , 24

16. Janina is writing a report for science class, and has to write numbers in scientific notation. If she wants to include the number 5,067,000,000 how should that be written? • 50.67 x 106 B) 50.67 x 108 C) 5.067 x 108 • D) 5.067 x 109 E) 5.067 x 1010

17. Janina is writing a report for science class, and has to write numbers in scientific notation. If she wants to include the number 5,067,000,000 how should that be written? • 50.67 x 106 B) 50.67 x 108 C) 5.067 x 108 • 5.067 x 109 E) 5.067 x 1010 • Scientific notation: ONE number to the left of the decimal point, then count how many places you need to get to the end– that will be the exponent on 10 (positive to the right, negative to the left)

18. The mean, sum, and product of three integers are all the same. If two of the numbers are 0 and 3, what is the other number? A) 0 B) -3 C) 0 D) 3 E) -6

19. The mean, sum, and product of three integers are all the same. If two of the numbers are 0 and 3, what is the other number? • 0 B) -3 C) 0 D) 3 E) -6 • (3)(0)(x) = 3 + 0 + x • 0 = 3 + 0 + x • -3 = x • Check: 0 / 3 = 0 for the mean

20. What is it that we heat, and then cool; make sour, then sweeten?

21. Riddle: Two boys were sent by their mothers to sell an equal amount of cupcakes each, worth one dollar per cupcake.They were told not to eat the cupcakes they are selling, and that they should sell all of the cupcakes.At the end of the day, all cupcakes were sold, yet neither boy gained nor lost a dollar.What happened?

22. Monique sold 50 magazines in the first week of the fund-raiser. In the second week, she sold 30% fewer subscriptions. How many did she sell in the 2 week period? • 20 B) 35 C) 70 D) 80 E) 85

23. Monique sold 50 magazines in the first week of the fund-raiser. In the second week, she sold 30% fewer subscriptions. How many did she sell in the 2 week period? • 20 B) 35 C) 70 D) 80 E) 85 • 30% of 50 = .3(50) = 15 • 50 – 15 = 35 • 50 + 35 = 85 (E)

24. Bonus: Can you arrange 4 pennies so they’re all touching each other?

25. If 40% < a < 5/8, which of the following could be a? • .25 B) .5 C) .65 D) .70 E) .88

26. If 40% < a < 5/8, which of the following could be a? • .25 B) .5 C) .65 D) .70 E) .88 • 40% = .40, and 5/8 = .625 • so .5 is the only value between .40 and .625

27. Bonus Riddle: John’s wife shot him, drowned him, and then hung him. Yet she won an award for this. Why?

28. If 25% of x = 50, what is 50% of 4x? • 25 B) 50 C) 200 D) 400 E) 500 • (Yes, it’s been awhile!)

29. If 25% of x = 50, what is 50% of 4x? • 25 B) 50 C) 200 D) 400 E) 500 • Without finding x: • 50% doubles it, and 4x multiplies it by 4 • 8 * 50 = 400 • D) 400

30. If 25% of x = 50, what is 50% of 4x? • 25 B) 50 C) 200 D) 400 E) 500 • Or, if you insist on finding x: • .25x = 50  x = 200 • 4x = 800 • .5(800) = 400 (D) still