This is about MathCounts

[MAS1]

Originally Posted by shadow123blast

4. An item in a store is originally priced at $4.00. A clerk marks the item up by 100%. After that, a second clerk marks the new price up by 200%. What was the final price after the two markups?

4 + 100%x4 = 4 + 4 = 8
8 + 200%x8 = 8 + 16 = 24
Final price = $24

[MAS1]

Originally Posted by shadow123blast

i will have a competition the 2 people have to be on at the same time
i will post problems (5 at a time) then the 1st to answer all correctly will win but remember you must schedule your time with another player or you won't get the prize
The prize is 50 points
This is VIP only(not to be discriminatory) but VIPs post instantly so i can see their answers
hints
-good typing skills
-fast thinking
-being prepared
I will attach the questions as a file
the 1st is problem set 1 the second problem set 2
to give you all a warm up and bonus 10 points for answering all 5 correctly

1. How many integers between 15 and 85 are divisible by 20?
20, 40, 60, and 80 are between 15 and 85 and are also divisible by 20. So 4 integers between 15 and 85 are divisible by 20.

2. How many edges does an octagonal prism have?
8 x 3 = 24 edges.

3. Mickey’s age is 4 years less than 300% of Jerry’s age. If Mickey is 14 years old, how old is Jerry?
M = 300% x J - 4
14 = 3J - 4
18 = 3J
J = 6 so Jerry is 6 years old.

4. A particular multivitamin contains 120 mcg of chromium which represents 125% of the recommended daily amount. What is the recommended daily amount of chromium, in mcg ?
120 = 125% of D
120 = 1.25 x D
D = 96 so the recommended daily allowance of chromium is 96 mcg.

5. What is the sum of the 10 smallest positive multiples of three?
3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 = 33 x (5) = 165

[MAS1]

Originally Posted by shadow123blast

10 points for the 1st person who answers all correctly

6. How many of the letters in MATHCOUNTS have a horizontal line of symmetry?
H, C, O so 3 letters.

7. Billy takes two marbles, without replacement, from a bag that contains only six yellow marbles and three blue marbles. What is the probability that he gets one marble of each color? Express your answer as a common fraction.
1/2

8. What is the volume, in cubic units, of a cube whose surface area is 600 square units?
S.A. of a cube = 6s^2 where s is the edge length of the cube.
600 = 6s^2
100 = s^2
s = 10
Volume = s^3 = 10^3 = 1000 cubic units

9. The only garments that a particular factory produces are dresses and shirts. It produces three dresses for every five shirts it makes. If the factory produced a total of 72 garments today, how many dresses did it make?
3 dresses for every 5 shirts makes a total of 8 garments.
72/8 = 9
3 x 9 + 5 x 9 = 27 + 45 = 72
So the factory made 27 dresses.

10. What is the number that yields the same value when it is multiplied by three and then increased by five as when it is multiplied by five then decreased by three?
3N + 5 = 5N - 3
8 = 2N
N = 4

[shadow123blast]

ok since you answered all correctly you will get 20 points 10 for the 2 warmups

[shadow123blast]

5. The points (4, 0) and (−4, 0) are two non-consecutive vertices
of a rhombus with an area of 80 square units. One of the other
vertices is (0, K) where K > 0. What is the value of K?

[MAS1]

Originally Posted by shadow123blast

5. The points (4, 0) and (−4, 0) are two non-consecutive vertices
of a rhombus with an area of 80 square units. One of the other
vertices is (0, K) where K > 0. What is the value of K?

One formula for the area of a rhombus is area = (0.5)AB, where A and B are diagonals of the rhombus.

(0.5)(8)(2K) = 80
8K = 80
K = 10

[shadow123blast]

do you get points ???? for this since i forgot if i should give you 0 or 2 points. wait this is a sprint problem but if you want the points you need to put it in the blog.

[shadow123blast]

the nationals are almost here they are in Orlando. Florida and you should watch it it will give you lots of experience on quick questions like the sprint and the countdown especially since these people are the best of the best.
it will be in the archives
www.mathcounts.org/webcasts
or you can watch it tomorrow live May 7th
go to http://www.mathcounts.org

[shadow123blast]

i am rooting for the NC champion Kavi Jain from my school an 8th grader and is excellent at math and got 1st with a perfect 46 in the 2nd most competitive state North Carolina. He is coached by Mrs. Pieper an excellent math teacher that teaches very advanced math like Algebra 1 and 2 and geometry and sometimes to excellent students pre calc for middle school students i took Algebra 1 in 5th grade and did excellent and scored the highest on the EOC, the end of course, which allows you to take credit for that course.

[shadow123blast]

the sad thing was the the NC champion only got a 31 out of 46 and 83rd out of the entire 150 people(i think its 150 im not sure...)