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Time fora short break

COLLEGE OF EDUCATIONMATHEMATICS TEAM QUIZ

BOWL

Gymnasium, MSU Gensan CampusFatima, General Santos City

July 14, 2013

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EASY ROUND

2. Jerry was mowing his lawn when he noticed Christy was also mowing her lawn next door. They stopped to talk and Jerry learned that Christy mows her lawn once every 8 days. Jerry mows his lawn once every 6 days. In how many days will they be mowing their

lawns together again?

24 daysAnswer:

SOLUTION:

Christy 8 16 24 32Jerry 6 12 18 24

Jerry and Christy will be mowing their lawns together again in 24 days.

4. Mr Green has a small farm near Steinbach, Manitoba. He has chickens and cows on his farm. If there are 32 legs altogether, what is the greatest number of cows possible?

7 Answer:

SOLUTION:

Chickens Cows Legs

0 8 322 7 32

Always maintain a constant total of 32 legs in total.If all the legs belong to cows only, then 8 cows (32÷4) are possible.But there must be at least 1 chicken on the farm.Exchange 1 cow for 2 chickens.There are at most 7 cows.

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average ROUND

1. A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?

a. 10/21 c. 11/21b. 2/7 d. 5/7

A. Answer:

SOLUTION:Total number of balls = (2 + 3 + 2) = 7.Let S be the sample space.Then, n (S)= Number of ways of drawing 2 balls out of 7

= 7C2

= (7 x 6)/ (2x1) = 21

Let E = Event of drawing 2 balls, none of which is blue.

Such that: n(E)= Number of ways of drawing 2 balls out of (2+3) balls. = 5C2

= (5x4)/ (2x1) = 10

Therefore:

P(E)= =

2. What does 1012000 mean? (in the common base of ten).

Answer:

one million 12 thousand

SOLUTION:If this represents a number written in the common base of 10, then "1012000" means "one million 12 thousand". If it represents a number written in the base of 3, then "1012000" means "eight hundred sixty-four". It it represents a number written in the base of 8, then "1012000" means "two hundred sixty-seven thousand two hundred sixty-four". It could represent a number written in any base, except 2 (binary).

3. How many five digit numbers can you make with 23456?

120Answer:

SOLUTION:

You gave me 5 digits. -- The first digit can be any one of the 5 digits. For each one, -- The second digit can be any one of the remaining 4 digits. For each one, -- The third digit can be any one of the remaining 3 digits. For each one, -- The fourth digit can be any one of the remaining 2 digits. For each one, -- The fifth digit can only be the remaining 1 digit. So there are (5 x 4 x 3 x 2 x 1) = 120 possible different arrangements.

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

9/ 20

4. In a class of 100, the mean on a certain exam was 50, the standard deviation, 0. This means a. half the class had scores less than 50 b. there was a high correlation between

ability and grade c. everyone had a score of exactly 50 d. half the class had 0's and half had 50's

Answer:

C.

SOLUTION:

A zero standard deviation means all scores are the same, and equal to the mean (what else could the mean be?)

1 23difficult ROUND

2. There are five people in a room, and each person shakes every other person’s handexactly one time. How many handshakes will there be?

Answer:

10

SOLUTION:SOLVE IT Get five friends to help with this problem.Make a list with each person’s name at the top of a column.Have the first person shake everyone’s hand. How many handshakes were there? Four.Repeat this four more times with the rest of the friends. Write down who each person shook hands with. Our table should look something like this:There were a total of 20 handshakes. But notice that each person actually shook everyone else’s hand twice. (For example, Rhonda shook Jagraj’s hand, and Jagraj shook Rhonda’s hand.) Divide the total number of handshakes by two to find out the total number if each person had shaken every other person’s hand only once. There were 10 handshakes.

3. Ten people arrive at a party. If the party is in Turkey , each person kisses every other person twice, once on each cheek. How

many kisses are there?

90Answer:

SOLUTION:

Making a list for 10 people reveals a pattern, and the pattern suggests another way to solve the problem.. If the number of people who come to the party is n, then the number of pairs who greet each other is n2- n/2. Since each person kisses every other person twice, the number of kisses is 2(n2- n/2).

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Do or die ROUND

3. What is the largest two-digit number that is divisible by 3 whose digits differ by 2?

75Answer:

SOLUTION:

99, 98, 97, 96, 95, 94, 93, 92, 91, 90,89, 88, 87, 86, 85, 84, 83, 82, 81, 80,79, 78, 77, 76, 75, 74, 73, 72, 71, 70, . . .Eliminate those numbers that are not divisible by 3:

99, 98, 97, 96, 95, 94, 93, 92, 91, 90,89, 88, 87, 86, 85, 84, 83, 82, 81, 80,79, 78, 77, 76, 75, 74, 73, 72, 71, 70, . . .From these, eliminate all numbers whose digits do not differ by 2:99, 96, 93, 90, 87, 84, 81, 78, 75, 72, . . .75 is the largest number that remains.

1. Customers at a particular yogurt shop may select one of three flavors of yogurt. Theymay choose one of four toppings. How many one flavor, ‑ one topping combinations ‑

are possible?

12Answer:

SOLUTION:

SOLVE IT Make an organized list. Use F and T to denote either flavor or topping. Use the numbers1 – 3 and 1–4 to mark different flavors and toppings.F1T1, F1T2, F1T3, F1T4F2T1, F2T2, F2T3, F2T4F3T1, F3T2, F3T3, F3T4Now count the number of combinations. There are 12 combinations possible.