Middle School Math Quiz
3 posters
Page 1 of 1
Middle School Math Quiz
I selected these 4 relatively easy questions from an actual quiz of 30 problems published in a math magazine. I also have the answers for these questions (with explanations) given in that magazine.
1. Each day Jane makes an openfaced sandwich using only one slice of bread. She uses 1 kind of meat or 1 kind of cheese or 1 kind of each. If she chooses from 4 kinds of bread, 5 kinds of meat, and 3 kinds of cheese, how many different sandwiches can she make?
2. Ten boys and girls write their names on slips of paper – one name per slip – to enter a prize drawing. Two of the names are drawn at random without replacement. If the probability that both winners are boys is 1/15, how many boys are in the group?
3. If Jack and Jill each randomly choose a whole number from 1 to 1000 inclusive, what is the probability that Jill’s number is larger than Jack’s?
4. Mental math – neither calculator nor pencil permitted. The sum of the first 50 positive odd integersis 50squared. Find the sum of the first 50 positive even integers.
1. Each day Jane makes an openfaced sandwich using only one slice of bread. She uses 1 kind of meat or 1 kind of cheese or 1 kind of each. If she chooses from 4 kinds of bread, 5 kinds of meat, and 3 kinds of cheese, how many different sandwiches can she make?
2. Ten boys and girls write their names on slips of paper – one name per slip – to enter a prize drawing. Two of the names are drawn at random without replacement. If the probability that both winners are boys is 1/15, how many boys are in the group?
3. If Jack and Jill each randomly choose a whole number from 1 to 1000 inclusive, what is the probability that Jill’s number is larger than Jack’s?
4. Mental math – neither calculator nor pencil permitted. The sum of the first 50 positive odd integersis 50squared. Find the sum of the first 50 positive even integers.
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
1. 4x5 + 4x3 + 4x3x5 = 92
charvaka Posts : 4347
Join date : 20110428
Location : Berkeley, CA
Re: Middle School Math Quiz
2. 3. Basically the denominator of the probability should be 9x10. Expressing it as a fraction of 90, we have 6/90. We also need teh numerator to be (n  1) x n where n is the original number of boys. So n = 3.
charvaka Posts : 4347
Join date : 20110428
Location : Berkeley, CA
Re: Middle School Math Quiz
4. 50squared + 50 = 2550. Basically each of the 50 even integers is 1 more than the corresponding odd number in the first series.
charvaka Posts : 4347
Join date : 20110428
Location : Berkeley, CA
Re: Middle School Math Quiz
3. My intuitive answer is 1/2. Neither of them have higher probability of picking the large number.
charvaka Posts : 4347
Join date : 20110428
Location : Berkeley, CA
Re: Middle School Math Quiz
Incorrect.
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
Which one? Or all of them?indophile wrote:Incorrect.
charvaka Posts : 4347
Join date : 20110428
Location : Berkeley, CA
Re: Middle School Math Quiz
charvaka wrote:Which one? Or all of them?indophile wrote:Incorrect.
Your answer to # 3 (i.e., 1/2) is incorrect.
Yours and HA's answers to 1,2,and 4 are correct.
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Middle School Math Quiz  ANSWERS
indophile wrote:
1. 92. Jane can make 4*5 = 20 kinds of meat sandwiches, 4*3=12 kinds of cheese sandwiches, and 4*5*3 = 60 kinds of meat and cheese sandwiches. Thus, she can make a total of 20+12+60 = 92 different types of sandwiches.
2. 3 boys. Let b= the number of boys. The probability that the first winner is a boy is b/10, and the conditional probability that the second winner is a boy is (b1)/9. The probability that both events occur is is the product of these two probabilities: b(b1)/(10*9) = 1/15. In order for b > 0, b = 3. There are 3 boys in the group.
3. 999/2000. By symmetry, the probability that Jill’s number exceeds Jack’s number equals the probability that Jack’s number exceeds Jill’s number. Therefore, 2*P(Jill’s number > Jack’s number) + P (Jill’s number = Jack’s number) = 1. The probability that Jack and Jill independently choose the same number is 1/1000. Then, (1 1/1000)/2 = 999/2000.
4. 2550. Sum the first 100 integers using Gauss method (Sum = n(n+1)/2). It’s 5050. Then subtract the sum of the first 50 odd integers: 50502500 = 2550 which is the sum of the first 50 even integers.
(Charvaka's solution is even easier than this)
indophile Posts : 4338
Join date : 20110429
Location : Glenn Dale, MD
Re: Middle School Math Quiz
Very nice... I had the idea that neither of them has an "edge," but didn't take it to the logical conclusion.
charvaka Posts : 4347
Join date : 20110428
Location : Berkeley, CA
Similar topics
» Middle School Math Quiz
» Middle School Math Quiz
» Middle School Math Quiz
» Middle School Math Quiz (no questions on probability)
» Middle School Quiz
» Middle School Math Quiz
» Middle School Math Quiz
» Middle School Math Quiz (no questions on probability)
» Middle School Quiz
Page 1 of 1
Permissions in this forum:
You cannot reply to topics in this forum

