Question

Dear Mitch,

My classes and I enjoyed yesterday's holiday questions you posted on your site and hope you will continue posting challenge questions throughout the season. I have one student who checks for me as soon as he gets in in the morning, and if there is anything holiday related we print it out and I use it to start my classes off before moving on to the homework assignment from the textbook our district uses. The textbook topics are important, of course, but it is nice to begin a period by having the students work in small groups to solve your holiday-related questions for ten or fifteen minutes before moving on to the next topic in the book.

So, at least from our point of view, it would be great if you could keep those holiday problems coming!

Thank you,

Mr. B

Answer

Dear Mr. B.,

Of course it is my pleasure to post questions that visitors to the site inform us are particularly useful, so check these out:

1. On the first night of Hanukkah, Jake received a bag of jelly beans. By the second night, he had consumed 25% of those candies, leaving him with a remainder of 72. How many jelly beans was Jake originally given?

2. At a particular school, there are 50 seniors. 29 of the seniors celebrate Hanukkah, and 36 celebrate Christmas. If every senior in the group celebrates Hanukkah or Christmas -- or BOTH Hanukkah *AND* Christmas -- how many of these seniors celebrate ** BOTH **holidays?

3. A certain Christmas tree was priced at $125.00. One day before the holiday was to begin, the tree still had not sold, so the store's manager decided to reduce its price by 20%. What is the new price for the tree?

(A) $95.00

(B) $100.00

(C) $105.00

(D) $112.50

(E) $120.00

(F) $122.50

4. For a Hanukkah gift, a builder decided to enlarge the size of his childrens' rectangular playroom. If he doubled the length and doubled the width of the original room, by what percent is he increasing the total area of that room?

5. The ratio of chocolate syrup to cranberry jam in a Christmas gravy is 5 to 2. If 8 pints of cranberry jam are used, how many pints of chocolate syrup are used?

(A) 3

(B) 5

(C) 10

(D) 16

(E) 20

(F) 40

I hope these questions provide some fun challenges to your students, and I will soon post the answers (with explanations). Still, for the time being, I would point out to the students that these problems are designed to seem simple and easy to solve, but -- in order to make them worthy of classroom time and effort, as well as helpful to students wishing to prepare for the kinds of standardized tests they will have to take in the future, these problems were also designed to mimic the deceptively simple-look of many of today's trickiest test questions. So... each of the above may require some discussion before a particular group comes to a correct agreement regarding their answer!

I hope all goes well. I also hope that you, your loved ones, and your students enjoy a happy and healthy holiday season.

-- Mitch