January 2013 Problems to solve. Focus: Math Practice 6: Attend to Precision.

1. January Problems
MP6: Attend to Precision

2. 1/2/13 Sums and Products
What three consecutive counting
numbers have a sum that is 20% the
product of the three numbers?

3. 1/3/13 Maximizing Regions
What is the greatest number of
regions you can get if you draw four
straight lines through a circle?

4. 1/4/13 What’s the Rule?
Complete the table by
determining the value of
each letter. What rule is
used to relate the
numbers in the y column
with those in the x
column?

5. 1/7/13 Alphanumeric Puzzle
Find the digits that represent the
letters E, F, G, and H to satisfy the
following puzzle. Each letter
represents a different digit.
E F G H
x 4
H G F E

6. 1/8/13 Rabbits and Cages
Two rabbits each weigh the same. Two cages
each weigh the same. If the total weight of the
two rabbits and the two cages is 24 pounds,
and the weight of one cage is 8 pounds, what
does one rabbit weigh?

7. 1/9/13 Solve this!
Replace each letter with a different counting
number from 1 to 10, inclusive. Each counting
number is to be used only once. Each number
must be the difference of the two above it. For
example, E = A – B or B – A.
A B C D
E F G
H J
K

8. 1/14/13 Zero the Hero!
Use each of the digits 1, 2, 4, 8 once
and only once to make at least two
different expressions that are equal to
0. You may use the operations +, –, x,
and ÷, but may use them more than
once. Parentheses may not be used.

9. 1/15/13 1000’s the Limit!
If you add the consecutive counting
numbers starting with 1, what number
will cause the sum to exceed 1000?
Justify your answer.
=3 1+2+
1+2 3=6
1 + 2 + 3 + 4 = 10

10. 1/16/13 Odd Constraints
Find an integer between 100 and 200
such that each digit is odd and the
sum of the cubes of the digits is equal
to the original three-digit number.
13 = 1; 23 = 8; 33 = 27,...

11. 1/17/13 Tick Tock Sum
By drawing two straight lines, you
can divide the face of a normal
clock into three regions such that
the sum of the numbers in each
region sum to the same whole
number. What would be the
common sum?

12. 1/18/13 A Prime Line
Arrange the integers 1 to 15 in a line
such that the sum of each adjacent pair
is a prime number. For example, 4, 1, 2,
3 would work since 4 + 1 = 5; 1 + 2 = 3;
and 2 + 3 = 5.

13. 1/21/13 How Many Oranges?
A basket of fruit contains only
bananas, apples and oranges.
The basket contains 2 bananas,
6 red apples and 8 green apples.
If the total number of pieces of
fruit is three times the number of
apples in the basket, how many
oranges are in the basket?

14. 1/22/13 Whoosh!
There are six teams in a
basketball league. Each team
plays each other team only
once during the season. How
many total games will be
played in the league during
the season?

15. 1/23/13 Weight your turn
A groups of 6 women and 12 men
weigh a total of 3090 pounds. If
the women in the group have an
average weight of 125 pounds,
what is the average weight of the
men in the group?

16. 1/24/13 What’s my number?
I am a number who is greater than
40 and less than 90. I am proud to
be a prime number. My ones digit is
also a prime number and so is my
tens digit. If you subtract my ones
digit from my tens digit, the answer
is not 2. Who am I?

17. 1/25/13 Buying Books
At a bookstore, books A and B
together cost $45 (excluding
taxes). Two copies of book A and
3 copies of book B cost a total of
$125. At this bookstore, how
much is one copy of book A?

18. 1/28/13 Three Landscapers
Three sisters run a landscaping
business. They charge $260 for each
job. If the oldest sister earns 50% more
than the middle sister, and the youngest
sister earns 50% less than the oldest
sister, how much does each sister earn
per job?

19. 1/29/13 Cubes Not Squares!
What is the smallest perfect cube
(integer of the form n3) that is
divisible by 16 but is not a perfect
square?
13 = 1; 23 = 8; 33 = 27...
12 = 1; 22 = 4; 32 = 9...

20. 1/30/13 A ☼ B
If A ☼ B means A – 3B, find all
possible values of x such that
x ☼ (2 ☼ x) = 1

21. 1/31/13 Inscribe It Again
In the figure at the right, the
smaller square is inscribed in
a circle, which is inscribed in
a larger square that is 8 x 8
cm. Approximately what
percent of the figure is
shaded?

22. adapted from NCTM’s Math
Teaching in the Middle School
Menu Problems
Mar 2006 & Oct 2007