Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2013 Grade 8 Number Sense

Problem
Hint
1) When you simplify the terms in the following sequence to reduced fractions an interesting pattern occurs. Find out what it is and use it to determine the value of the tenth term as a reduced fraction.
Start simplifying the terms from the simplest to the more complicated ones. You'll notice that your previous simplification can be used for each successive simplification. At some point, you may notice a pattern.




The 10th term = ______

2) What is the missing term in this sequence?
    1, 3, 3, 9, ___________, 243.


Each term involves multiplication with previous terms.

Problem
Hint
3) What is the digit in the one's place of 6734?

This kind of problem relies on the fact that some numbers have repeating one's place digits when taken to increasing powers. Keep taking powers of 3 (2,3,4, ...) until you notice a pattern. Divide the power you want by the number of repeating digits. The remainder will be the number of the digit in the repeating sequence.






The one's digit is _____
4) Counted cross stitch is a way of painting by stitching with silk thread. Each cross stitch fills a (3/16) inch x (3/16) inch square. How many stitches go in to a 12 x 15 inch cross stitch painting?

Compute the area of the cross stitch and the area of the painting and divide the area of the painting by the area of the cross stitch.



______ stitches are in the painting.
5) Ruby selects earrings from a rack that are all priced the same. The store has to charge 10% tax. If there was no sales tax, then Ruby could buy one more pair of earrings for the same amount of money she is spending. How many pairs of earrings is she buying? Let N = the number of pairs of earrings Ruby is buying.
The amount Ruby pays totally is (in terms of N) __________
Set that equal to one more pair of earrings and solve for N:



N = _____