Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2007 Grade 6 Number Sense
Problem
Solution
1) Damian has a 7 digit phone number. The first 3 digits are consecutive in strictly decreasing order and sum to 6. The last 4 digits make up an odd number that is the product of the squares of two consecutive odd numbers and make the number as large as possible. What is Damian's phone number? 1. There are only 3 numbers in decending order that sum to 6.
    These 3 numbers are 3, 2, and 1
2. Fill out this table until you find 2 consecutive odd numbers that the multiple of their squares is odd and is under 9999:
  N     N1 =
N+2   		    N2     N12    N2 x N12
7949813969
911811219801
111312116920449
3. Put the first 3 numbers together with these 4 numbers (the last column) to
    make the telephone number: 321-9801

2) HT6 is a 3 digit number that is a multiple of 3 and 14. The sum of H + T is a multiple of what number? 		1. The least common multiple (LCM) of 3 and 14 is 3 x 14 = 42
2. Since this 3-digit number is a multiple of this least one, list the multiples of this LCM that are
(a) 3 digits long and
(b) end in 6: (you just need a couple)
    42 x 3 = 126
    42 x 8 = 336
    42 x 13 = 546
3. The sum of the first 2 digits of all of these numbers is divisible by 3

Problem
Solution
3) The Van Hogens have a bulb farm. They hire Janice to help them harvest the bulbs. They take her to a field and tell her to dig out 5/6 of the bulbs in each row based on plant size. Then she must sort out the best 3/4 of the bulbs she dug out. Finally she must take half of the sorted bulbs and put them in a crate and the other half in a bin in their store. How many bulbs went in the crate if a row holds 96 bulbs? 1. Multiply 5/6 x 3/4 x 1/2 to get the fraction of bulbs in a row that she dug up =
    5/6 x 3/4 x 1/2 = 15/48 = 5/16
2. Multiply this by the number of bulbs =
    96 x 5/16 = 30 bulbs

4) A store buys potatoes from a local farmer at 45 cents/lb and then sells these same potatoes at 99 cents/lb. What percent profit does the store make on these potatoes? Round your answer to the nearest 1 percent.		 Take the price the store sells the potatoes for and subtract the amount he/she paid and then divide by the price he/she paid =
    (99 - 45)/45 = 120% profit.

5) Jerri has 2 3/4 yards of rope. He needs pieces that are 2/3 yard long to make belts for costumes. How many belts can he make?		 1. Convert all measurements to inches.
    2 3/4 yards = 99 in.; 2/3 yard = 24 in.
2. divide the length of rope by the length of belts =
    99/24 = 4.125
3. Round down to the next number of belts = 4 belts