Hands-on math!

Washington State Math Olympiad
Hints and Solutions
2012 Grade 7 Number Sense

Problem
Hint
1) Jimmy is 10/9 as tall as Ying'ai. Ishmael is 4/5 as tall as Amanda. The difference between Amanda and Ying'ai is 4 inches. Ishmael is 14 inches shorter than Ying'ai. Ying'ai is 4 feet 6 inches tall. How tall is Jimmy? With this type of problem you start at the bottom and work backwards. First, convert all heights to inches for easy comparision
  1. Ying'ai is ____ inches.
  2. Since all you want is Jimmy's height, you can forget Ishmael and Amanda.
  3. Jimmy's height is ____________

2) A two digit number is divided by a two digit number with quotient a one digit number. The five digits used are 1, 2, 4, 7, 8 and each is used only once. What is the larger two digit number?
  1. The larger number must start with a 4, 7 or 8 for it to be divided by another number to make a single digit quotient.
  2. It must also be even and end in 2,4 or 8 for it to be divisible evenly by the remaining numbers because there is no 3 here.
  3. Try several combinations:


  4. The higher number is _____
3) Donna has 1/8 tank of gas remaining when she pulls into a gas station. After she puts 15 gallons of gas in her car, the gas gauge reads 3/4 full. How many gallons does Donna's tank hold?
  1. The 15 gallons occupied _____ of the tank.

  2. The total tank capacity is _____ gallons.

Problem
Hint
4) One tactic for adding fractions with complicated denominators is to use their prime factorizations to find a least common multiple. Try that here: What is the denominator for the sum
    a     +     b  
  924       364
when expressed as a single fraction in lowest terms?
  1. Prime factorization for 924:

    ___________________________
  2. Prime factorization for 364:

    ___________________________

  3. Common prime factors = _________

  4. So the greatest common factor (GCF) of 924 and 364 is ____
  5. Using the GCF-LCM equation:
    LCM (924,364) = ________
5) What is the smallest whole number n so that
  1. Compute (34)n for n = 1,2,3, ... until it falls below 13
    n = _____