Category 3 - Number Theory
Solutions
October, 1998

Meet#1, October 1998
 
ANSWERS
CATEGORY 3
Number Theory
  1. 84
  2. 421
  3. 8
  1. Listing the multiples of six between 60 and 100 is a reasonable strategy, due to the short size of the list. Numbers from that list can be eliminated by using the other clues, thus leaving the number 84.
     
  2. Prime numbers between 80 and 90: 83, 89
    Composite numbers: 81, 82, 84, 85, 86,87, 88
    (81 + 82 + 84 + 85 + 86 + 87 + 88) - (83 + 89)
    = 593 - 172
    = 421
  3. For a number to be divisible by 18, it must be divisible by 9 and by 2. Whereas W is a units digit, the only reasonable candidates are 2, 4, 6, 8 or 0. The sum of the five digits must be divisible by 9, so the only possible value for W is 8, making the sum of the digits 27, which is divisible by 9.

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