Download 2004-2005 Meet 1

SOML MEET
EVENT 2
Number Sense
1.
NAME: _____________
TEAM: _____________
SCHOOL: _____________
[2 Points]
A number is “perfect” if the sum of its proper factors is equal to the
number itself. For example 6 is perfect because the sum of its proper factors, 1 + 2 + 3 =
6. Which, if any, of the following numbers is perfect?
10, 28, 46
ANS: _________
2.
[3 Points]
A friend opens a book and multiplies the two page numbers together, then
turns one page and multiplies those two page numbers together. The sum of these two
products is 2246. What were the page numbers?
ANS: _________
3.
[5 Points]
Any number less than 900 is prime if none of the following primes are
among its factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. What is the largest three-digit
prime number such that each of its digits is prime?
ANS: _________
SOML MEET
EVENT 2
Number Sense
1.
[2 Points]
NAME: ___KEY______
TEAM: _____________
SCHOOL: _____________
A number is “perfect” if the sum of its proper factors is equal to the
number itself. For example 6 is perfect because the sum of its proper
factors, 1 + 2 + 3 = 6. Which, if any, of the following numbers is perfect?
10, 28, 46
Solution:
10 ≠ 1 + 2 + 5
28 = 1 + 2 + 4 + 7 + 14
46 ≠ 1 + 2 + 23
ANS:
2.
28
[3 Points]
A friend opens a book and multiplies the two page numbers together, then
turns one page and multiplies those two page numbers together. The sum
of these two products is 2246. What were the page numbers?
Solution:
Guess and check around:
.
2246
≈ 33.5
2
Pages 32, 33, 34, and 35
ANS: Pages 32, 33, 34, and 35.
3.
[5 Points]
Any number less than 900 is prime if none of the following primes are
among its factors: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29. What is the largest
three-digit prime number such that each of its digits is prime?
Solution:
The largest possible prime digit is 7 then 5, 3 and 2 in that order. Try 7 in
the hundredths, tenths, and ones place. Since 777 has a factor from the list
continue testing the prime digits systematically from largest to smallest.
777 is not correct because it has a factor of 7.
775 is not correct because it has a factor of 5.
773 is the largest number that is not divisible by the list of primes.
ANS:
773 .