1.The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers?

2. How many integers between 100 and 500 have at least two 3s as digits?

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- Sep 18th 2013, 09:31 PMNadeshikoIntegers
1.The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers?

2. How many integers between 100 and 500 have at least two 3s as digits? - Sep 18th 2013, 10:16 PMchiroRe: Integers
Hey Nadeshiko.

Hint: Calculate the arithmetic mean as a function of n (n is the first number) and derive an inequality based on this. (you are going to have (10n + blah)/10 = 3 for your mean relationship). - Sep 19th 2013, 05:28 AMHallsofIvyRe: Integers
If "x" is the first of "10 consecutive even numbers" then the numbers are x, x+2, x+ 4, x+ 6, x+ 8, x+ 10, x+ 12, x+ 14, x+ 16, and x+ 18

What is the mean of those 10 numbers?

For the second, note that these numbers are of the form 133, 233, 433, 3x3 or 33x where x can be any digit from 0 to 9 except 3.