<p>random math question..
can anyone show me how to solve?
how many even integers between 100 and 200 are divisible by 3?</p>
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<p>Ok, so clearly 102 and 198 are gonna be your first and last (if you need help with that one-- any number whose digits add up to a number divisible by three is also divisible by three... 1 + 0 + 2 = 3, 1 + 9 + 8 = 18, etc.)</p>
<p>So 102 and 198 are your first and last ones.</p>
<p>Divide both those by three, you get 34 and 66. So that means 3 times every number between 34 and 66 (inclusive) is in that set. So start with 66, take away all the numbers below 34... 66-33 = 33.</p>
<p>3<em>34, 3</em>35 ... 3<em>65, 3</em>66 are all the numbers divisible by three in that set. 33 numbers.</p>
<p>An even integer divisible by 3 means it's an integer divisible by 6. 100/6 = 16.67 and 200/6 = 33.33 . So the integers in question are from ceiling(16.67)<em>6 to floor(33.33)</em>6, in multiples of 6</p>
<p>17<em>6, 18</em>6, ...., 33* 6 or (1+16)<em>6, (2+16)</em>6 .... (17+16)*6</p>
<p>There are 17 such integers.</p>
<p>Oh my bad, I didn't see the "even" part. Yeah, 17.</p>
<p>lol I didn't either... it's these type of small things that really ruin the 800 score... you have to be super careful on the math section because even one or two wrong drops you down to like 750 and below.</p>