<p>How many positive 3-digit integers contain the digit 9?</p>
<p>A.180
B.190
C.200
D.252
E.648</p>
<p>explain your reasoning, thanks.</p>
<ol>
<li>I figured 900-999 is 100 of them. Plus another 80 for units digits. Plus another 72 for tens digits. It's hard to explain my reasoning, sorry.</li>
</ol>
<p>There's 19 in every group of one hundred (109, 119, 129... 189, 190-199). That's 10 groups of 19 for 10 one hundreds, so 190.</p>
<p>That's my quick guess.</p>
<p>^Um....what about the 900's...</p>
<p>^ 100 answers between 900 and 999.</p>
<p>choklitrain is correct.....let me explain</p>
<p>See, that's why I'm bad at rushing math. >_></p>
<p>1.first,think that u r putting the 9 in the hundreds place....then u have 10 choices for tens place(0 to 9---10 choices) and u have 10 choices for the units place...so 10x10=100 numbers
2.now u r putting the 9 in the tens place.then u have 8 choices for the hundreds place(1 to 8------0 and 9 doesnt qualify coz 0 will make it a two digit number and 9 is already used before) and u have 10 choices for the units place......so 8x10=80 numbers
3.now u put the 9 in the units place....so u got 8 choices for the hundreds place(mentioned it before why its like this) and u will have 9 choices for tens place(this is really tricky,u have to understand that u can't choose 9 for tens place coz u already chose it once) so 8x9=72 numbers...</p>
<p>so in total u have 100+80+72=252 numbers</p>
<p>tomorrow is my SAT.....please pray for me..... :)</p>
<p>math is so awesome......i wish SAT didn't test ENGLISH :( i m so bad at english</p>
<p>Gluttony and Chokolit are correct! Thanks guys.</p>