Math Question - english translation issue

<p>A number is considered "odd-mult" is it is the multiple of exactly two consecutive odd numbers. How many positive numbers less than 400 are "odd-mult"?</p>

<p>Note: this is a grid-in question</p>

<p>What does this mean: "is the multiple of exactly two consecutive odd numbers." I incorrectly thought that this meant that the number cannot be the multiple of any other number except these two consecutive odd integers. For example, 15 is the multiple of 5 and 7, and the multiple of no other number.</p>

<p>It's a poorly worded question. We'll need a lawyer to figure out whether it means that the consecutive odd factors are the only factors or that they are two of the factors and that there could be others. I'm inclined to think that the question writer did not intend to "confuse" or "trick" the test taker. This is a math problem and not a CR problem after all.</p>

<p>So:</p>

<p>The factors are 2n+1 and 2n+3, where n is equal or greater than zero,
and N=(2n+1)*(2n+3)<400, or n=0, 1, ..., 9.</p>

<p>I don't quite understand why the factor would be 2n+1 and 2n+3. Where did the 2 come from?</p>

<p>The answer in Princeton Review was 10. </p>

<p>Yeah, the wording is confusing. Hopefully collegeboard writers will only ask questions that are not ambiguous.</p>

<p>This is a terrible question and obviously wasn't written by the college board. If you are just worried about SAT preparation, then I would not spend any time worrying about this question.</p>

<p>If you're interested in the question out of mathematical curiosity, then we can reword it several diferent ways to come up with a few different "interesting" questions.</p>

<p>To expand my previous post and answer ...</p>

<p>A generic odd number is an even number plus 1 -- i.e. 2n + 1 where n is an integer. So when n=0 you get 1, with n=1 you get 2*1 + 1 = 3, and then 5, 7, etc.</p>

<p>Two consecutive odd numbers are 2n + 1 and 2n + 3. So with n = 0 you get 1 and 3, and with n = 1 you get 3 and 5, and so on.</p>

<p>The equation (2n + 1)<em>(2n + 3) < 400 has 10 possible answers -- with n = 0 you have 1</em>3, with n =1 you have 3 * 5, etc. and finally with n = 9 you have 19<em>21 which is barely less than 400. With n = 10 you get 21</em>23 which is greater than 400.</p>

<p>So that's how you get 10.</p>

<p>You can also just write it out: 1,3,5,7,9,11,13,15,17,19,21,23, ... and look at the pairs 1<em>3,3</em>5,5<em>7, ...19</em>21. This way you'll quickly see that the answer is 10.</p>

<p>FYI, a very similarly worded question (or two) was in the blue book. Instead of the weird symbols, they can do these questions too.</p>

<p>An evident observation is that 20*20=400, so the max you'll go is around 20.</p>

<p>You start multiplying every consecutive odd number then - 3<em>1(if the answer's 10, they consider 1 odd), 3</em>5, 5<em>7, 7</em>9...<em>17</em>19, but just check 19*21 anyway, and it turns out to be 399. So there you are.</p>

<p>Actually, this is ALMOST a good question. If you change the word "multiple" to the word "product", you have a very realistic SAT-type question.</p>

<p>Agreed pckeller. That is most likely the question that was intended.</p>