<p>edited: The number 6 has 4 factors: 1, 2, 3, 6. If x is a two digit number with three factors, what is x? (Grid-In)</p>
<p>Isn't there no possible answer? I spent a good 10 minutes during the test on this problem to no avail.</p>
<p>The question didn’t say x had to be prime. Otherwise, this entire statement would be a a contradiction; were x prime, it would only have two factors by definition.</p>
<p>To solve the problem, realize that two of the three factors must be 1 and the number itself. As a result, you can find x by squaring the third factor. The possible answers are 25 (factors 1, 5, 25) and 49 (factors 1, 7, 49).</p>
<p>^ thanks, got it</p>
<p>25 and 49 were possible answers. Their factors are 1, 5, 25 and 1, 7, 49 respectively. The first time through I wrote 16 (1, 4, 16) and then the second time while I was checking I realized that that did not make any sense (it has 1, 2, 4, 8, 16) and changed my answer to 25.</p>
<p>But this question was badly worded. It asked for a positive 2-digit number with “exactly three different factors” and I assumed it meant different factors from that of 6. So I concluded 16 would make sense as its factors were 1, 2, 4, 8, and 16 (three of which are different than the factors of 6)…</p>
<p>I believe that it did say that 6 has four different factors, namely 1, 2, 3, and 6. So you can extrapolate to assume that three different factors means three unique factors.</p>
<p>Edit: did it say if x is a number squared? I’m pretty sure it didn’t.
Edit: it better not have… or I will not be happy.</p>
<p>hm I thought it said “6 has four factors: 1, 2, 3, 6. What is a positive 2-digit integer that has exactly 3 different factors?”</p>
<p>And I assumed that if ‘different’ was used in the question, that it was actually asking for different factors from the example. I mean, it would make less sense for a person to count a factor twice so what would be the point of that clarification</p>
<p>if someone could post the exact question word for word on how it was worded, and if it is proven to be badly worded without a doubt, someone could send an email of complaint to collegeboard regarding the question’s wording and if everyone is lucky, the question wont be part of the score.
- I didn’t have this test version, so I wouldn’t know what the question was.</p>
<p>Agreed! Someone with a photographic or eidetic memory please post. But seriously, is there any way to directly address this issue?</p>
<p>They do sometimes take out questions (though usually in RC). Although would that not make the curve worse for those of us who got it right? After all, removing a level five (I assume this is level five) question would definitely change the test.
Also, they might have been better off saying “unique,” but it is clear that they have to say something. 8 might be considered by someone to have three prime factors if they don’t specify. Not specifying that the factors are different is more prone to lawsuits than specifying it vaguely.</p>
<p>But clearly a person should get it wrong if they had asked for the ‘total’ factors of 16, and then they say it has six factors when it clearly has five. It makes sense to say the factors are 1, 2, 4, 8, 16 but would make no sense to count the 4 twice. I don’t understand why this would need clarification in any case. And I don’t really understand what you mean when you’re talking about the factors of 8 since we’re not talking about prime factor numbers. They clearly asked for ‘different’ factors when stating the question, but I definitely wish someone could remember it exactly. I’m pretty sure it said something like:</p>
<p>“6 has four factors: 1, 2, 3, 6. What is a positive 2-digit integer that has exactly 3 different factors?”</p>
<p>Can this not be read two different ways?</p>
<p>Collegeboard does a lot to make sure that their questions are clear, but they’re not perfect. I only remember that it asked for a number with three different factors.</p>
<p>Yeah and the key lies in asking for ‘different’ factors. If they suddenly used that word in asking the question, following their information about the number 6, then would it not be correct to read it a different way?</p>
<p>Well, as I said, they’re not perfect, and neither is my memory.</p>
<p>I just wish there could be a way to actually see this question again, and possibly bring it to the attention of collegeboard if necessary. Sounds like overkill, but I kinda need the 800 M</p>
<p>Wow, I’m glad I didn’t have this question. Best of luck to you guys/girls.</p>
<p>I agree with you; it was a bit ambiguous</p>
<p>ikr one scenario:</p>
<p>“6 has four factors: 1, 2, 3, 6. What is a positive 2-digit integer that has exactly 3 different factors?”</p>
<p>Interpret as TOTAL factors:
25 (1, 5, 25)
49 (1, 7, 49)</p>
<p>Interpret as DIFFERENT factors:
16 (1, 2, 4, 8, 16) The 1 and 2 are shared factors = 3 different factors
24 (1, 2, 4, 6, 12, 24) The 1, 2, and 6 are shared factors = 3 different factors
35 (1, 5, 7, 35) The 1 is a shared factor = 3 different factors
Possibly a couple others</p>
<p>Send that in to collegeboard, imo. it will probably be a small chance, but nevertheless a chance that it might be omitted.</p>