<p>Is CB using different tests? I can’t remember this question showing up on my test…</p>
<p>Same; is this version 2?</p>
<p>It was kind of obvious, I don’t even think it was Dl5 or 4. My answer was 14, the smallest possible answer. (factors 1,2,7). Sorry if I ruined it for you all.</p>
<p>It may be that they listed the factors of 6 to show that you were intended to consider all of the factors and not just the “proper divisors”.</p>
<p>There is a blue book question that explores this same theme. I don’t remember which one, but you had to find a number that had only 3 factors and the answer is 121. The idea is that a numbers factors come in pairs unless the factor is a perfect square. So to have only 3 factors, one of them has to be a square.</p>
<p>@LeBombedTest 14 is a factor of 14.</p>
<p>My friend told me about this question and i figured it out in like 2 seconds and get 49 or 25 as my answers… 2 digit squares is what youd have to check for.</p>
<p>Bhph that’s not what the question asked for. I seem to remember the question asking for a number with exactly 3 different factors from the ones listed. I put 35 because it has 5, 7 and 35</p>
<p>35 has four factors </p>
<p>the question was more worded like this : “Given that 6 has four factors: 6, 3, 2, 1, What is one possible positive 2-digit integer that has exactly 3 different factors?”</p>
<p>Please someone send it the the college board already two other questions wrong…</p>
<p>If this was in fact how it was worded…</p>
<p>“Given that 6 has four factors: 6, 3, 2, 1, What is one possible positive 2-digit integer that has exactly 3 different factors?”</p>
<p>…then this is a completely valid question as written with only 25 and 49 as answers. No point sending it to college board…</p>
<p>I really think they listed the factors of 6 to be nice! They were trying to say “hey, don’t forget about 1 and the number itself when you are counting the factors.”</p>
<p>The key word is GIVEN. This means that when the word DIFFERENT is used, they are asking for a number with exactly 3 factors DIFFERENT from the factors 6 has.</p>
<p>Ok guys I’m going to send an email to collegeboard about the ambiguity of the question right now. So anyone else who had issues with it PLEASE also send an email. If there are more of us complaining about it, rather than just one, I think it is very likely we can get it thrown out.</p>
<p>The collegeboard site says:
“Test Error or Ambiguity
If you encounter a test error or ambiguous question, continue testing. Report the problem to the supervisor before you leave the test center, then write to us, including the test section, the test question (as well as you can remember it), and an explanation of your concern. The SAT Program will respond to written inquiries.”</p>
<p>For obvious reasons, you can say that you didn’t report the problem to the test supervisor because you were unaware that you were supposed to do so, but you did realize that it was badly worded at the time.</p>
<p>Send the email to: <a href="mailto:satquestion@info.collegeboard.org">satquestion@info.collegeboard.org</a></p>
<p>Give accurate and detailed responses!</p>
<p>VanillaThunder said:</p>
<p>"The key word is GIVEN. This means that when the word DIFFERENT is used, they are asking for a number with exactly 3 factors DIFFERENT from the factors 6 has. "</p>
<p>No such number could exist. The number will certainly have 1 as a factor which is of course also a factor of 6. “Different” must be taking about from each other – so that you don’t double-count squares.</p>
<p>@pckeller
Of course a number like that could exist…</p>
<p>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>And I honestly think it’s weird that collegeboard would need to use that phrasing as clarification for not double-counting squares. I mean a person should not count 4 twice when it is clearly one factor of 16…</p>
<p>34 doesn’t work: 1,2,3,4,6,8,12,24 - 4 “different” factors 4,8,12, and 24.</p>
<p>Perhaps they should have used 9 as an example instead of 6. They used the word different to indicate not to double count the root of the square, but they showed the example to indicate they intended for the number itself to be a factor. Many people, when asked to list factors don’t consider the number itself, when they should. </p>
<p>If they had not used the word different, how many people would have come up with 10 or 14, 15, 21,35… They could have used the work unique, but they had means different from the factors of 6, they would have written “other.”</p>
<p>None of those numbers have 3 factors that are different from those of 6.</p>
<p>Who said anything about 34?</p>
<p>And I understand that the example was given to clarify that you count 1 and itself. However, I still don’t believe that their use of the word ‘different’ was clear in any sense. It is obvious that a person should only count 4 as one factor since it is clearly one factor. Counting it twice makes no sense regardless. If they had simply omitted the word ‘different’ then the question would have made sense.</p>
<p>“Given that 6 has four factors: 1, 2, 3, 6. What is one possible positive 2-digit integer that has exactly 3 factors?”</p>
<p>Now THAT would make it clear. If people were to count the square twice, then there would be no possible numbers that would fit the question, so I don’t see how a person could get confused. This way they’re just asking for a number with 3 factors while still making it clear that you count 1 and itself</p>
<p>Factors of an integer are assumed to be <em>distinct</em> factors. Factors of a number are assumed to be positive as well – otherwise all number theory conjectures such as whether odd perfect numbers exist would be ill-defined.</p>
<p>It happens that a positive integer n has an odd number of factors if and only if n is a perfect square (this is fairly easy to prove). In particular, the square of a prime number has three factors: 1, p, p^2. The only possible two-digit integers that satisfy this property are 25 and 49.</p>
<p>Apparently from 2005 to 2008 College Board only took out 6 questions (three just for misprints!) eh this sucks [Appealing</a> a Test Score - New York Times](<a href=“Appealing a Test Score - The New York Times”>Appealing a Test Score - The New York Times)</p>
<p>Have faith! We got this! Lets throw it in their faces</p>
<p>I still hold that the word “different” didn’t appear in the question. If it had, the answer could also be that none exist, because stating that the number has “three DIFFERENT factors” from 6 could also mean that the number you are trying to find has factors that 6 does not have.</p>
<p>I completely understand the point you are making, but perhaps the word “different” simply appeared on this forum when someone restated the question looking for an answer. Personally, I am 99% sure the word was not in the question.</p>