<p>If X is the set of positive integers each with one distinct prime factor and Y is the set of integers from 1 to 50 inclusive, then the intersection of X and Y contains how many elements?</p>
<p>(A) 15
(B) 16
(C) 21
(D) 23
(E) 24</p>
<p>This one takes forever to figure out. How would you guys solve something like this without wasting 5mins?</p>
<p>This is not an SAT math question, so don’t waste your time trying to figure out *** a distinct prime factor is.
I would guess A or B if its on math2 though i still doubt it’ll be</p>
<p>There’s a table near the top: [Prime</a> Factor – from Wolfram MathWorld](<a href=“http://mathworld.wolfram.com/PrimeFactor.html]Prime”>Prime Factor -- from Wolfram MathWorld)</p>
<p>I agree with square. This question would probably not show up on the SAT. If it did, it would be in the experimental section.</p>
<p>Thanks a lot guys.
This **** was in a Kaplan SAT practice test.</p>
<p>Both my sons took the Kaplan course and both achieved significantly higher scores on the actual SAT than they did on any of the Kaplan practice tests. I think Kaplan intentionally makes their practice test questions more difficult than those likely to be encountered on the actual SAT hoping customers will be pleased with the Kaplan course for making it possible to get higher scores than they could have gotten just from buying a test prep book.</p>
<p>kaplan and prince review are both useless.</p>
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<p>My favorite part of PR is that they offer free practice SAT’s and SAT II’s to people (that are unbelievably difficult compared to the real thing) and try to lure customers in. I took their free Math II exam, and wrote on the bottom of the answer sheet, “Hi, I know this is a ploy to give me a bad score and have me pay way too much money for your course. Sorry, I ain’t stupid enough to fall for your pathetic marketing strategy. Go to hell.” I still got an 800 on that ridiculous test. :)</p>
<p>The point is this: PR (and probably Kaplan) courses are overpriced and useless.</p>
<p>^Kaplan courses are useless. I took a test from the BB before the course and after the course and only raised my score 70 points. After I self-studied I raised my score 200+ points.</p>
<p>This shouldn’t take too long. Natural numbers 50 or less with only one distinct prime in their prime factorizations.</p>
<p>2 and its powers: 2, 4, 8, 16, 32
3 and its powers: 3, 9, 27
5 and its powers: 5, 25
7 and its powers: 7, 49
11
13
17
19
23
29
31
37
41
43
47</p>
<p>How many was that? It wouldn’t take too long if I could just count 'em and didn’t have to type 'em.</p>
<p>^ When was the last time you made a list that long?</p>
<p>What if the number was 5000? How many can you list now? It won’t take too long if this is an SAT question because there are always tricks and shortcuts.</p>
<p>Definitely not SAT-like…it would be more like an SAT problem if they had asked:</p>
<p>“How many of the postive EVEN integers less than 100 have only one distinct prime factor?”</p>
<p>Still a hard question but the list is much smaller. You would just have to realize that they are asking for powers of 2. The SAT does ask questions that address simple common ideas in unexpected ways.</p>
<p>Square, with paper and pencil, it would have taken me less than 90 seconds–perhaps less than 60–to make that list.</p>
<p>If the question were “natural numbers less than or equal to 5000,” obviously it would be much harder. But it wasn’t, and I think it wasn’t for a reason.</p>
<p>I will admit the possibility that there’s a trick I don’t see, but this looks to me like a question for which the key is to have a sensible strategy and a little information. You need to know primes less than 50. You need to know powers of those primes. The hardest thing about this particular question, IMO, is the wording: you have to know what the question-writers mean by the phrase “one distinct prime factor.”</p>
<p>A real SAT problem will not hinge on whether you know the primes up to 50. It is silly information to memorize and the process of checking for prime-ness is repetitive and unrevealing – you would learn just as much about the test-taker by asking whether ONE number is prime or not. </p>
<p>The much more interesting part of the problem is in recognizing that in addition to the primes, you are also looking for powers of primes. That part of the question IS like the hard questions on the SAT: it requires very little time after you’ve had the insight and really no way to get it right without the insight.</p>
<p>"The much more interesting part of the problem is in recognizing that in addition to the primes, you are also looking for powers of primes. That part of the question IS like the hard questions on the SAT: it requires very little time after you’ve had the insight and really no way to get it right without the insight. "</p>
<p>I agree. And for this reason, I think this is a good SAT review question, even if this question per se would never turn up on an SAT.</p>