Help for Writing + Math Questions

Test Preparation SAT Preparation
1

<p>Hey guys! Here are some questions that I had questions about:</p>

<ol>
<li>Introducing new ideas and replacing old ones is always a highly controversial matter, especially when there is already tension between an older and a younger generation. </li>
</ol>

<p>The answer is E (No Error).</p>

<p>Because there are two subjects, wouldn't this sentence be better (and correctly) written as
[quote]
Introducing new ideas and replacing old ones are always highly controversial matters

[/quote]
</p>

<ol>
<li>Just when those who were watching from the sidelines feared the worst, the athletes themselves are the most confident.</li>
</ol>

<p>The answer is D. Why is that the case and how would you correct this?</p>

<ol>
<li>How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which are prime?</li>
</ol>

<p>(A) Zero
(B) One
(C) Two
(D) Three
(E) Four</p>

<p>The answer is D. 21,22, and 26 are the supposed answers. Initially I answered A (Zero) because nothing has just two factors. Personally, I feel like the wording of this questions is messed up and confused me to pick zero. This might sound convoluted, so I'll express what I mean the following way:</p>

<p>21 has factors 1,3,7, and 21. Thus, according to the question, it is not the product of exactly two different numbers. It could also be the product of 21 and 1, both of which are not a prime. </p>

<p>Thanks in advance!</p>

<p>(It's late so I might sound stupid as I tried to describe my thinking in number three)</p>

2

<ol>
<li><p>Notice the latter part of the sentence reads ‘a highly controversial matter’. The two actions are being treated as one, as they are related.</p></li>
<li><p>I think the answer is D because ‘were’ should replace are, as the first part of the sentence took place in the past</p></li>
<li><p>Thats EXACTLY what i did for number 3, i think the wording is a bit off…</p></li>
</ol>

3

<p>Did you take this test for Elite? LOL.</p>

4

<p>21 = 3<em>7 and 3 and 7 are both prime.
22 = 2</em>11 and 2 and 11 are both prime.
23 = You might think of 1<em>23, but 1 is not prime.
24 = 3</em>8 or 4<em>6, or 2</em>12, or 1<em>24, but none of
those is the product of 2 primes.
25 = 5</em>5, 5 is prime but the two 5’s are not different numbers.
26 = 2<em>13 and 2 and 13 are both primes.
27 = 3</em>9 but 9 is not prime.
28 = 4<em>7 or 2</em>14 but neither is a product of two primes.
29 = You might think of 1*29, but 1 is not prime.</p>

5

<p>For the number N the prime factors are divisors other than 1 and N. That’s the definition.</p>

6

<p>LoseYourself,</p>

<ol>
<li>How many integers greater than 20 and less than 30 are each the product of exactly two different numbers, both of which are prime?</li>
</ol>

<p>Remember, 1 is not prime, therefore it cannot be a prime factor. The prime numbers start from 2 and go on as 3, 5, 7, 11…</p>

<p>The question requires a number that is (1) greater than 20, (2) less than 30, and has (3) exactly 2 factors that are (4) prime and (5) different.</p>

<p>21 is because its prime factorization is 3 * 7
22 is because its prime factorization is 2 * 11
23 is not because its prime factorization is 23
24 is not because its prime factorization is 2 * 2 * 2 * 3
25 is not because its prime factorization 5 * 5
26 is because its prime factorization is 2 * 13
27 is not because its prime factorization is 3 * 3 * 3
28 is not because its prime factorization is 2 * 2 * 7
29 is not because its prime factorization is 29</p>

<p>Hope I helped,
SilverAurora</p>

7

<p>Thank you guys! I kind of understand the first two now.</p>

<p>

</p>

<p>No, why do you ask?</p>

8

<p>

</p>

<p>The question never said anything about prime factors or divisors.</p>

<p>

</p>

<p>This is the wording problem I had earlier. You see… no number between 20 and 30 has only 2 factors…Technically speaking, no number would fit this description as 1 is not a prime number. </p>

<p>Seriously though… am I the only one who is getting tripped up by the wording of this?</p>

9

<p>I think that you’re overthinking this question.</p>

<p>Do a quick review of the definition of “primes”, “divisors”, “factoring of integers”. It’s all very straightforward. The SAT (assuming that this question is coming from an actual SAT) expects that you know these definitions. My sense from your posts is that the detailed definitions are new to you.</p>

<p>The question as stated is not attempting to trick you in any way.</p>

<p>… “exactly 2 factors that are prime and different” means that the number must be “factorable into exactly two unique primes”.</p>

<p>You can solve problems of this kind very simply and systematically.</p>

<p>N=p1*p2, where p1 and p2 are prime and not equal to 1 or N. Start with the smallest prime that’s not 1 or N – i.e. p1=2, and look for values p2 greater than p1. Now what are possible values for p2? Only p2=11 or 13. What’s the next smallest prime p1 – i.e. p1=3. And for this value what are the possible values of p2? Only p2=7. The next smallest prime is p1=5. But for this value there are no p2s (p2>p1). There is no point to try still larger p1s since we know that there won’t be a p2.</p>

<p>Try the same problem where the product is greater than 30 but less than 50. Here again start with p1=2. p2 can be be 17, 19, 23. Then work with the next smallest p1 – i.e. p1=3. p2 can be 11, 13. Then the next smallestp1 – i.e. p1=5. For this p2 can only be 7. The point in requiring that p2>p1 is to avoid double counting.</p>

<p>Underlying questions of this kind is a fundamental theorem in arithmetic – that an integer (assume positive) is uniquely factorable as a product of primes.</p>

10

<p>Thank you for explaining the question!</p>

<p>

</p>

<p>I still have a problem with this. When I first saw the question, I comprehended that the number had to have only 2 factors, of which also have to be prime and different. This might be more semantics than anything because I know how to do the question if it was rephrased like:</p>

<p>

</p>

<p>IMHO, that would be less confusing.</p>

11

<p>Anybody want to comment or correct my thinking on the wording of the math problem?</p>

12

<p>So I’m the only who construed the meaning of this question in a messed up way?</p>

13

<p>^ no haha i did the same thing as i stated above, dont worry :P</p>

14

<p>^</p>

<p>:D. Now I’m really scared that this will happen on the real SAT. :'(</p>

15

<p>I thought that problem was straightfoward and not misworded. </p>

<p>(got an 800 Math and 800 Math Level 2)</p>

16

<p>^</p>

<p>Thank you for the response, SheepGetKilled!</p>

17

<p>Were these questions from practice test 10? LOL cause I just took it</p>

18

<p>^</p>

<p>Yup.</p>

<p>tanchar.</p>