<p>The explanation on my book doesn't provide me enough detail. So please give me an explanation for each questions.</p>
<p>1) What is a possible value of x if 3/5 < 1/x < 7/9?</p>
<p>2) For how many integers, a , between 30 and 40 is it true that 5/a, 8/a, and 13/a are all in the lowest terms?</p>
<p>1) put it in common denominator form. 27/45 less than 1/x less than 35/45. anything from 28/45 to 34/45 would work. since it’s 1/x, you invert it so it could be something like 45/30, which reduces to 3/2=x. </p>
<p>2) so it is my understanding that the terms cannot be divisible by either 5, 8, or 13, otherwise you could reduce at least one of them. 31 is prime and thus indivisible by those terms. 32 is divisible by 8. 33 and 34 cannot be divided by those terms. 35 is divisible by 5. 36, 37, and 38 are not divisible by those terms. 39 is divisible by 13. Thus, 6 terms is the correct answer (31, 33, 34, 36, 37, 38).</p>
<p>The easy way to defeat these types of questions, and the methods I used to get me an 800 on math2:</p>
<p>1: Bring the 3/5 and 7/9 togerther with a common denominator, then plug in the answers, whichever comes out as true, is the correct answer.</p>
<p>2: test all the numbers between 30 and 40 and count how many work. That amount is your correct answer. </p>
<p>Just plugging in answers can be used for so many of the questions on the math section, and can make many questions much easier than they seem.</p>
<p>That question says numbers between 30 and 40. Does that mean 30 and 40 are not included?</p>
<p>34 isn’t in lowest term, when you divide by 8, you can further simplify</p>
<p>1) What is a possible value of x if 3/5 < 1/x < 7/9?</p>
<p>You can flip the fractions and signs, giving the following:
5/3 > x > 9/7</p>
<p>Then find the LCD:
35/21 > x > 27/21</p>
<p>2) For how many integers, a , between 30 and 40 is it true that 5/a, 8/a, and 13/a are all in the lowest terms?</p>
<p>This is true when all the numbers are relatively prime to each other i.e. share no common factors between one another (besides 1). 5, 8, and 13 are all relatively prime to each other (especially since 5 and 13 are prime numbers), and as such a needs to be relatively prime to all three. Which means, that a cannot have the factors of 5, 8, or 13. Which means a is not an even number, doesn’t end with a 5, or is a multiple of 13. The only numbers between 30 and 40 that fits this is 31, 33, and 37. Thus 3 numbers. Reasons are listed below:</p>
<p>30 - even number
31 - is a prime number, thus is relatively prime to other prime numbers, is rel. prime to 8
32 - even number
33 - is not a multiple of 2, 5, or 13, thus is relatively prime to the numbers in question
34 - even number
35 - is a multiple of 5, thus 5/35 will reduce
36 - even number
37 - is a prime number, thus is relatively prime to other prime numbers, is rel. prime to 8
38 - even number
39 - is a multiple of 13, thus 13/39 will reduce
40 - even number</p>
<p>Although you’d have to look at your answer choices whether they mean inclusion or exclusion of the bounds, it’s irrelevant in this case since 30 and 40 are both even numbers.</p>