<p>Hi guys. I was wondering if anybody was up for solving SAT math problems and help explain these problems to me at the same time. Thanks!</p>
<ol>
<li>When positive integer n is divided by 5,
the remainder is x. When 2n is divided by
5, the remainder is y. Which pair (x, y) is
not possible?</li>
</ol>
<p>2.The positive integer x is a product of three different prime numbers, p, q, and r. If r>q>p, which of the following must be true?</p>
<p>I. The greatest prime number that is a factor of x is r.
II. If p > 5 then x is not divisible by 5.
III. x2 is divisible by p, q, and r. </p>
<p>a. III only
b. I and II only
c. I and III only
d. II and III only
e. I, II and III</p>
<p>If number 1 is a multiple-choice question, please provide the answers so that I can answer it for you.</p>
<p>For number 2, plug in numbers. 6 is a product of 1 x 2 x 3.
1, 2, and 3 can be known as prime numbers since they only have 1 and itself going into themselves.</p>
<p>r is greater than q greater than p.
3 > 2 > 1</p>
<p>Since 3 is biggest factor of 6 here, we can assume that I is true.</p>
<p>P > 5. 10 is one, but 10 is composite and divisible by 5; it’s not prime. So II is untrue.</p>
<p>x^2 = 6^2 = 36 is divisible by 1, 2 , and 3. 1 into 36 is 36, 2 into 36 is 18, and 3 into 36 is 12. III is true.</p>
<p>Therefore, answer is C. Please double check it to make sure that I’m right or else it means I’ve given you the wrong answer or explanation.</p>
<p>Since x is a product of 3 different prime numbers, the only way for it to be divisible by 5 is is one of the prime numbers p, q, or r is 5
If p<5, then p≠5
And since p is the smallest number out of the 3, that means q and r cannot equal 5</p>
<p>If you construct a number by multiplying 3 prime #s, the only factors will be the original 3 primes and any combination of the products of those 3 primes. So if you start with 3 primes all greater than 5, there is no way for 5 to be a factor of the resulting product.</p>
<p>If you don’t see it, try using say 7, 11 and 13. When you multiply them, the factors of the resulting number will be 7, 11, 13, 77, 91, and so on…but not 5.</p>