<p>Hello guys,
Can you help me with these 3 questions?</p>
<ol>
<li><p>When 53 is divided by a positive integer n, the remainder is 3. How many values of n are possible?</p></li>
<li><p>A restaurant has 36 tables that can seat up to 4 people each. If two of these tables are put together, the two tables can seat up to 6 people. What is the maximum number of people that can be seated if there are the same number of 4 person and 6 person table configurations?</p></li>
<li><p>2^x = 8^y, where x and y are positive integers, which of the following is equivalent to 8^(x+y)?</p></li>
</ol>
<p>a. 2^(3x)
b. 2^(4x)
c. 2^(3x^2)
d. 2^x^4
e 2^(3x) +2^x</p>
<ol>
<li><p>This is equivalent to finding all divisors of 50, as 50 leaves remainder 0 when divided by n. 50 has 6 positive integer factors. But we have to exclude 1 and 2 because the “remainder” wouldn’t be 3.So the answer is 4.</p></li>
<li><p>Three tables altogether seat 10 people. 36 tables can seat at most 120 people.</p></li>
<li><p>8^(x+y) = (8^x)(8^y)</p></li>
</ol>
<p>8^x can be written as (2^x)^3 and 8^y can be written as 2^x. Multiplying these two gives (2^x)^4. This is equivalent to choice B (in choice D, I believe you find x^4 then raise 2 to that power).</p>
<p>THANK YOU VERY MUCH !!!
I believe that you have a really high score in the SAT right?
Your explanations are SO clear.
I believe you will be an amazing math guru if you want to be.</p>
<p>Just one simple question:
Why do we care in the first problem that 50 leaves remainder of 0 when divided by n?
Is this the step to make when we have a remainder problem?
I understand the solution for this problem. I just don’t get why did we start from there.
( My math teachers didn’t teach me the remainder ( International student) )</p>
<p>By the way, since you seem to own the May 2013 QAS, you might want to google SATQuantum and check the video tutorials. Tipping my hat to one more of the nice contributors to this site. :)</p>
<p>Yeah, problem 3 is a pretty easy plug-in question. I usually don’t plug in (but that’s just my personal preference) although I may pick random x,y just to check.</p>
<p>However I would not recommend plugging in for #1 (i.e. dividing 53 by 1, 2, 3, etc.).</p>
<p>18 individual tables which seat 4 people each (so, 72 people) + 18 other tables, which we combine every two tables for to make 9 tables which seat 6 people each (so, 54 people).</p>