SAT Math Question

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1

<p>Hi all,</p>

<p>I'm confused with this question..</p>

<p>1, 2, 3</p>

<p>If m, n, and k are to be assigned different values from the list above, how many different values will be possible for the expression (m + n)^k ?</p>

<p>(A) Three
(B) Four
(C) Five
(D) Eight
(E) Nine</p>

<p>I chose C, but the correct answer is A.</p>

<p>Here's my work, what's wrong with it?</p>

<p>( 1 + 2 ) ^ (3 or 1) = 27, 3
( 1 + 3 ) ^ (2 or 1) = 16, 4
( 2 + 3 ) ^ (1) = 5</p>

<p>Five values, correct? It would be (A) if (1+2)^1 and (1+3)^1 didn't count as a 'different value'. Someone please explain why the answer is (A)?</p>

2

<p>

</p>

<p>What’s wrong with your work? Why do you have two values for k? </p>

<p>There are only three solutions:</p>

<p>(1 + 2) ^ 3
(1 + 3) ^ 2
(2 + 3) ^ 1</p>

3

<p>Oh wow, I didn’t see that. LOL.
Thanks for pointing out my error though. :)</p>

4

<p>By saying that each letter must have a different value, it means that you can use each value only once. So those two possibilities that you listed would not count. I. Other words, your math is fine. You just misunderstood what the question was saying.</p>

5

<p>Also, would you mind explaining this:</p>

<p>In triangle ABC, AC = 6, and BC = 3. Point P lies on AB between A and B such that CP is perpendicular to AB. Which of the following could be the length of CP?</p>

<p>(A) 2
(B) 4
(C) 5
(D) 7
(E) 8</p>

6

<p>Don’t feel bad, I make careless mistakes all the time :).</p>

<p>About your second problem, is ΔABC a right triange?</p>

7

<p>It’s not specified in the problem.
I just assumed it to be (C), 5, but the correct answer is (A), 2.</p>

8

<p>I remember seeing this problem a couple of weeks ago. DrSteve’s explanation may help. Good luck!</p>

<p><a href=“http://talk.collegeconfidential.com/sat-preparation/1176816-math-help.html[/url]”>http://talk.collegeconfidential.com/sat-preparation/1176816-math-help.html&lt;/a&gt;&lt;/p&gt;

9

<p>I think the answer is (a) because the length of an altitude has to be greater than its adjacent sides.</p>

10

<p>@OP you can also solve it logically, the adding part doesn’t really matter because order of addition doesn’t matter, leaving you only with the three values for the exponents.</p>

11

<p>Sorry, I was half asleep when I wrote my previous post. I’ll explain it a little more. </p>

<p>

</p>

<p>CP is an altitude of triangle ABC because P lies on AB and CP is perpendicular to AB. The triangle is now divided into two right triangles. CP is a leg of both right triangles. The two hypotenuses of the two right triangles are AC and BC, the lengths of which are 3 and 6. You know that the length of a hypotenuse must be greater than the length of a leg, so the length of CP must not exceed 3 or 6. The answer is (A) 2.</p>