Explation for Princeton Review question please

Test Preparation SAT Preparation
1

<p>It says:
17. A student took five tests. He scored an average(arithmetic mean) if 80 on the first three tests and an average of 90 on the other two. Which of the following must be true?</p>

<p>I. the student scored more than 85 on at least one test
II. the average score for all five tests is less than 85
III. the student scored less than 80 on at least two tests</p>

<p>(a) I only
(b) II only
(c) I and II
(d) II and III
(e)I and III</p>

<p>their answer and explanation:
C<br>
Notice the word "must" in the question? Let's plug in so that we can work with real numbers and because the word "must" is in the problem, we can expect to plug in more than once. Because we want to use numbers that are easy to work with, lets use 78, 80,and 82 for the first three tests, and 88 and 92 for the last two. That makes I true, II true, and III false. Since the question asks for what must be true, and we've seen an example in which III is false, we can eliminate any answer choice that contains III. Good bye, (D) and (E)!</p>

<p>They stop there, please explain the rest, or the whole thing in a better way please. Thanks in advance :)</p>

2

<p>They use the same type of questions over and over haha. I actually did a problem very similar to this on a practice test today.</p>

<p>Anyway, I’ll use their numbers to explain it.</p>

<p>Since the average of the first three tests is 80, we can say the first three scores are 78, 80, and 82. They also say at the average for the next two tests is a 90, so we can say the scores for those two tests are 88 and 92. To recap:</p>

<p>78, 80, 82, 88, 92 are the five scores.</p>

<p>I. The student scored more than 85 on at least one test - TRUE - He scored more than 85 on two tests.</p>

<p>II. The average score for all five tests is less than 85 - TRUE - If you add up the test scores, you get 420. Divide this by five and you get 84, which is less than 85.</p>

<p>III. The student scored less than 80 on at least two tests - FALSE - He only scored less than 80 on one test.</p>

<p>So, I and II will ALWAYS be true, since they used the word “must” in the question. Any values that you plug in for test scores (that fit, obviously) will make I and II true. Try it out if you want.</p>

<p>The answer is C.</p>

3

<p>oh ok, thanks for clearing that up :slight_smile: i was wondering, bc they didnt specify exactly towards why a and b were incorrect, but tht cleared it up, thanks :)</p>