Good way to solve weird Average problems

Test Preparation SAT Preparation
1

<p>Hi guys,</p>

<p>Yesterday I was solving some real exam that required question like that.</p>

<p>6)The least and greatest numbers in a list of 7 real numbers are 2 and 20,respectively. The median of the list is 6,and the number 3 occurs most often in the list. Which of the following could be the (average arithmetic mean) of the numbers in the list?</p>

<p>I- 7
II 8.5
III 10.</p>

<p>1)I only
2)I and II only
3)I and III only
4)II and III only
5)I,II,and III</p>

<p>so we have here the list is composed of
2,3,3,6,x,y,20</p>

<p>Here we try choose the least values for x,y respectively I know it says real values,but in the SAT I don't think they will complicate the matter too much because they expect you to be able to solve the problem.</p>

<p>So lets get least values for x,y = 6,7 respectively.</p>

<p>Least = (2 + 3 + 3 + 6 + 7 + 8 + 20) / 7 = 7;</p>

<p>We choose for the most 18.5 and 19.5.</p>

<p>Most = (2 + 3 + 3 + 6 + 18.5 + 19.5 + 20) / 7 = Approximetly 10</p>

<p>I just choosed 18.5 and 19.5 to show it would work even with real values,but just more ranges for smallest and biggest numbers.</p>

<p>So the answer is E.</p>

<p>Just thought it was a good question and this way wouldn't require to brute force the problem and lose time solving for it.</p>

2

<p>That’s one way to do it but you can always make an equality</p>

<p>(2+3+3+6+6+6+20)/7 = 6.57</p>

<p>(2+3+3+6+20+20+20)/7 = 10.57</p>

<p>6.57 < x < 10.57</p>

3

<p>Is this the math problem from the SAT Practice Test 11 - 12 of CollegeBoard? I’ve just done it yesterday :slight_smile: </p>

<p>Tomorrow is my big day, my SAT day =.=</p>

4

<p>Yeh your right @BallsBalls.</p>

<p>@IvyAble</p>

<p>Yeh its from that test I have done it too my test is also tommrow :smiley: so good luck to you and all who is taking test tommrow.</p>