09-10 Math Problem

Test Preparation SAT Preparation
1

<p>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 (arithmethic mean) of the numbers in the list?</p>

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

<p>A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II and III</p>

<p>My response is answer C.(I and III only) Based on the answer sheet the stated answer is E.</p>

<p>Can someone explain this</p>

2

<p>Basing on the question, the list of numbers you should have looks like this:
2;3;3;6;x;y;20
Because you can have real numbers, you can have almost whatever numbers (decimals, fractions etc.) you want in steads of the x and y. However, since the median is 6 you should have only positive numbers; and since the three places with values of less than 6 are taken by 2 and two threes you must have numbers higher than 6.
You should try to find the range in which the average of these numbers may vary. For example, if you take 6.1 and 6.2 (approx. of the least you can take in the places of x and y) you’d get an average mean of 6.71. The highest values you could have for x and y would be about 18 and about 19 (you can have 18.99999 or 19.99999). You’d get approx 11.
You can basically have an average mean of anything between 6.7 and 11.</p>

3

<p>Thnx. I overlooked that they state REAL NUMBERS and not integers</p>

<p>Basically I worked with the notion that the value of x+y could have only been an integer (considering only whole numbers)</p>

<p>Look at this</p>

<ol>
<li>If a is not equal 0. and 5/x= 5+a/ x+a, what is the value of x?</li>
</ol>

<p>A) -5
B) -1
C) 1
D) 2
E) 5</p>

4

<p>I think it’s:
5/x=(5+a)/(x+a)</p>

<p>If that is the case, using proportional qualities, we can get:
5(x+a)=x(5+a)
5x+5a=5x+ax
5a=ax
(cancel out a’s)
5=x</p>