Nice sat math question

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1

<p>Hi,
I am solving SAT math bibble it got some interesting question,but this math question is interesting so I thought I share how I solve it.</p>

<p>In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and last numbers is 4. What is the average of three numbers?
1)2
2)2.5
3)3
4) 3.5
5) 4</p>

<p>Here how I solved it:
Let x and y and z be the three numbers.</p>

<p>x + y / 2 = 2;
x + y = 4;</p>

<p>y + z / 2 = 3;
y + z = 6;</p>

<p>x + z / 2 = 4;
x + z = 8;
z = 8 - x;</p>

<p>y + 8 - x = 6;
y + 8 - 6 = x;
y + 2 = x - 2;</p>

<p>x + x - 2 = 4;
2x = 6;
x = 3;</p>

<p>y = 4 - 3;
y = 1;</p>

<p>1 + z = 6;
z = 5;</p>

<p>3 + 5 + 1 / 3 = 9 / 3 = 3;</p>

<p>If you have any better way to solve this please let me know too.
This took just 40 seconds to solve.</p>

2

<p>With a little practice you can do a problem like this in under 10 seconds. When I solve this I just do the following 2 computations:</p>

<p>4+6+8=18
18/6=3</p>

<p>Think about this and see if you can explain what I did. After you attempt to explain it I will post a more detailed explanation.</p>

3

<p>ahhh really nice logic I see what you did there since when you add them together you have them simply repeated.
This is the same as this:</p>

<p>x + y / 2 = 2;
x + y = 4;</p>

<p>y + z / 2 = 3;
y + z = 6;</p>

<p>x + z / 2 = 4;
x + z = 8;</p>

<p>x + y + y + z + x + z = 4 + 6 + 8</p>

<p>2x + 2y + 2z = 18;</p>

<p>1/2(2x + 2y + 2z) = 18 * 1/2;</p>

<p>x + y + z = 9;</p>

<p>x + y + z / 3 = 9 / 3;</p>

<p>Really nice logic DrSteve.</p>

4

<p>equations like that can almost always be solved by either adding them together or subtracting them</p>

5

<p>Good. You understood what I did. I combined 2 standard sat strategies - changing averages to sums, and performing a simple operation. </p>

<p>One note on the notation you’re using. x + y/2 is misleading. What you should really write is (x+y)/2</p>

6

<p>Yeh its misleading I should have used parenthesis they should do a program that you can write mathematics notation on forums.</p>

7

<p>I hope you realize that this is actually a bad problem. Read it again and see how the numbers 1,3 and 5 respond to the problem statement.</p>

<p>The average of 1 and 5 is 4? Only in the world of people who write such garbage.</p>

8

<p>@Xigi</p>

<p>I am sorry but I don’t get b what you mean by 1,3,5 ? those are the answer I don’t see any statement referring to them in the question. The 1,3,5 I see are only in my answer which I solved for them. The question also never stated the average of 1 and 5 is 4 also in my answer I don’t have any of 1 and 5 average only.</p>

<p>Can you please clarify what you mean?</p>

<p>Thanks.</p>

9

<p>Quote: In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and last numbers is 4. What is the average of three numbers?</p>

<p>What are your first two numbers?</p>

<p>What are you last two numbers?</p>

10

<p>Yeh the wording of the question is weird,but I thought he wanted to make the question more complicated.</p>

<p>I understood it as the average of the sum of the first two numbers,also same thing for last two numbers I understood as the average of second member and third member of the three numbers.</p>

<p>Your right though the wording should have clarified more I just liked the idea of this question seemed like one of type of questions that might come as hard questions.</p>

11

<p>^^ It is not weird; it is plain wrong.</p>

<p>Original question:
In a set of three numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and last numbers is 4. What is the average of three numbers?</p>

<p>Answer? No possible answers.</p>

<p>Should be:
In a set of three numbers, the average of the first two numbers is 2, the average of the last two numbers is 4, and the average of the first and last numbers is** 3**. What is the average of the three numbers?</p>

<p>Answer: </p>

<p>The average is 3. The proof with 1, 3, and 5. </p>

<p>1/2 of 1 + 3 = 2
1/2 of 3 + 5 = 4
1/2 of 1 + 5 = 3</p>

12

<p>If I understand, the problem with this question is the use of the word “set”. A “set of numbers” is a collection, not necessarily ordered. But if you choose to designate an order, you could put them in increasing or decreasing order, not just the order that you happened to designate while searching for them.</p>

<p>If they had begun by saying: A sequence of three numbers has the following properties… then there would be no problem. Unlike sets, sequences have order. (Officially, a sequence is a function which has the positive integers as its domain).<br>
So is this nitpicking? Not really – if a problem worded this badly made it on to the actual SAT, it would actually make the newspapers.</p>