Nerds Make Science Fun!

I want to try something new today. I’m going to post an article below this introduction that contains a major flaw in mathematical reasoning and convention, and I want you to tell me what the flaw is. Think of it as a small exercise to justify your time reading a blog when you could have been doing real work.

“Take a look at this SAT math problem:

How many ordered pairs of positive integers (a,b) can make the statement
5a+7b < 20 true?

A)    1
B)    2
C)    3
D)    4
E)    More than 4

Now this is a fairly simple problem. All you have to do to solve it is constantly plug in numbers for (a, b) until the statement becomes untrue. In this case, the sets of positive numbers that make the statement true are (1,1), (2,1), and (1,2). Indeed, the SAT itself says this, and the answer given is three.

However, this is blatantly wrong. There are two ordered pairs of (a,b) that make this statement true, as (1,1) does not count.

Here’s why: the key bit of information here is the parentheses, (a,b). Because it is written as (a,b), it is implied that the two numbers that make up the ordered pair are distinct, since a does not equal b unless explicitly stated to do so, which implies that the set is made up of  two distinct positive integers. This means that while a and b can switch values, they cannot share one value at the same time, meaning that (1,1) cannot be a set used for the statement, thus making the statement true for only two ordered pairs (a,b).”

So, what’s the flaw? Post it below in the comments!

William

The integral z squared dz,

From 1 to the cube root of 3,

Times the cosine

Of 3 pi over 9

Is the log of the cube root of e.

Bill and I spent an awkward couple of minutes verifying this, and it took longer than it should have because the thing is a bit vague.