I had my biggest parental fail yet last week. I was in the process of unbuckling my son out of his high chair when I got distracted and turned my head. When I turned back, he’d tumbled forward and taken a spill. He and I were both pretty shaken up by the whole experience, but he’s on the mend and will be just fine.
In the days following, I’ve been a little paranoid and extra careful. But I wonder: had I left him in that dangerous position before? It could be that this was the first lapse I’d had and it turned out poorly, or it could be that I’d made this mistake before and gotten lucky because nothing bad had happened.
I don’t have a nanny cam running in my home 24-7 to monitor my parental performance, so I can’t really know the answer to that question. But if I did, this accident might not have happened. There’s a benefit to being able to review your performance, even if the end result turned out just fine.
Let’s carry that lesson over to the test prep world. Sure, it makes sense to spend most of your review time going over problems you missed so that you’re better able to understand what went wrong and how you can do better next time. However, it does make sense to spend some time going over the questions you get correct as well. At minimum it can reinforce good habits, and potentially you may spot mistakes that didn’t end up costing you a correct answer on this problem. However, you may not be so lucky next time.
For instance, if asked for the square root of 9, and given an answer choice of 3 you won’t be penalized for forgetting that -3 was also an option. However, if you review that correct answer and realize your mistake you’re less likely to make the same mistake where your error is the difference between a right answer and a wrong one.
As I’ve seen this week it’s helpful to learn from a wrong choice, but it’s even better if you can learn without suffering the consequences.
The positive numbers m and p are variables in the following equation:
4m + 5mp + 10 = 50m
What is p in terms of m?
A) 46/5 m
B) 9m + 5
C) 46/5 – 2/m
D) 5/m + 2
E) m/5 + 46
There’s always going to be an algebraic solution to this problem, but this one is… a little ugly. The solution doesn’t come out neatly, so there’s a fair amount of potential to make a mistake or lose confidence as you’re working through it. I hope you respond to that by saying, “Don’t worry! I see variables in the answer choices, so I can just plug in my own numbers!” That’s a wonderful thought, but here is how that might go wrong if you try it.
“Well, I know I’m supposed to pick numbers that are easy to calculate, so let me just use m = 2 and p = 3. If we plug those in to our original equation we get:
4(2) + 5(2)(3) + 10 = 50(2)
8 + 30 +10 = 100
48 = 100
When plugging in your own numbers into a problem, it’s important to know that your numbers need to follow the rules set up in the problem. But don’t worry, that doesn’t mean you need to magically pick a pair of numbers that works out of the air. Notice, in this case we don’t see both variables in the answer choices, only m. So, let’s pick a value for m, plug that into the equation and see what value it spits out for p.
4(2) + 5(2)p + 10 = 50(2)
8 + 10p + 10 = 100
10p = 82
p = 41/5
So now we have a pair of numbers that works for this equation. We know that when m=2, p=41/5. Now we can just test that pair against our answer choices to see which equation gives us the value of p that we found.
A) 46/5 m; 92/5… Nope
B) 9m + 5; 23… Nope
C) 46/5 – 2/m; 41/5… YES
D) 5/m + 2; 9/2… Nope
E) m/5 + 46; 232/5… Nope
Plugging in numbers can be a valuable strategy, but make sure you’re using it correctly!
“In a sport where a percent of players have a body fat percentage below b, c times out of d a randomly selected player will be above the threshold for obesity.”
How many times did you have to read that until it made sense? Two? Three? More? Try this version:
“In a sport where 50 percent of players have a body fat percentage below 15, 1 time out of 3 a randomly selected player will be above the threshold for obesity.”
Much easier to understand, right? All we did is define those variables as you can see from a quick chart:
a = 50
b = 15
c = 1
d = 3
The difference in the readability of those two sentences should tell you a lot about the usefulness of picking numbers. When you have answer choices that are written in terms of variables, such as “(ad/c) +b” rather than trying to parse exactly what that means it’s much easier to plug in your variables (50*3/1 +15) and see if that matches what you need it to. If it does, you’ve likely come across the correct equation.
Those who love pure equations often scoff at this approach and need to see the logic behind every equation. However, in a timed, multiple choice test you simply don’t have the luxury of going deep into every single problem. And the reality of the situation is that a deep understanding isn’t rewarded any more than a lucky guess. All that matters are correct answers.
So, the next time you notice variables in your answer choices, or are struggling to understand what’s going on through all the variables, try assigning values and see how much it helps!
I recently read an article that proclaimed Washington D.C. as the nation’s fittest city. Having lived in DC for three years, I was curious, so I read through the article. The American College of Sports Medicine apparently decided that it would be interesting to figure out which is America’s fittest city. The people running the survey, not wanting to introduce their own personal biases figured that they would come up with an objective list of factors, collect the data, and declare a winner.
One of the factors that seemed to carry heavy weight is spending on parks. The ACSM reasoned that heavy spending on parks makes them attractive and safe places to spend time, and thus would likely lead to a more fit population. They suggest that municipalities target approximately $100 per capita in parks spending. They note to Washington’s great credit that the city spends $398 per capita.
Stop and think about that for a minute. Does that necessarily mean that DC is filled with many beautifully manicured parks where citizens can safely enjoy exercise? No. In fact, as a former resident of the area, I remember many times when we had to scramble to fit some suitable space for a softball game or some pick-up soccer. Very rarely could you find a space big enough to accommodate a good game without being right up against other groups of people or having to deal with concrete walkways cutting through the field.
So how could DC have such great park spending and not have great recreational facilities? Simply speaking, DC’s parks aren’t parks, they’re monuments. The National Mall is a huge park, but it’s not made for fitness and it’s not really made for locals. It’s made for the thousands of tourists that flock to the city. Spending money to repair the Washington Monument doesn’t make DC fitter, but it does go into DC’s park budget.
You get the idea here. The point is that when you put garbage information into your formula, you get garbage out. When you’re working through a math problem making a simple mistake in transcribing the information is just as deadly as a gap in math knowledge. Be diligent, be careful and make sure you’re putting the right information into your formulas, because if it’s not right going in, it’s garbage coming out.