Join Vince Kotchian for an in-depth discussion in this video Backsolving technique, part of PSAT Test Prep.
- Another way to make tough math questions easier is to just check the answer choices to see which one of them works. In this video, I will show you how to work backwards from the choices. Let's check out this problem and then we'll talk about the technique. A companies manager estimated that the cost C, in dollars, of producing N items is C equals seven N plus 350. The company sells each item for 12 dollars and the company makes a profit when total income from selling a quantity of items is greater than the total cost of producing that quantity of items.
Which of the following inequalities gives all the possible values of N for which the manager estimates that the company will make a profit? We could, again, solve this algebraically, but let's say for the sake of argument that you don't know how or maybe you don't feel like it. Let's see if we can get away with checking the answer choices here. Of course, this says all possible values of N. We have to make sure that it's not just the right answer choice, but that it captures all of the values.
We're going to have to do a little bit of experimentation to make sure. Let's just start maybe with choice A and test it out. If N is less than 70, maybe N is 69. We're going to write this equation. C equals seven times 69 plus 350. 69 times seven is going to give us 483. If I add 350 to that, I end up with 833.
833. Now what I have to do is calculate what the profit is. I know that I have 69 items here and each item sold for 12. I'll just do that math as well. 69 times 12. That's going to give me 828 dollars. I can see that my cost, which is represented by the top equation, is 833. That's more than my profit. That's not good.
That's not going to work to make a profit for me. I know it's not choice A. From here, I'm going to test another choice. I'm going to go, if I think about it a little bit, I'm going to go straight to choice C, and I'll tell you why. I'm pretty close, right? The profit was almost at my cost. If I would just bump it up above 70, I think I can get there. Let's see if I'm right. Let's check this out. This time we're going to do C equals seven times 71, which is more than 70 plus 350.
Let's see what that equals. 71 times seven is 497. If I add that to 350, I end up with 847. 847 is my cost. Now, let's check out my profit. Remember, each item is 12 dollars. I'll do 71 times 12 to see what my profit is, or to see what my revenue is, I should say.
71 times 12 is 852. 852. Now I can see that, hey, I have revenue that is above my cost. I actually made a profit. The right answer is choice C. If I had tested choice D or even choice B, I might have got an answer that worked, but remember, I have to be careful. I have to make sure that I pick something that gives all possible values of N.
I really need to find the smallest answer that works. That would be choice C. Remember, checking the answer choices is a good method to practice. Just like any math problem, you want to see if you can solve things multiple ways. It's always good to have more than one tool to do so.
- Understanding the structure of the PSAT
- Preparing a study timeline
- Reviewing sample questions
- Reading efficiently and critically
- Recognizing wrong answers in the reading section
- Answering grammar and punctuation questions
- Backsolving math problems
- Decoding charts and graphs
- Working without a calculator