Tough Questions: Part 1

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Occasionally on the SAT (or other standardized or nonstandardized tests), you’ll come across a problem that’s absolutely atrocious. Sometimes it will seem nearly impossible. Other times, you may know how to solve the question, but it’s so difficult and time-consuming that you may be better off skipping it entirely. Take a look at this example of a hard SAT math problem:

 

“In a car race, David gives Peter a head start of 10 miles. David’s car goes 80 miles per hour, and Peter’s car goes 60 miles per hour. How long, in minutes, will it take David to catch up to Peter if they leave their starting marks at the same time?

ANSWER: _____________________________”

Hard SAT Math Problem: Confusion

This is a perfect example of a question I would love to skip. I’ll even guess on this question if I’m running out of time, because I already know it’s going to take a few minutes to set up and solve the problem. And because it is a multi-part problem, I’m much more liable to make a calculation error at some point. If that happens, all my hard work will be for naught, so I may as well guess with an equally low chance of getting the question right. Remember, the SAT doesn’t penalize you for guessing, so it’s always in your best interest to answer every question. Even outrageously difficult free response math questions.

 

Okay, let’s pretend you finished the entire math section with a few minutes to spare. You’re feeling confident, and you notice this problem which you’d initially set aside. You guessed at the question and even bubbled in an answer on your answer sheet. But now you’d like to solve it. As I already mentioned, this is a multi-part question, and the first step is simply understanding what is being asked and how to utilize the numbers given. The problem itself asks you to find how long it will take David to overtake Peter in a car race with some given conditions. Notice that they’ve asked you to solve in minutes, but the cars’ speeds are given in miles per hour. This a great example of how overlooking one small detail can cause you to make a calculation error, thus wasting your valuable time. (Just to reiterate: guessing isn’t bad.)

 

So, I personally like to convert the speeds given to miles per minute to make the following calculations easier. Also, the numbers lend themselves nicely, as 60 mph = 1 mpm, and 80 mph = 1.33 mpm. Now, we want to know when the two cars will meet if Peter (in the slow car) has a 10 mile head start. Here, we have to assume both cars are capable of accelerating from 0 to maximum speed instantaneously, which is a tragic flaw in many math problems. In any case, we can set the distances each car travels equal to each other in the following equation:

 

(1 mile/min) X min + 10 miles = (1.33 miles/min) X min

 

Solving for X, we find:

 

10 miles = (0.33 miles/min) X min → X = 30 mins

 

Of course, once we parsed the necessary information from the question, translated it to a useful format, converted units and created an equation, the calculation was simple. But each of those steps invites us to make an error, especially when nerves are high as they often are during the SAT. It’s important to take a systematic approach to these types of problems, but it’s also important to know when a question is more trouble than it’s worth.

If you want more advice about improving your score on the SAT, sign up for KallisPrep today. Our online SAT prep course includes hundreds of video lectures, skill quizzes for each question topic, and thousands of practice questions. 


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