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Question

 

Dear Mitch,

While you're doing the SAT and PSAT tricks (or 'tips', as you teachers call them), can you tell me if it is true that there are certain math questions that appear over and over again on the test, like almost every time the test is given, and if that is true is it true that they keep repeating them just because everybody gets them wrong all the time?

And, of course, if there is any truth to that, can you clue us in to what one might be?

Thank you,

Kurt Tinslow

Attending High School in Seattle

Answer

Dear Kurt,

Although it is unusual for the SAT OR PSAT to repeat the exact same question with the same numbers and menu of multiple choices, IT IS ABSOLUTELY TRUE THAT THE TEST-MAKERS SEEM TO HAVE FAVORITE CONCEPTS THAT REAPPEAR IN REMARKABLY SIMILAR FORM FROM YEAR TO YEAR. And yes, it is also true that these concepts tend to be ones that a high percentage of students do not answer correctly. NOTE: There is one other factor that these questions typically have in common: The reason for the high percentage of incorrect responses is not a result of any part of the question that presents any intellectual challenge beyond the average SAT question. No, the questions that are 'favorites' are almost always considered easier than their results would indicate. And to drive home this point, they are almost always written so that if one uses common sense, one can eliminate all but two of the five choices without bothering to pick up one's pencil. After that, one can either close in on the correct one with one's pencil, or one can think it over a bit more carefully and the answer will shine. A last resort is to plug in each of the two answers. The one that works to make the 'story' true is your correct answer. Fill in its oval and move on.

So, you'd like to see one of those 'favorites', correct?

Here goes:

EXAMPLE: Mr. Jimmy J. Jimmeson, known to many as an excellent driver, drove his car from point A to point B at an average speed of 40 miles per hour. He then immediately traveled back from point B to point A at an average speed of 60 miles per hour. What was the average speed of Mr. Jimmy J. Jimmeson's car for the round-trip?

A) 54 miles per hour

B) 52 miles per hour

C) 50 miles per hour

D) 48 miles per hour

E) 45 miles per hour

Any guess as to what the most commonly selected answer is?

That's right, most people select choice c. It is not correct.

The people who like choice c simply take the 40 and average it with the 60, figuring it was the same distance, as indicated by the words 'round trip'.

But the question involves something called 'weighted averages', which means that rather than just averaging two numbers you have to see which one (if there is such a one) that occurs more often than the other. In other words, if there are two groups of people in a room and one group weighs 50 pounds each and the other group weighs 70 pounds each, they do not necessarily average to 60 pounds each, because the group with the fifty-pound members may have two hundred members while the other group may have only four members...

Likewise, here the driver spent more time driving at the slower speed (same distance at slower speed takes longer), and since miles per hour is dependent upon how fast a person was driving per minute, Jimmy's increased number of minutes at that slower speed would weight the average down below the center point of the slow and fast speeds.

So, since 50 is dead center between the 40 and the 60, we know the answer has to be less than fifty. So you can cross off choices: A, B, and C.

Now you may pick up your pencil to select either D or E.

One way to quickly figure out the answer is to pick a distance for the path from A to B. And when doing so, pick a number that will work easily using the numbers they've given you. Pick a number that 40 and 60 go into easily and neatly, like 120 miles. So, if A to B is 120, then B to A is also 120 miles, making the round trip 240. So A to B at 40 miles per hour means it took him 120 miles divided by 40 = 3 hours. His return trip at 60 miles per hour took him 120 divided by 60 = 2 hours. And so the whole round-trip of 240 miles took him five hours. 240 divided by 5 hours.

240/5 = 48 miles per hour. Choice D.

At any speed, though, don't forget to buckle up, exercise good judgment, and obey all laws.

Hope this helps,

Mitch