Math Arguments

Which Question is Harder?

As we all know, the questions in an SAT test get harder as you get to the end of a section. I warn my students repeatedly that, as they approach the end of a section,

"If you can't see what all those people thought was the obvious answer ...
and clearly see why that obvious answer is wrong, ...
then you are one of those who will jump to the wrong conclusion and you'll get it wrong, too."

You see, the question at the end aren't really difficult usually. They can be badly worded but they're rarely HARD. They are usually four-step problems that everyone else is so sure about, and the answer is so obvious that they get suckered in. These two were rated the same level of difficulty, and were answered correctly by about 3%-5% of the students.

Which one is harder?

25. A woman drives to work each day at an average speed of 40 miles per hour and returns along the same route at 30 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the trip?

1. 30


2. \(30\dfrac{1}{7}\)


3. \(34\dfrac{2}{7}\)


4. 35


5. 40
   

24. A 25 foot ladder is placed against a vertical wall of a building with the bottom of the ladder standing on concrete 7 feet from the base of the building. If the top of the ladder slips down 4 feet, then the bottom of the ladder will slide out.

1. 4ft


2. 5ft


3. 6ft


4. 7ft


5. 8ft

In each case, can you say why the obvious answer is wrong?

.