Tutoring For All Ages

Set a timer and see how long it takes you to answer this hard SAT problem:

The price of 10 pounds of apples is d dollars. If the apples weigh an average of 1 pound for every 6 apples, which of the following is the average price, in cents, of a dozen such apples?

A) 20d
B) 50d/3
C) 5d
D) d/5
E) d/20

There are several ways to approach the right answer here. Some take more time, others, less.

1. Algebraically. If 6 apples weigh 1 pound, then a dozen apples weighs 2 pounds. If 10 pounds costs d dollars, then 2 pounds, or 10 divided by 5, costs d/5 dollars, or (100d)/5 cents, which simplifies to 20d.
2. Picking Numbers. Let’s say these apples are really cheap, say fifty cents a pound, so that 10 pounds costs 5 dollars. (This means that d = 5 in this scenario.) That means that a dozen apples, or 2 pounds, costs $1 or 100 cents. If I plug in d = 5 for each of the answer choices, I should get 100 cents when I come to the right answer. The only answer choice which comes to 100 when I plug in 5 for d is choice A, so that’s the right answer.

Now, every student is different. For some students, the algebra is obvious, and picking a number just seems confusing. But for many students, the algebra takes extra time and there’s always the possibility of making a careless error — did you, for example, fall for the trick answer D?

For those students, picking a reasonable number makes the problem less abstract and easier to understand, and typically eliminates the chances of making a careless algebra mistake. Using picking numbers, many students can correctly solve hard SAT questions like this in under 30 seconds.

So the question is, what type of student are you?