No matter how you slice it, there are some tricks on the SAT. Tricks can mean anything from the little details (did you know that ‘0’ is an even integer?) to, well, stuff that is just plain tricky.
For the first variant of trickiness, try the following:
How many consecutive integers are from -5 to 5, inclusive?
Inclusive, by the way, means including the numbers -5 and 5. You might think, oh easy. There are ten digits. But here’s the trick: don’t forget zero. If you look on a number line, perched right between -1 and 1 is a big zero. And to pass over him just like that is to no longer have a consecutive series.
Now, imagine I ask you to find the sum of the consecutive integers starting all the way from -1000 (that’s right: negative 1000) to 1000. Well, you might think I’ve just given you a task worthy of Hercules (or unworthy of anyone with a social life). Well, it’s a pretty dirty—or neat, depending on your proclivities—trick. Each integer when added to its “negative self” will equal zero (-1000 + 1000 = zero). So, the numbers will all cancel out and the sum will be zero. Told you some of this stuff is just plain tricky.
Okay, now that you’ve got some tricks up your sleeve, literally (oh wait, that might still be figurative), have a go at this week’s challenge problem.
The sum of m consecutive integers is 8. What is the value of m?
(E) Cannot be determined by the information provided
After you’ve tried the problem yourself, watch this week’s video Friday to see if you got it right!
And of course, leave me any questions or comments you have in the comment box below. See you next week. 🙂