Question

Dear Mitch,

I'm sure yore probably going to think "Oh, here's another slacker... asking for a last-minute trick to help him on the SAT...", but the test is over and I'm taking the advice you gave out last year, to begin preparing AT ONCE for the next test! I get it now, because if you sit around and wait till the scores come back and THEN decide to take it again, it's too late to do much. Now that I've taken the test twice and gotten results back twice, I finally totally get what you mean! So, I'm not "Slacking", I'm doing the opposite!

But I still really like those things you call "last minute SAT TIPS", you know, the ones you've been giving out for the last couple of weeks. And since the test was this weekend, and the next one is in less than a month, could you post more of them between now and then?

It's cool when you do that.

Take care,

Barry W.

Answer

Dear Barry,

Sure!

Here's something important thing to remember, as it accounts for far more errors than it should: When a question asks about an "increase" or "decrease", be careful not to automatically think only in linear terms when the subject of the question is not one that is measured in linear units. For example: AREA is 2-dimensional, like when the question is about floor-space), or VOLUME, which is 3-dimensional, like when the question is about a fish tank.)

So, here's how it comes up: If they say there is a fish tank whose shape is a perfect cube, and its measurements are doubled to form a bigger cube, how much bigger is the tank?

A) twice the size

B) three times the size

C) four times the size

D) six times the size

E) eight times the size

The correct answer is E, eight times the size.

Why?

It's a three-dimensional unit, a cube (though any fish tank would be 3-dimensinal and measured in cubic units, even if it was more 'rectangular' than a cube, or it wouldn't be able to hold fish and keep them alive), so... pick easy numbers: say the tank was one cubic foot. That means it is one-foot by one-foot by one-foot – remember, it's 3-dimensional. "By" in math is times, so it is 1 foot x 1 foot x 1 foot.

Or one cubic foot.

If its measurements are "doubled" as the problem states, it becomes 2 foot by 2 foot by 2 foot, which is 2 x 2 x 2 = 8 cubic feet.

And 8 cubic-feet is 8-times the size of 1 cubic-foot.

Congratulations on beginning to prepare so quickly!

Hope this helps,

Mitch