The SAT math section is not a straightforward math test. Yes, it does test your math skills, but mostly it tests your math skills under intense time pressure. So you need to be able to find the right answer in the shortest amount of time possible.
Often, this means not solving out problems like you are taught to do in school. It will behoove you to find quick and dirty shortcuts that work (which are not the same as sloppy, pie-in-the-sky crazy thinking like “Well, there was a 2 in the problem so I thought the answer would have a 2 in it somewhere…”)
Here’s one of my favorites that stuns my students.
The conventional math-class method
In math class, when you are given two or more equations, you are taught to solve down for one variable, then substitute it into the other equation and then solve for the second variable. Such as the following:
Solve for a.
- Rewrite the top equation as a=9-b
- Rewrite the bottom equation as c=7-b.
- Then substitute those values into the second equation so (9-b) + (7-b)=8.
- Simplify to 16-2b=8 then -2b=-8 and then b=4.
- Then take that value and sub in back into the top equation so a+4=9.
- Therefore a=5.
The quick and dirty method
This one works like a charm on the SAT. (I wouldn’t try it outside the SAT, though. It’s an SAT trick, not a math trick.)
Just shove them all together.
- Adding up all the values you would get 2a+2b+2c=24.
- Since we know that b+c=7, double that value to get 14 and subtract that from each side so 2a=10
- Therefore a=5.
Here’s a question from the Blue Book, page 849. Don’t get distracted by the abundance of cute furry animals.
A certain scale only registers weights that are greater than 6 pounds. A person who wanted to know the weights of a puppy, a kitten and a bunny weighed them in pairs and got the following results:
- The kitten and the bunny weighed 7 pounds
- The kitten the the puppy weighed 8 pounds
- The bunny and the puppy weighed 9 pounds
What is the weight of the puppy?
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