# Combinations

Yesterday, physicists at the European Organization for Nuclear Research confirmed that they had finally detected the Higgs Boson or so-called "God Particle." The Higgs Boson is basically the particle that binds all matter in the universe together. Physicists predicted the existence of the Higgs Boson years earlier, but until recently, they had not confirmed its existence. This video is a great (and simple) explanation of the significance of the Higgs Boson. The discovery of the Higgs Boson would make a great current event "Excellent Example" for your essay.

## 7/5 Combinations

Read the following SAT question and then select the correct answer choice.

As always, remember to follow the Knowsys method for math. Read the problem carefully and identify the bottom line (what you are looking for). Then, consider your options. How could you solve it? How should you solve it? Next, attack the problem using the method that you selected. Finally, loop back and verify that your answer matches the bottom line.

If  is a number from Column  and  is a number from Column  in the table above, how many different values are possible for ?
You might be tempted to just treat this like a permutation problem. Since there are 3 choices for X and 3 choices for Y, it looks like you could just multiply 3x3 and say that there are 9 choices. However, if you stop and think about it for a moment, you should notice something. You don't care about which numbers are chosen, you only care about the sum of those numbers. In other words, X=2 and Y=5 is the same as X=1 and Y=4. Instead, think about the range of possible numbers you could get. The smallest number you can possibly get is 5 (X=1 and Y=4). The largest number you can get is 9 (X=3 and Y=9). That means that you have 5 possible outcomes (5, 6, 7, 8, and 9). Now, take a look at the answer choices and see which one matches your prediction.

(A) nine
(B) eight
(C) seven
(D) six
(E) five

The correct Answer Choice is (E).

On sat.collegeboard.org 37% of the responses were correct.

For more help with math visit www.myknowsys.com.