# Logic

Today’s question is a numbers game, and numbers are very important to species on the edge of extinction.  Some politicians support measures to save endangered species, but there is one Russian politician who is going above and beyond to show his devotion to restoring healthy populations of Siberian white cranes.  Read about Vladimir Putin here and think about the impact that stunts such as this can have on politics.  What would you think if the President of the United States did this?  Is this a current event that you could remember for your essay?

## 9/6 Logic

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

It is just as essential to read math questions carefully as it is to read reading questions carefully.  If you miss any information, you could solve for a question that is not being asked.  To avoid errors, make a note of the bottom line.  Then assess your options and choose the most efficient method of working the problem.  Attack the problem, clearly writing any scratch work, and loop back to make sure that your answer addresses the bottom line.

The sum of the positive odd integers less than 50 is subtracted from the sum of the positive even integers less than or equal to 50. What is the resulting difference?

Your bottom line is the difference between two sums.  This question is very simple mathematically because it only asks you to add and subtract integers, but it would take a long time to add and subtract all of the integers involved.  The people who created this test know that you do not have a lot of time, so there must be an easier way to solve this problem than writing every single number out.  Think about the question logically.

Start with the two sums.  One is the sum of all the even integers less than or equal to 50.  Write out a few of these numbers so that you can check for patterns.  Remember that zero is an integer, but not a positive number!  The problem calls for positive even and odd integers.  Did you read carefully?

2 + 4 + 6 + 8… 50

The sum of the positive odd integers is subtracted from the first sum, so write a few of these numbers underneath the first set.

2 + 4 + 6 + 8… 50
- ( 1 + 3 + 5 + 7… 49)

Notice that if you subtract each number individually, you will always get 1. Two minus one is one.  Four minus three is one.  You get the idea.  This happens all the way up to fifty minus forty-nine is one.

Your problem really looks like this:

2 + 4 + 6 + 8… 50
- ( 1 + 3 + 5 + 7… 49)
1 + 1 + 1 + 1…+1

Now you just need to figure out how many ones to add together.  Think about it this way: you need an even integer and odd integer for each additional one.  How many positive even integers are less than or equal to 50?  Well, half of the integers are even, so the answer is 25.  If you add the number one twenty-five times, what will you get?  Look down at your answer choices.

(A) 0
(B) 25
(C) 50
(D) 100
(E)200