Absolute Value

Happy St. Patrick’s Day!  If you like celebrating holidays, consider tracing the history of a holiday celebration as one of your historical events, or even tracing the history of a holiday up to the present for a current event.  There are many misconceptions about the origins of ideas and traditions, and the way that certain practices came about is fascinating.  Think about how this article about the history of St. Patrick’s day could be used to answer the following SAT essay questions:

(1)  Should people change their decisions when circumstances change, or is it best for them to stick with their original decisions?
(2)  Do you think that ease does not challenge us and that we need adversity to help us discover who we are?
(3)  What motivates people to change?

Algebra: Absolute Value

Read the following SAT test question and then select the correct answer.
If , which of the following could be true?

Bottom Line: which of the following COULD be true?

Assess your Options:  You could come up with answers to solve this problem, but that will be a waste of time if they are not included in your answer choices.  Instead, look at the answer choices and methodically eliminate incorrect answers.

(A) a = 0
(B) b = 0
(C) a = b
(D) a = -b
(E) a = 1

For a “which of the following” question, Knowsys recommends that you begin with answer choice (E).

Hint:  Instead of thinking of the bars in your equation as absolute value, think of them as simply showing where a positive number will be.  If you do this, you will not have to plug in actual numbers and you can check each answer choice using logic. (This works because an absolute value simply tells you how far a number is from zero.  The double bars only affect negative numbers, making them positive.)

(E) a = 1    Plug a = 1 into your original equation.   Is there any way to start out with the number 1 and subtract a positive number to get the answer 5?  There is not.  Eliminate this answer.

(D) a = -b     This answer choice has a negative sign, but remember that any negative sign will go within the bars and come out a positive number.  So if you plug in b where the variable a is in this equation, you still end up with bb = 5.  Is that possible?  No!  Anything minus itself will be zero.  Eliminate this answer.

(C) a = b     This answer is essentially the same as the last one!  If you plug in b where you have an a, you wind up with bb = 5.  Again, anything minus itself will be zero.  Eliminate this answer.

(B) b = 0     Plug in 0 for the b in your equation.  You now have a positive number minus 0 equals 5.  Is that possible?  Yes!  5 – 0 = 5.  You are finished.  You don’t have to know that a can be either negative 5 or 5, and you don’t have to check the last answer choice.  Let’s check it just for practice.

(A) a = 0     Is there any way to start with 0 and subtract a positive number to get 5?  No!  Eliminate this choice.