# SAT Question of the Day (ACT too!): May 22, 2014

If you are reading this in an email you received from me, do not click the link to sat.collegeboard.org below. Use the link to my website that is farther down on the email.

http://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20140522&oq=1 (This link takes you to today’s question. If you use my archive, you will see the question related to my SAT explanation for that date.)

Reading this blog is 10% about learning how to answer today’s questions and 90% learning how to apply strategies and analyze questions you may see on test day.

The answer is E.  Yes, you could do the algebra as described in the SAT test writer’s explanation.  But I found it much faster and I was less likely to to make a silly mistake by just plugging in integers.  I can see that if x = 7, I would get 2 for an answer.  Trying 6, I got 1; 5 gave me 0.  Then, 4 gave me -1 but I need the absolute value of -1 which is +1; so that’s a fourth possible value for x.  Plugging in 3 gave me -2 which becomes +2 for the fifth value for x that works.  (I could have stopped right now because “Five” is the largest answer for the test question but just to make sure I’m on the right track, I continued.)   Then when I plugged in 2, I got -3 which has an absolute value of +3 which is too big.  That means all other values of x that are smaller than 3 don’t work.  That gave me a total of 5 possible values for x, Answer E.  (Fortunately, you can do this question this way in your head faster than it takes to explain it!)

That’s two ways you can do this problem: the math teacher way as explained by the College Board website and just plugging in (substituting) actual integers and counting how many work.

There’s no correct or best way to do any particular math question on either the SAT or ACT.  Practicing is going to help you figure out how to do different kinds of questions on the test.  Play a little game with yourself.  See how many ways you can do the questions you use for practice.  You’ll be surprised what you discover and doing so will also help you improve your score.

Let’s see what the ACT folks have for us today.

The answer is A.  Yes, there will be questions that are this easy on both the ACT and SAT.  Sometimes you just need to know a simple math rule and apply it.  In this case, you needed to remember to factor out all the perfect squares from a number to simplify it.  20 = 4 x 5.  The square root of 4 is 2; therefore 2√5 is the answer.

However, you won’t see this type of question on the test anymore because all you would do if you didn’t see my shortcut is to plug √20 and the answers into your calculator!  You easily would have seen Answer A is equivalent.  This question would have been on the test prior to allowing calculators but not any more.

QotD Words of “Wiz-dom”:

I’ll be off the grid again for the weekend.  Tune in again next week.  Keep practicing and if you have a question, send me an email.  I’ll be able to respond on Monday or Tuesday.

Bob Alexander, the “SAT and ACT Wizard”