Ignorance is Bliss (Well, sometimes) – GMAT Question

I live in New York, so I do not spend very much time driving.  However, a couple weeks ago I was visiting my family out of state and I found myself behind the wheel.  Driving down a busy street at forty miles per hour, I had to watch for changing lights, for pedestrians and for other cars.  But what I found most remarkable, was what I did not even notice.  The color of the pavement, the trees lining the curb, and the birds flying through the air.

You are probably wondering what this could possibly have to do with the GMAT.  Just as I found the case to be when driving, on most GMAT problems we focus on all of the information we need, but, it is just as important to make sure that we ignore any superfluous information.

Most GMAT problems only give you the data you need to solve, but every once in a while that will not be the case.  And when this happens, you want to make sure that you are ready for it.  Before you start to solve, look at the the answer choices and consider what you have been told in the question.  If you think you can get to one of those answers (or, even better, you know you can) using only some of the information provided, go ahead and try to, especially when doing practice problems.  You do not want to spend time doing any unnecessary work, so learning when you can disregard information is a key skill in reaching some answers quickly.

The practice problem below is one such question.  Give it a try, and see if you can identify the information that you do not need to reach the solution.

Problem:

If negative integers k and p are NOT both even, which of the following must be odd?

(A)      kp

(B)      4(k + p)

(C)      k – p

(D)      k + 1 – p

(E)      2(k + p) – 1

Solution:

Since this is a problem that tests evens and odds, you should immediately suspect that the fact that k and p are negative is not important.  Positive and negative integers follow the same rules for evens and odds, so we can disregard the fact that they are negative.

Next, we are told that k and p are not both even, meaning that either one is even and the other is odd or they are both odd.  However, that also might not be important to finding the answer.  While we will need to look at our options to know if this is the case, you want to remember that if you find a choice that must be odd if k and p are any two integers it will be the answer.  Let’s scan through our choices and see if we find one that is always odd.

(A)      will vary depending on the values of k and p

(B)      will always be even.  If we multiply 4 by any integer value, and k + p will be an integer, the result will be even, since an even times any integer is even.

(C)      will vary depending on the values of k and p

(D)      will vary depending on the values of k an p

(E)      will always be odd.  The explanation here is similar to option (B).  2(k + p) will always be even, since an even times an integer is even.  However, when we subtract 1 we will end up with an odd integer, because an even – odd = odd.

If (E) must be odd when k and p are any two integer values, it still must be odd if we restrict k and p so that they cannot both be even.  Thus, (E) is the correct answer.