SAT Question of the Day 21th July 2013

(absolute value of x minus 5) is less than or equal to 2

How many integers satisfy the inequality above?

A.     None

B.     One

C.     Two

D.     Three

E.     Five

We have an inequality on our hands (it has a < or a > sign) and also an absolute value hidden inside. We know that when we take an integer and subtract five of that number and change the sign of the answer to a positive we obtain a number that is smaller or equal to 2.

How many non-negative integers are there that are smaller or equal to 2? well there is 2 (equal), 1 (smaller), and 0 (a non negative). We obtain 0 by X=5, we obtain 1 by X=6 OR by X=4 (remember that absolute value function turns negative to positives), and the same for 2 – we will obtain it by X=7 or X=3.

We conclude there are 5 such integers.

43% out of 222,000 concluded the same.

Other techniques involve solving the inequality – I suggest the graphical approach since it is faster.

Leave a Reply

Your email address will not be published.