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SAT Question of the Day 21th July 2013

### 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.

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