The students in one of my SAT classes recently worked on the following SAT math problem:
It is given that X to the Y power = 4096. X and Y are positive integers. What is the greatest value of X – Y?
My students promptly began pounding away on their calculators. Within a few seconds several students confidently raised their hands and proclaimed 62 as the answer. When asked to explain their answer, my students declared that 64 squared = 4096. So 64 – 2 = 62. They were shocked to learn that 62 is not the greatest possible value of X – Y. I then asked my students to try again without using their calculators. After some initial consternation (“What are we supposed to do? This problem is impossible!) one of my students had an Ah Ha moment and figured out the answer. Prompted by his statement that “Its really simple. All you have to do is think.” several other students soon realized that 4096 to the first power = 4096. So X – Y is equal to 4095!
My student was right when he said, “All you have to do is think!” The calculator is a wonderful SAT tool. However, it is not invincible and it is not indispensable. Many SAT math problems are intentionally designed to test your mathematical reasoning powers. So before pounding away at your calculator, stop and use a calculator that is even more powerful than your TI-82 – your BRAIN!

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