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Reasoning on GMAT number theory questionsThe GMAT is a reasoning test.

It’s not a math test. It’s not an English grammar test. It’s not a writing test. Sure, there are elements of all of that in the questions you have to answer. But ultimately, the GMAT is a reasoning test.

For proof, look no further than the names of the four major sections on the GMAT:

  1. Analytical Writing Assessment
  2. Integrated Reasoning
  3. Verbal Reasoning
  4. Quantitative Reasoning

So what does this mean and why is it important?

Sometimes on the GMAT, a question will pop up on your computer screen that you don’t immediately know how to do. There isn’t a simple, straightforward formula to solve it. It doesn’t fit into a nice, neat “math box” where the process for solving it is identifiable and straightforward.

So, what are you to do in those cases?

You need to reason your way to a right answer.

The famous computer scientist and cryptographer Alan Turing defined reasoning this way:

“Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity.”

In other words, on hard GMAT questions where the mathematical solution isn’t cookie-cutter, you need to call upon your intuition and ingenuity to work through the problem and arrive at an answer.

Sound intimidating? It doesn’t have to be. Reasoning is a skill that can be learned, especially as you’re exposed to different question types that fall in this category. Many of them are what we call GMAT number theory questions, as with this example:

Question: What is the units digit of the solution to 177²⁸ – 133²³ ?

(A) 1
(B) 3
(C) 4
(D) 6
(E) 9

Give it a try and post your answer/questions below.

If you’re feeling stuck or just want some more tips about how to implement reasoning on the GMAT, watch this detailed explanation to the question above:

Enjoy, and may it empower you to dominate the GMAT!