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Sometimes you can look for patterns in questions to solve seemingly impossible questions.


What is the units digit of 3⁸⁰¹?


Am I going to sit here and calculate 3⁸⁰¹? Will they have to call security to get me out of the test center after it closes? Surely that sneaky Mr. GMAT must have made this question with a shortcut!


Indeed, use Find Patterns and it shows up pretty quickly:

3¹= 3
3²= 9
3³= 27
3⁴= 81
3⁵= 243
3⁶= 729

Every 4 powers and you get the same number as the units digit. We know 800 is a multiple of 4. And 801 is therefore one greater than a multiple of 4. So the units digit is 3, as above when the exponent is 1 greater than a multiple of 4.

 

	800score Tip: When you see a question where you scratch your head and think it will take an hour to do.... odds are that there will always a shortcut. Using Backsolve, Plug In, Find Patterns or math shortcuts, you will likely find the easy way to solve it.

GMAT Math Introduction Chapter 1: Table of Contents Section 1: Introduction   Section 2: 8 Math Strategies (advanced)    1. Plow    2. Don't Do That Math!    3. Backsolving    4. Plug-In (Testing Numbers)    5. Ballpark (Possible Range Strategy)    6. Experiment    7. Find Patterns    8. Ladder of Difficulty   Section 3: 5-Step Method (advanced)   Ladder of Difficulty

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2.6 Experiment	2.8 Ladder of Difficulty