Graduate Management Admission Test (GMAT) Practice Test

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If x³ ends in 1, what can be inferred about the ending of x?

x ends in 0
x ends in 1
x ends in 2
x ends in 3

The correct answer is: x ends in 1

When considering the last digit of a number raised to a power, it is essential to analyze the patterns that arise from the last digits of different base numbers. We specifically need to look at how the last digits of integers behave when cubed. For a number $ x $ ending with a specific digit, we can find the last digit of $ x^3 $ by examining each possible last digit of $ x $: - If $ x $ ends in 0, then $ x^3 $ ends in 0. - If $ x $ ends in 1, then $ x^3 $ ends in 1. - If $ x $ ends in 2, then $ x^3 $ ends in 8. - If $ x $ ends in 3, then $ x^3 $ ends in 7. - If $ x $ ends in 4, then $ x^3 $ ends in 4. - If $ x $ ends in 5, then $ x^3 $ ends in 5. - If $ x $ ends in 6, then $ x^3 $ ends in 6. - If \( x