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n is an integer. What is the units digit of n^5-5n^3+4n?

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by Max@Math Revolution » Mon May 13, 2019 11:40 pm

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B

C

D

E

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[GMAT math practice question]

n is an integer. What is the units digit of n^5-5n^3+4n?

A. 0
B. 2
C. 4
D. 6
E. 8
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by Max@Math Revolution » Wed May 15, 2019 11:27 pm
=>

n^5-5n^3+4n = n(n^4-5n^2+4) = n(n^2-1)(n^2-4) = n(n+1)(n-1)(n-2)(n-2) = (n-2)(n-1)n(n+1)(n+2). Thus, n^5-5n^3+4n is a product of five consecutive integers.
Since it is divisible by 2, 3, 4, and 5, it is a multiple of 10.
Thus, its units digits is 0.

Therefore, the answer is A.
Answer: A
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