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F(n) denotes the units digit of a positive integer n. What is the value of F(38+715)?

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F(n) denotes the units digit of a positive integer n. What is the value of F(38+715)?

by Max@Math Revolution » Tue Jun 23, 2020 12:50 am

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[GMAT math practice question]

F(n) denotes the units digit of a positive integer n. What is the value of F(3^8+7^15)?

A. 3
B. 4
C. 7
D. 8
E. 9
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Re: F(n) denotes the units digit of a positive integer n. What is the value of F(38+715)?

by Max@Math Revolution » Thu Jun 25, 2020 12:41 am
=>

The units digit of the exponents of 3 repeats 3^1 ~ 3, 3^2 ~ 9, 3^3 ~ 7, 3^4 ~ 1 every four times when multiplying by 3.
The units digit of the exponents of 4 repeats 7^1 ~ 7, 7^2 ~ 9, 7^3 ~ 3, 7^4 ~ 1 every four times when multiplying by 7.

F(3^8 + 7^15) = F(3^4 + 7^3) = F(1 + 3) = F(4) = 4.

Therefore, B is the correct answer.
Answer: B
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