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<x> denotes the unit digit of x. For example, <123> = 3. What is <719+789>?

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by Max@Math Revolution » Mon Aug 10, 2020 12:18 am

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[GMAT math practice question]

<x> denotes the unit digit of x. For example, <123> = 3. What is \(<7^{19}+7^{89}>?\)

A. 0
B. 1
C. 3
D. 8
E. 9
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Re: <x> denotes the unit digit of x. For example, <123> = 3. What is <719+789>?

by Max@Math Revolution » Wed Aug 12, 2020 12:18 am
Solution:

The unit digit of the powers of 7 repeats 7->9->3->1 and has a period of 4.

Since 19 = 4·3 + 3 and 19 has a remainder 3 when it is divided by 4, the units digit of 719 is 3, 719 ~ 73 ~ 3.

Since 89 = 4·22 + 1 and 89 has a remainder 1 when it is divided by 4, the units digit of 789 is 7, 789 ~ 71 ~ 7.

< 719 + 719 > ~ < 3 + 7 > ~ <10> ~ 0.

Therefore, A is the correct answer.

Answer: A
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