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# What is the unit's digit of 7^75 + 6? a. 1 b. 3 c. 5 d. 7 e.

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Manager
Joined: 20 May 2006
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What is the unit's digit of 7^75 + 6? a. 1 b. 3 c. 5 d. 7 e. [#permalink]

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10 Aug 2007, 19:23
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What is the unit's digit of 7^75 + 6?

a. 1
b. 3
c. 5
d. 7
e. 9

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Intern
Joined: 10 Aug 2007
Posts: 30

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10 Aug 2007, 19:52
My guess would be E) 9

The units' digit of the powers of seven follow the same pattern:

7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401

7^5 = 16807

This pattern of four can be repeated in its entirety 18 times with a remainder of 3. The third units' digit in the series is 3 which if we add 6 to, we get 9.

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Senior Manager
Joined: 29 Nov 2006
Posts: 318

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Location: Orange County, CA

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11 Aug 2007, 00:22
Agree with Entranced for reasons already mentioned.

Key these types of questions: find the repeating pattern for the digits (usually 4 or 5 different digits that repeat).

This one may trick a few who forget to add the 6.

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11 Aug 2007, 00:22
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