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What is the ten’s digit of 7^195? (Cyclicity concept Number Theory)

Number Theory GMATWhat is the ten’s digit of 7^195?

A) 3
B) 4
C) 5
D) 6
E) 7

Solution

This question is based on the cyclicity concept in number theory.

Ten’s digit of powers of 7 follows a cyclic pattern as depicted:

7^1 = 07                7^5 = 16807

7^2 = 49                7^6 = 117649

7^3 = 343                7^7 = 823543

7^4 = 2401                7^8 = 5764801

Every fourth power of 7 has its ten’s place repeated.

Now, let’s break 195 (power of 7) into multiple of 4

195 = 48 * 4 + 3

The 7^195 will have its tens digit the same as 7^3 has, i.e. 4

Correct Answer: B

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