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by Tushar14 » Mon Apr 14, 2014 2:06 am
As 75=4*18+3 then the last digit of 7^{75} is the same as the last digit of 7^3, which is 3. Units digit of 7^{75} + 6 will be: 3 plus 6 = 9.
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by [email protected] » Mon Apr 14, 2014 11:18 am
Hi sgr21,

The GMAT doesn't expect you to calculate the value of 7^75; instead, let's try to figure out the pattern behind this math....

The question asks for the UNITS DIGIT, so we'll focus on that...

7^1 = 7
7^2 = 49
7^3 = 343
7^4 = ends in a 1

7^5 = ends in a 7
7^6 = ends in a 9
etc.

The pattern is 7931 7931 7931 etc.

So the units digit will follow this repeating pattern of 4 digits...

75/4 = 18r3

Thus, the 75th number will be the "third number" in the pattern...a 3

The question asks us to ADD 6 to this number though....

3+6 = 9

Final Answer: E

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