What is the unit's digit of 7^{75}+6?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
the answer i get is 1 bt some of my friends got their answer as 9
helppp plzzzz
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
