17^27 has a units digit of:

Question

17^27 has a units digit of:
 
(a) 1 
(b) 2 
(c) 3
(d) 7 
(e) 9

Abhishek009 · Answer

7^1 = 7 
 7^2 = 9 
 7^3 = 3 
 7^4 = 1

7^5 = 7 
 7^6 = 9

So, 7 has Cyclicity of 4

Now,  17^{27} = 17^{4*6}*7^{3}

Since ,  7^4 = 1  thus  7^{24} = 1  and  7^3  = Units digit 3

Thus,  17^{27}  will have units digit as 3, Answer must be (C)

Bismarck · Answer

OA:C 7 has the cyclicity of 4 (7,9,3,1). 7^1 = 7 7^2 = 4 9 7^3 = 34 3 7^4 = 240 1 7^5 = 1680 7 7^6 = 11764 9 and so on 17^{27}= 17^{6*4+3} So the unit digit of 17^{27} would be 3 . please check below link for more info about cyclicity concept https://gmatclub.com/forum/cyclicity-on ... 13019.html

Aviv29 · Answer

Great - Thank you both very much!

masoomjnegi · Answer

We know that 7n can have unit digit of 7 , 9, 3 and 1. 
We can find the unit digit by dividing n by 4. If the remainder is 1 then the unit digit will be 7, for remainder =2 unit digit = 9, for remainder = 3 unit digit = 3 for remainder = 0 unit digit = 1.
So, dividing 27 by 4 we get a remainder = 3.
Hence, the unit digit is 3.

fskilnik · Answer

? = \left\langle {{{17}^{27}}} \right\rangle = \left\langle {{7^{27}}} \right\rangle

\left\langle {{7^4}} \right\rangle = \left\langle {{7^2} \cdot {7^2}} \right\rangle = \left\langle {\left\langle {{7^2}} \right\rangle \cdot \left\langle {{7^2}} \right\rangle } \right\rangle = 1

\left\langle {{7^{24}}} \right\rangle = \left\langle {{7^4} \cdot {7^4} \cdot \ldots \cdot {7^4}} \right\rangle = {\left\langle {{7^4}} \right\rangle ^6} = 1

? = \left\langle {{7^{24}} \cdot {7^3}} \right\rangle = \left\langle {{7^{24}}} \right\rangle \cdot \left\langle {{7^3}} \right\rangle = 1 \cdot 3 = 3

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

MathRevolution · Answer

17^{27}

=> For unit digit, consider  7^{27}

=>  (7)^{4*6}  *  7^3

=>  7^4  *  7^3

=>  7^5  *  7^2

=> 7 * 49

=> unit digit 3

Answer C

JyotirmayeeGMAT · Answer

for any question like this if we have to find the units digit the power will be given. we can get solution by following the same process

Here the units digit is 7 and 
the units digit of 
7^1 = 7
7^2 = 9
7^3 = 3
7^4 = 1
7^5 = 7
so this cycle repeats after every four digits
therefore we divie 27/4 and then count the remaining 3 
therefore the ans to this is 3

Similarly for any digit it is the same process
for ex: last digit is 3 then 
3^1 = 3
3^2=9
3^3=7
3^4=1
3^5 = 3
this way for 3 also the cyclic is 4 digits

17^27 has a units digit of:

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17^27 has a units digit of:

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