OG 11 QP 194

[mandy12]

OG 11 Q 194

What should be the approach to solve these kind of questions ?

Q . What is the unit's digit of 13^4*17^2*29^3 ?

A. 9
B. 7
C. 5
D. 3
E. 1

I got the answer but I am not sure if my approach was the best.

[simplyjat]

The best approach is to only consider the units place.

for example,
what is the units place for 123456789 * 987654321? Answer is 1*9 = 9...

in the the question you specified,
13^4*17^2*29^3
= 13*13*13*13*17*17*29*29*29
as you are asked about units digits, reduce the equation in units...
= 3*3*3*3*7*7*9*9*9*9
Now carry out multiplication and just keep the units digit at each level...
3*3 = 9
9*3 == 7 (discard 2 from 27)
7*3 == 1 (discard 2 from 21)
1*3 = 3
3*7 == 1 (discard 2 from 21)
1*7 = 7
7*9 == 3 (discard 6 from 63)
3*9 == 7 (discard 2 from 27)
7*3 == 1 (discard 2 from 21)

and the answer is 1....