Problem Solving

what is the unit digit of (13)^4(17)^2(29)^3?

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

plz give the best way to find out the unit digit

pradeepkaushal9518 wrote:what is the unit digit of (13)^4(17)^2(29)^3?

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

plz give the best way to find out the unit digit

just consider the unit digits
(3^4) *(7^2) *(9^3)
Even while calculating 3^4 , notice that the unit digit is 3*3 = 9*3 = ..7*3=..1
7^2 = 49
29^3 = 9*9 = 81*9=..9
now 1*9*9 = ...1

kstv's explanation is the best way to solve this Q. You know there is no way you can be expected to calculate the number. Since the units digit of a product depends only on the units digit of each term in the multiplication, we can just focus on the units digit of each term. In general, if I'm stuck on pattern problems, I start solving manually until I see the pattern develops.

This is OG12 Problem solving #190. OG Companion 12th Solution is attached.

-Patrick

yep.

The units digit of sequential integer powers of a given base follows a cyclic pattern.

For example:

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

3^5 = ....3 (again!)

So, the 1st, 5th, 9th, 13th, etc powers of 3 result in units digit of 3.
Likewise, the 2nd, 6th, 10th, 14th etc powers of 3 result in units digit of 9.
And so on.