Problem Solving

Find the units digit of 214^870 + 149^127.

1. 7
2. 1
3. 3
4. 9
5. 5


ans. 5

in 214 ^ n (214 * 214 * 214 * 214 ....)
the last digit is in pattern 6,4,6,4... similarly in 149 its 1,9,1,9...

6+9 in units place will leave 5

satish.nagdev wrote:in 214 ^ n (214 * 214 * 214 * 214 ....)
the last digit is in pattern 6,4,6,4... similarly in 149 its 1,9,1,9...

6+9 in units place will leave 5

Hi Satish:
How did u get 6 for 214^870 and not 4?
I got 9 in 149^127 because of 9x9x9x9x9x9x9 = 7th 9-digit because its power ends in 7 (127).
Could you help me please?
Thank you,
Silvia

ssuarezo wrote:

satish.nagdev wrote:in 214 ^ n (214 * 214 * 214 * 214 ....)
the last digit is in pattern 6,4,6,4... similarly in 149 its 1,9,1,9...

6+9 in units place will leave 5

Hi Satish:
How did u get 6 for 214^870 and not 4?
I got 9 in 149^127 because of 9x9x9x9x9x9x9 = 7th 9-digit because its power ends in 7 (127).
Could you help me please?
Thank you,
Silvia

For every odd power (214^1, 214^3, 214^5 etc) the unit's digit is 4 (214^1=214,214^3=9,800,34). For every even power (214^2, 214^4 etc) the unit's digit is 6. So for 214^870, the unit's digit is 6.
Work the same way with 149: for 149^1, the unit's digit is 9, for 149^2, the digit is 1. Since 127 is odd, the unit's digit of 149^127 is 9.
9+6=15.
I hope that helps

djkvakin wrote: For every odd power (214^1, 214^3, 214^5 etc) the unit's digit is 4 (214^1=214,214^3=9,800,34). For every even power (214^2, 214^4 etc) the unit's digit is 6. So for 214^870, the unit's digit is 6.
Work the same way with 149: for 149^1, the unit's digit is 9, for 149^2, the digit is 1. Since 127 is odd, the unit's digit of 149^127 is 9.
9+6=15.
I hope that helps

thank you djkvakin (don't know how to read it ! )

Find the units digit of 214^870 + 149^127.

1. 7
2. 1
3. 3
4. 9
5. 5

The simplest way of solving such questions as per me is

divide the powers by 4 and see the remainders:

i.e.

870/4 gives the remainder 2 and then raise 214 by 2 and then the unites digit is 6.
now divide 127/4 and the remainder is 3 and then raise 149 by 3 and the units digit is 9

So 6 + 9 = 15 so units digit is 5.

Cheers