What is $346_7 + 165_7 $when expressed in base-$7$?

Question

Hi I used a converter to do this question - and answered the second option. But still unsure, if I made it right.

score 6 · Accepted Answer · answered Feb 23 '16 at 17:24

6

You can eliminate the other answers by simply considering the units. The units digits are $6$ and $5$. Their sum is $11$, which is congruent to $4$ mod $7$. So the solution must have a $4$ in the units digit.

answered Feb 23 '16 at 17:24

The Chaz 2.0

10,464

And then we can conclude 544 must be the right answer ;) – Martin Andersen Feb 23 '16 at 17:25
Sure. You could also rule out $511$, their sum in decimal, and $277$ (for the leftmost digit being too small). – The Chaz 2.0 Feb 23 '16 at 17:43

score 1 · Answer 2 · answered Feb 23 '16 at 18:40

1

$$346_7+165_7=(3\cdot7^2+4\cdot7^1+6\cdot7^0)+(1\cdot7^2+6\cdot7^1+5\cdot7^0)=$$ $$=277=5\cdot7^2+4\cdot7^1+4\cdot7^0=544_7$$

answered Feb 23 '16 at 18:40

Adi Dani

16,949

What is $346_7 + 165_7 $when expressed in base-$7$?

2 Answers2