# If 263+441 = 714 what is the base used. Please help me. A.5 B.6 C.7 D.8 E.9

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### 1 Answer

You need to be little tricky here.

The familiar base for us is base 10. As you know we use numbers 0 to 9 under base 10 to define any number. What important is we never use 10.

So if it is base 2 we never use 2. If it is base 4 we never use 4. The largest number we can use to define a number is 1 less than the base. If base is 10 the highest is 9. If 2 highest is 1 and for 4 it is 3.

`263+441 = 714`

Here we have number 7. So according to the above explanation you will never get base 5,6,7 as the answer.

Let us assume the answer is base 8.

`263_8 = (64xx2+8xx6+3)_10 = 179_10` (Because we are familiar with base 10)

`441_8 = 289_10`

`(263+441)_8 = 179+289 = 468_10`

`714_8 = 460_10`

So base 8 is not the answer. So definitely base 9 would be the answer.

`(263+441)_9 = 81xx2+9xx6+3+81xx4+9xx4+1 = 580`

`714_9 = 81xx7+9xx1+4 = 580`

*So the answer is base 9. Answer is E.*