GATE | GATE MOCK 2017 | Question 7

If (4446)_x + (2222)_x = (10001)_x then value of (2342)_x – (1656)_x = (?)_x
(A) 453
(B) 353
(C) 893
(D) 686

Answer: (B)
Explanation: in base 10 we know 6+2= 8 but in this question it is given 1 so we have to find the base of these numbers.
Now let the base be x so 6+2=8 -x= 1 thus base =7 (because in base 7, 8 will be represented as 1 carry and 1 addition ).
Now subtracting given numbers in base 7.

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