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A person uses the base x for his number system, where x ≤ 10. A student had to add two-digit numbers. None of the digits was 0. By oversight, he reversed the digits of both the numbers and added them. He later found that the difference between his answer and the correct answer was $(84)_­­10. If this value is the maximum possible for x, then what is the value of x.









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Option(C) is correct

The difference between a number $pq$ with non-zero digits and its reverse $qp$ in base $x$ is $|p-q|(x-1)$.

This is maximum when $\{p,q\}= \{x-1, 1\}$.
This difference is $(x-2)(x-1)$.

For the sum of two numbers and the sum of their reverses.
It is $2(x-2)(x-1)$
$2(x-2)(x-1) = 84.$
⇒ $x =$ 8.

(2) Comment(s)

Apoorv Jain

the solution provided is not that satisfying... Huh Shocked

Ramesh Sidhdhant

On the contrary I believe, the solution provided is very good.

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