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Question

In a certain system of writing of numbers, we write (12Φ)4=(124)Φ, where Φ is the units digit in the first place and number of digits in that system in the second place. How many values of Φ are possible?

A
1
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B
3
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C
Infinite
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Solution

The correct option is A 0
124Φ shows that value of Φ should be 5 or more than 5 (since 4 is a digit used in this system).
(12Φ)4 shows that value of Φ can be at max 3 (since the system = 4).
Now, this is a contradiction. Therefore, no such value exists.

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