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Quantitative Aptitude

Base Systems

P is represen...

Question

P is represented as $P = x_{a} y^{a} + x_{a - 1} y^{a - 1} + . . . . . x_{1} y + x_{0}$ where $0 < x_{0} . . x_{a} \leq y - 1$ . If x and y are positive integers and y=4, then which of the following could be a representation of an integer with y as a base?

12343

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132421

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132321

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none of these

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Solution

The correct option is C
132321

When the base is 4, the maximum digit the number can contain is 3, it cannot contain 4.

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P is represented as P=xaya+xa−1ya−1+.....x1y+x0 where 0<x0..xa≤y−1. If x and y are positive integers and y=4, then which of the following could be a representation of an integer with y as a base?

The correct option is C 132321 When the base is 4, the maximum digit the number can contain is 3, it cannot contain 4.

P is represented as $P = x_{a} y^{a} + x_{a - 1} y^{a - 1} + . . . . . x_{1} y + x_{0}$ where $0 < x_{0} . . x_{a} \leq y - 1$ . If x and y are positive integers and y=4, then which of the following could be a representation of an integer with y as a base?

The correct option is C
132321

When the base is 4, the maximum digit the number can contain is 3, it cannot contain 4.