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Algebra Level 2

Does the following equation has a solution?

$\large \lceil x \rceil + \lceil 2x \rceil = 16$

Notation : $\lceil \cdot \rceil$ denotes the ceiling function .

Not enough information to determine Yes No

1 solution

Denton Young
May 13, 2016

At x = 5, $\lceil 5 \rceil$ + $\lceil 10 \rceil$ = 15

For any x greater than 5, $\lceil x \rceil$ is at least 6 and $\lceil 2x \rceil$ is at least 11, so $\lceil x \rceil$ + $\lceil 2x \rceil$ is at least (6 + 11) = 17.

Therefore, there is no solution.

Moderator note:

How would you describe the range of $\lceil x \rceil + \lceil 2x \rceil$ .

I'd describe it as "jumpy" It skips over all integers of the form 3n + 1.

Denton Young - 5 years ago

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1 solution

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