It's Popcorn on the floor!

Algebra Level 4

A = e π + e B = e + π e C = π e + e D = π + e π \begin{aligned} A & = & \lfloor e^{\pi} \rfloor + \lceil e \rceil \\ B & = & \lfloor e \rfloor + \lceil \pi^e \rceil \\ C & = & \lfloor \pi^e \rfloor + \lceil e \rceil \\ D & = & \lfloor \pi \rfloor + \lceil e^\pi \rceil \\ \end{aligned}

Which of the following is correct?

Notations : \lfloor \cdot \rfloor denotes the floor function and \lceil \cdot \rceil denotes the ceiling function .

C > A C>A B > D B>D B > A B>A C > D C>D D > A D>A A > D A>D

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1 solution

Tom Engelsman
Jan 12, 2019

Taking e π 23.14 , π e 22.46 e^{\pi} \approx 23.14, \pi^{e} \approx 22.46 , we compute the following:

A = 23 + 3 = 26 , B = 2 + 23 = 25 , C = 22 + 3 = 25 , D = 3 + 24 = 27 A = 23 + 3 = 26, B = 2 + 23 = 25, C = 22 + 3 = 25, D = 3 + 24 = 27

Of the provided choices, D > A \boxed{D > A} is correct.

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