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MissPhiladelphia
The problem is not clear if the percent composition is in terms of mole or mass. I will just present the two.

For mole percent.

Total number of moles of element per mole CH4 = 1 mol C + 4 mol H = 5 mol

therefore we have
% mol C = 20%
% mol H = 80%

for mass percent'

Molar mass of CH4 = 16 g/mol
 molar mass of C = 12
molar mass of H = 4*1 =4

thus
% mass C = 12/16 = 75%
% mass H = 4/16 = 25%

both answers are in the choices but percent composition is usually expressed in mass therefore I think choice A would be the best answer. 

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