Here is the solution of the marathon problem
A
 no of formula units = 40 X 10^6X10^12 (40 million trillion)
mass of the 40million trillion = 4.6mg = 4.6 X 10^-3g 
 no of formula units in one mole = 6.022 X 10^23
no of moles in 40 million trillion units = 40 X 10^6X10^12/6.022 X 10^23 = 6.642 XX10^-5
mass  of  6.642 X 10^-5  moles = 4.6 X 10^-3 g
mass of one mole is   = 4.6 X10^-3/ 6.642X10^-5  = 69.26 g
Amount of carbon =  37.5 X 69.26 /100 = 25.97g
 mass of Metal in A in one mole = 69.26 – 25.97 = 43.3 g ( Ca metal )
 no of moles of carbon = 25.97/12.0 = 2.2  ~  2
metal in A is Ca  and formula unit is CaC2


B
Moles of H in B = 5.36 g / 1.008 =  5.13 moles of H
Moles of O = 42.5 /16.00= 2.66 moles of O
H:O  = 2  : 1
Hence B is H2O

C
Moles of Carbon = 33.8gCO2 X 12 .0g C /44g of CO2  X 1mole of C/ 12.0 g of C = 0.77 moles`
Moles of H =  6.92 g of water X  2.016 g of H/18.016 g of water  X  1mole of H / 1.008 g of H  = 0.77 moles Of H
                C:H = 1:1
Molar mass of C is 26 (from molecular ion peak of mass spectra)
Empirical formula mass is 13.008 g
n = molar mass /empirical formula mass = 26/13.008     ~ 2
hence C  is (CH)2  = C2H2
          
D
Since metal is Ca hence its hydroxide is Ca(OH)2

CaC2  +  2H2O   -------->  Ca(OH)2  +  C2H2
A              B                     C                    D