A-level Transition metal mc question

When vanadium reacts with chlorine at 400°C, a brown compound is obtained. When an aqueous solution containing 0.193 g of this compound was treated with aqueous silver nitrate all the chlorine in the compound was precipitated as silver chloride. The mass of silver chloride (AgCl) produced was 0.574 g. Which one of the following could be the formula of the brown compound?

A VCl
B VCl2
C VCl3
D VCl4


The answer is D, idk why tho. Please help

Step 1. Moles of AgCl. moles = 0.574g/(107.9+35.5) = 0.00400 moles
The equation is: (This was the hard part as the equation involved algebra)
VClx + xAgNO3 -> xAgCl + VNO3
Step 2. The mole ratio is 1:x for VClx : xAgCl
step 3. Brute force - find mole of VCl to VCl4, use mole ratio for mole AgCl, has to be 0.004
Try VCl, so x = 1
moles VCl = 0.193/(50.9+35.5) = 0.002 mole ratio is 1:x, so is 1:1 so AgCl formed is 0.002 X, need to be 0.004 so cannot be A
Try VCl2 so x = 2
moles VCl2 = 0.193/(50.9+71) = 0.0015 mole ratio 1:2, so AgCl formed is 0.003 X cannot be B
Try VCl3 so x = 3
moles = 0.193/(50.9+71+35.5) = 0.0012 mole ratio is 1:3, so AgCl formed is 0.0036 mole X cannot be C
must be D but let us check
Try VCl4, so x = 4
moles = 0.193/(50.9+71+71) = 0.001 mole ratio is 1:4, so AgCl formed is 0.004 moles as required so is D

All this work for 1 mark…

Not quite how I would have done it, because that isn’t the most time-efficient approach, but it works.

(1. If the product is VClx and the relative masses of V and Cl are 50.9 and 35.5, respectively, what is the Mr of VClx in terms of x?

(2. You have the mass of VClx (0.193 g) and already calculated the moles of AgCl (0.00400 mol, which should be x times the moles of VClx), so therefore, if you use mass/mol = Mr, then Mr/x = what? (Then multiply both sides of this expression by x to get a second expression for the Mr in terms of x)

(3. Set your expressions for the Mr to be equal and solve for x.

Thanks, when I saw these type of questions, I thought the only method was brute force