Is the answer to this question E?

I guess E because to calculate the gross profit, you need to know
A). The Cost Price (CP) and Selling Price (SP) for the Armchair (if X = CP of the Coffee table, then 1.1X = CP of the Armchair)
B). The CP and SP of the Coffee Table (if Y = SP of the Coffee table, then 1.2Y = SP of the Armchair)

Statement 1 tells us that the CP of the Armchair is 10% > the CP of the Coffee Table - INSUFFICIENT

Statement 2 tells us that the SP of the Armchair is 20% > the SP of the Coffee Table - INSUFFICIENT

Combining both statements you'll notice that the SP of the Armchair is given relative to the SP of the Coffee Table and not the CP of the Armchair; therefore, you cannot algebraically solve for the Gross Profit because you cannot say 1.2Y-1.1X. If we knew the values of X and Y then both statements would be sufficient hence my choice of E.

Let me know if my reasoning makes sense

Use logic. Gross is in terms of actual numbers, percent is not. You can have no way to determine this answer. No calculations should be necessary.