Data Sufficiency

Martha bought an armchair and a coffee table at an auction and sold both items at her store. Her gross profit from the purchase and sale of the armchair was what percent greater than her gross profit from the purchase and sale of the coffee table?

1. Marth paid 10 percent for the armchair than for the coffee table
2. Marth sold the armchair for 20 percent more than she sold the coffee table



Is the answer E because we don't know that price of either the coffee table or armchair?

Sheet of paper. We're looking for:

ARMprofit
________ (divided by)
COFFEEprofit


where ARMprofit = ARMretail - ARMwhole
and COFFEEprofit = COFFEEretail - COFFEEwhole

(1) and (2) give us certain variables but don't deliver by themselves, so let's try putting them together. (1) tells us that ARMwhole = 1.1 COFFEEwhole. (2) tells us ARMretail = 1.2 COFFEEretail.

We plug those into the main division formula (do some switching)... and it doesn't go anywhere. And you know, I think we actually could have solved this if they told us that the armchair cost 20% more, instead of 10% more, because we could have pulled out a 1.2 in the main division formula.

To answer your question, exact values would be enough to solve, but so would a simplified formula.

(E)

See: if they had told us ARMwhole = 1.2 COFFEEwhole, the formula would reduce to:
ARMretail - ARMwhole
__________________
COFFEEretail - COFFEEwhole

equals:
1.2 COFFEEretail - 1.2 COFFEEwhole
______________________________
COFFEEretail - COFFEEwhole

... and the we could have just pulled out the 1.2 in the numerator and that would be our answer, regardless of specific values for each of those variables. Yeah I did some extra work here...

Isnt it coffee profit/arm profit since cofee profit is greater?