The total amount of profits of Brandeburgh Bicycle Company (BBC) must

The total amount of profits of Brandeburgh Bicycle Company (BBC) must have increased dramatically over the last 5 years. After BBC developed a light and strong new material for its bicycles, total sales increased to twice what they were 5 years ago. Nevertheless, sales of certain types of bicycles, for which the new material is not used due to its high cost, have remained constant or, as is the case with bicycles for children, have decreased. Four years ago, sales of children’s bicycles constituted 30 percent of the total bicycle sales of BBC, and now they constitute barely 20 percent of all BBC’s sales.

Which of the following must be assumed in order for the assertion that the total amount of profits of BBC has increased dramatically over the last several years to be true?
(A)Increased sales always result in increased profits. --- too strong (always) for assumption .An assumption is a mild statement
(B)BBC bicycles are not significantly more expensive than 5 years ago. -- That doesnt help knowing bicycles were expensive 5 yrs ago !
(C)Over the last 5 years, total sales of BBC racing bicycles did not decrease by more than 70 percent. ---out of scope ...Racing bicycle is not mentioned !
(D)Over the last 5 years, the average amount of profit gained by BBC per bicycle sale has decreased by less than 50 percent. ---correct see explanation below
(E)The proportion of bicycle market occupied by bicycles of BBC has not decreased over the last 5 years. -- the total market share of bicycles in not known ..and even if mkt share decreased , it could still have made greater profits !


The answer should be (D) -

Lets asssume P1 (profit 5 years ago) (we know there was profit as question stem says - increase profit substantially) and P2 (after 5 years)
Let sales 5 years ago be S , after 5 years it would have been be 2S (as sales doubled)

So now lets take case when P2 didnt not increase substantially and is equal to P1

(P1/S) - (P2/2S) / (P1/s) * 100 (CALCULATE %diff in profit per bicycle when P2=P1)

substitiute P2=P1

(P1/S) - (P1/2S) / (P1/s) * 100 = 50 %

so it proves to maintain same profit levels the average profit gain per bicycle should be 50 % of was 5 years ago . So we need profit per bicycle to descrease by
50 % for profit to increase !

hope this helps !