The cost, c and the revenue, r are related via the equation

[BTGmoderatorAT]

The cost, c and the revenue, r are related via the equation c =ar+b. By how much is the cost increased if the revenue is increased by $10?

1) a=0.5
2) b=5

What's the best way to determine whether statement 1 is sufficient? Can any experts help?

[GMATGuruNY]

The cost, c and the revenue, r are related via the equation c =ar+b. By how much is the cost increased if the revenue is increased by $10?

1) a=0.5

What's the best way to determine whether statement 1 is sufficient?

Statement 1: a = 0.5
Case 1: original r = 10, new r = 20
In this case:
Original c = (0.5)(10) + b = 5+b
New c = (0.5)(20) + b = 10+b
Cost increase = (new c) - (old c) = (10+b) - (5+b) = 5.

Case 2: original r = 20, new r = 30
In this case:
Original c = (0.5)(20) + b = 10+b
New c = (0.5)(30) + b = 15+b
Cost increase = (new c) - (old c) = (15+b) - (10+b) = 5.

Since the cost increase is THE SAME in each case, SUFFICIENT.