During a 7-year period the profits of Midas, Inc. changed by

Dear iliavko,

My friend, thank you for your kind words. I am happy to respond.

The first thing I'll say is that when we have a series of percent changes, one after the other---say a 40%, then a 30% increase on that, then a 20% decrease--never think addition. Think multiplication.

In fact, for any percent increase or decrease, you should be thinking about these in terms of multiplication. Read this thoroughly:
Understanding Percents on the GMAT

Thus, to accomplish the proposed series of percent changes above, we would find the multipliers for each and multiply them together (I used a calculator to get the product--that's beyond what the GMAT would expect you compute in your head!)
(1.4)*(1.3)*(0.80) = 1.456
Thus, if we have an initial amount, and we increase by 40%, then increase by 30%, then decrease by 20%, that's equivalent to a 45.6% increase over the initial amount.

Now, if you read the blog thoroughly and understand all that, we can look at this problem:
During a 7-year period the profits of Midas, Inc. changed by what percent from the sixth year to the seventh year?
(1) The profits of Midas, Inc. during the seventh year were 50 percent greater than the profits during the third year.
(2) The increase in the profits of Midas, Inc. was the same for each year during the 7-year period.

The individual statements are not sufficient. Let's deal with the combined statements. Let's say that x is the percent change from year to year, written as a decimal. Thus, x would be the answer to the prompt question, because the change from year 6 to year 7 would be the same as the change from any other year.

The multiplier for a change from one year to the next is (1 + x). Let P3 be profit in the third year, P4, profit in the 4th year, etc. We know

P4 = P3*(1 + x)
P5 = P4*(1 + x) = P3*(1 + x)^2
P6 = P5*(1 + x) = P3*(1 + x)^3
P7 = P6*(1 + x) = P3*(1 + x)^4

Now, since we also know that P7 = 1.5*P3, that allows us to set up an equation:

1.5 = (1 + x)^4

We'd need a calculator to solve for the exact value, but that doesn't matter. This is DS, it's enough to know that we could solve for the exact value of x and answer the prompt question. Both statements together are sufficient. Answer = (C).

BTW, x = .10668192..., about 10.67%

Does all this make sense?
Mike