melguy wrote:
* what if we change the Q to - After 15% discount the price of a shirt is $51. What is the original cost of the shirt? If i take 51 and multiply it by 1.15 then i get 58.65 (which is incorrect). What am i doing wrong?

There's an important distinction here - important because it's tested on the GMAT all the time. If you decrease something by 15%, then increase it by 15%, you don't get back to where you started. The reason is that the 15% increase is being applied to a smaller value than the 15% decrease, so ends up being a smaller change in dollar terms. That's why you didn't get all the way to $60 in your calculation.

When you have a percent increase/decrease question, it is crucially important to get the direction of the increase right. If the price of a shirt is $60, then we decrease that by 15%, we have the following 'flow chart':

$60 ----(-15%)----> ???

Here we can find the resulting value by taking 15% of 60 away from 60, so the resulting price is 60 - 0.15(60) = 60 - 9 = 51. Alternatively, you can just multiply 60 by 0.85.

In your second example, we know that the price *after* the 15% discount was $51. So we have the following 'flow chart':

??? -----(-15%)----> $51

Notice here that we are applying the 15% *not* to the $51, but to the unknown starting price. If we call that x, we get the equation:

x - 0.15x = 51
0.85x = 51
(17/20)x = 51
x = (51*20)/17 = 3*20 = 60

I like to be able to visualize problems anyway, so I almost always draw 'flow charts' like the ones above in any percent change question. It's a helpful way to avoid applying the percentage to the wrong quantity.