Problem Solving

Strongt wrote:Dinner cost $230 including a 15% tip.
How much was dinner without the
tip?

My answer is 195.5

OA is
Answer: $200
If $230 includes the cost of the dinner plus an additional
15%, then it is 115% of the cost of the dinner, so 230 =
(115/100)x.
x 200 = x[/spoiler]

If you arrived at the answer 195.5, you've answered the wrong question - you've reduced $230 by 15%. The 15% in this question is not applied to the $230 at all; it's applied to the original cost of the dinner before the tip. We know that if we add 15% to the cost of the dinner, we get to $230, so if the dinner cost $d before the tip, the dinner cost $(1.15)d after the tip. That leads you to the equation

(1.15)d = 230
d = 200

It is crucially important, in many GMAT questions, to be certain you understand how this works. If, for example, someone sells a painting for $1100 and makes a 10% profit, we do not apply the 10% to the $1100 to find the amount of profit. If you make a 10% profit, your selling price is 10% greater than your purchase price. If your purchase price is p, then 1.1p = 1100, and p = 1000, so your profit is $100 (which is not equal to 10% of $1100). Similarly if the price of a share falls by 25% to $150, then this final price is 25% less than (or 75% of) the initial price; if you solve the equation 0.75x = 150 you'd find the original price was $200. We would not apply the 25% to $150.