Explanation

This question describes three fraction of a particular amount of inventory. Notice that, on the second day, it's saying that a third of the original inventory was sold, not a third of the remaining inventory after the first day, since those two interpretations will lead to different results. So half the inventory plus a third of the inventory plus an eighth of the inventory adds up to a number that is seven less than the inventory. If the inventory is X, then that means



The fractions can be eliminated by multiplying both sides of the equation by 24. Or you can give the fractions on the left a common denominator of 24:





We are now getting somewhere with this equation, because is all of the inventory except 7 units. In other words 7 is of the inventory. The total inventory is, therefore, . The correct answer is (C).

This question can be solved efficiently in a number of different ways, some closely similar, some more different. For example, we basically cut off the algebra when we realized that 7 had to be of the total inventory. If we hadn't noticed that, we could have proceeded with solving in a more brute-force manner by multiplying both sides by 24, subtracting 23X from both sides and adding to both sides, and finding that . That finish is mathematically identical, although for most people it is easier to make an error along this path and also more difficult to figure out what the error was. Another method is to solve backwards. A great many GMAT questions can be solved purely backwards. You can start with 144, and see whether half of it plus a third of it plus an eighth of it yields 144 - 7. This method is sometimes far and away the most efficient way to solve a GMAT question, while sometimes an algebraic method is only viable method, so you will want to cultivate both methods. The correct answer is (C).