Of an inventory of a particular item received at a store, one week, 1

In questions involving fractions, instead of assuming x or 1 as the value for the unknown, it’s better to assume it to be the LCM of the denominators. This way, you can cancel out the denominators and hence deal with whole numbers only.

Since the fractions given in the question are ½, 1/3 and 1/8, the total inventory can be assumed to be 24x. The x is to account for the fact that the question mentions that there are 7 units remaining.

So, on the first three days, the number of units sold will be 12x, 8x and 3x respectively. These add up to 23x, which leaves us with x. This x should represent the remaining 7 units.

If x = 7, then 24x = 168 which represents the total number of units sold.

The correct answer option is C.

Hope this helps!

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

X/2 + X/3 + X/8 = X - 7

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:

12X/24 + 8X/24 + 3X/24 = X - 7

We are now getting somewhere with this equation, because 23/24 is all of the inventory except 7 units. In other words 7 is 1/24 of the inventory. The total inventory is, therefore, 24*7 = 168.

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 1/24 of the total inventory. If we hadn't noticed that, we could have proceeded with solving 23x/24 = X - 7 in a more brute-force manner by multiplying both sides by 24, subtracting 23X from both sides and adding 24*7 to both sides, and finding that 24*7 = X. 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).