I think to answer this question, it needs to be slightly rephrased. According to my girlfriend - who is wrong, by the way - skim milk should be avoided because when there is less fat, there is more sugar, and sugar metabolises faster than fat, so it becomes more fattening than fat (strangely enough). So the implied question is not so much whether skim milk has more sugar than whole milk, but rather, is skim milk more fattening because it has more sugar than whole milk? While the concept of sugar being more fattening than fat may be true in general, we will see that this argument doesn't hold true for whole and skim milk.
First, the question that was asked, in its original form: Is there more sugar in skim milk? Think of it like this: Put a glass of whole milk on the table; now skim out the fat. Since you have removed a part of the milk, there is not only less fat in the glass, but also less milk overall in the glass. There is still the same amount of sugar in the glass (remember, I didn't tell you to add any sugar).
Now consider the following analogy: Imagine you are in school, and your final grade is determined by five assignments, each worth 20% of the final grade; then your teacher tells you that the class won't have time to do the final assignment, so your grade will only be based on the first four assignments. Now, all of a sudden, each assignment is worth 25%; even though there is no more work involved in those assignments, they are worth proportionally more than they had been.
The same is true in our milk problem. Because the amount of milk has decrease, but the amount of sugar has stayed the same, it becomes proportionally bigger than it had been when there was more milk. If you drink that glass of milk, you will drink the same amount of sugar you would have drunk had you drunk the original glass of whole milk; on the other hand, if you top up the glass with skim milk until it is full again, you will have added a little bit of sugar. However, when dealing with proportions, we have to know what the original proportion is to know just how much we have increased. A quick look over some nutritional labels of whole milk and skim milk tells me that skim milk has about 1.1 times as much sugar (since there is relatively low sugar, this extra 0.1x of sugar is also extremely low - almost insignificant). On the other hand, whole milk has about 1.9 times as many calories as skim milk, and has about 30 times as much fat (most of which is saturated fat - the bad kind).
Another thing to consider is that you shouldn't confuse table sugar (properly called sucrose, which is added to recipes to make them sweeter, digests quickly, and is very fattening) with the sugar in milk (called lactose, which is a natural sugar similar to the natural sugars in fruit, which is so hard to digest that many people who do not drink milk on a regular basis develop lactose intolerance - the inability to digest the sugar in milk at all because their bodies no longer produce the necessary enzymes, which incidentally applies to most of the non-western world - and hence lactose does not digest quickly, and is far less fattening than table sugar).
As a result, we can conclude that skim milk has marginally more sugar than whole milk, but since there is relatively little sugar in milk to begin with, this tiny little bit of added sugar is almost insignificant; this sugar is also far less fattening than most of the sugars we are used to discussing; and skim milk is also far less fattening due to a much more significant drop in both fat (especially saturated fat) and calories.
First, the question that was asked, in its original form: Is there more sugar in skim milk? Think of it like this: Put a glass of whole milk on the table; now skim out the fat. Since you have removed a part of the milk, there is not only less fat in the glass, but also less milk overall in the glass. There is still the same amount of sugar in the glass (remember, I didn't tell you to add any sugar).
Now consider the following analogy: Imagine you are in school, and your final grade is determined by five assignments, each worth 20% of the final grade; then your teacher tells you that the class won't have time to do the final assignment, so your grade will only be based on the first four assignments. Now, all of a sudden, each assignment is worth 25%; even though there is no more work involved in those assignments, they are worth proportionally more than they had been.
The same is true in our milk problem. Because the amount of milk has decrease, but the amount of sugar has stayed the same, it becomes proportionally bigger than it had been when there was more milk. If you drink that glass of milk, you will drink the same amount of sugar you would have drunk had you drunk the original glass of whole milk; on the other hand, if you top up the glass with skim milk until it is full again, you will have added a little bit of sugar. However, when dealing with proportions, we have to know what the original proportion is to know just how much we have increased. A quick look over some nutritional labels of whole milk and skim milk tells me that skim milk has about 1.1 times as much sugar (since there is relatively low sugar, this extra 0.1x of sugar is also extremely low - almost insignificant). On the other hand, whole milk has about 1.9 times as many calories as skim milk, and has about 30 times as much fat (most of which is saturated fat - the bad kind).
Another thing to consider is that you shouldn't confuse table sugar (properly called sucrose, which is added to recipes to make them sweeter, digests quickly, and is very fattening) with the sugar in milk (called lactose, which is a natural sugar similar to the natural sugars in fruit, which is so hard to digest that many people who do not drink milk on a regular basis develop lactose intolerance - the inability to digest the sugar in milk at all because their bodies no longer produce the necessary enzymes, which incidentally applies to most of the non-western world - and hence lactose does not digest quickly, and is far less fattening than table sugar).
As a result, we can conclude that skim milk has marginally more sugar than whole milk, but since there is relatively little sugar in milk to begin with, this tiny little bit of added sugar is almost insignificant; this sugar is also far less fattening than most of the sugars we are used to discussing; and skim milk is also far less fattening due to a much more significant drop in both fat (especially saturated fat) and calories.
