Data Sufficiency

You don't necessarily have to solve this problem algebraically. When you're two distinct designations of price or quantity, (such as 5-lb and 10-lb bags, $3 and $4 widgets, etc), you know that there are only a limited number of combinations that will add to the given total (in this case, $130). You can quickly write out a chart for all of the possible pairings that will give you that total:


If we want to know how many 5-lb bags there are, we really want to know - can we narrow it down to a single pairing?

1) the number of 5 pound bags sold was 2 more than 4 times the number of 10-pound bags sold
Here, we can intuit that this will only be true for a single pairing. Or we can look at our chart and see where this is true:




2) the store sold 50 more pounds of potatoes in 5-pound bags than in 10-pound bags.
Again, we can intuit that this will only be true for one pairing. Or, we can look at the chart:



In this problem, writing out the chart was somewhat time-consuming, so algebra or intuition might have been more helpful. In other cases, though, if there are only 6 or 7 pairings that work, it can be a quick-n-easy way to approach the problem. And it's always good to have options!