Well, there's no hard and fast rule that I could give you to distinguish between the two. I have seen some websites that say use more with plural words and greater with singular ones, but that's not necessarily true. After all, we could easily say: John drinks more wine than I do (wine is singular, so why not use greater?).
Perhaps it may be clear if you consider these two sentences:
John has more friends than I do.
John has greater friends than I do.
What's the difference? In the first sentence, we are suggesting, for example, that I have 10 friends whereas John has 20. The second sentence, in contrast, suggests that the friends that John has are more impressive than mine. For example, maybe I am friends with Gary the Grocer while John is friends with the Queen of England. In that sense, certainly John has greater friends.
The word greater is often used on the GMAT with the words amount and number. We should not say, for example, that the number of people visiting the grand opening of store X was more than the number visiting the grand opening of store Y. One number cannot be more than another number. It can, however, be greater. 10,000 is a more impressive number than 5,000 so we can say that 10,000 is a greater number.
Similarly, we might say: The amount of money spent on gifts this year is expected to be greater than that spent last year.
Elias Latour
Verbal Specialist @ ApexGMAT
blog.apexgmat.com
+1 (646) 736-7622