How many elements in a vector are greater than x without using a loop

Use length or sum:

> length(x[x > 10])
[1] 2
> sum(x > 10)
[1] 2

In the first approach, you would be creating a vector that subsets the values that matches your condition, and then retrieving the length of the vector.

In the second approach, you are simply creating a logical vector that states whether each value matches the condition (TRUE) or doesn't (FALSE). Since TRUE and FALSE equate to "1" and "0", you can simply use sum to get your answer.

Because the first approach requires indexing and subsetting before counting, I am almost certain that the second approach would be faster than the first.