I think the section that delighted you is actually called the "analytical reasoning" section. The "logical reasoning" section gives you a paragraph about some subject, and that asks about inferences and deductions you can make from that.

There are samples from both sections here for comparison: http://www.lsac.org/jd/lsat/about-the-lsat/

I too found analytic reasoning delightful, both during practice tests and during the actual test. One thing about the actual test that kicked it up a notch over practice tests (aside from the pressure of it being for real) was that you could not bring scratch paper to the real test. There was a fair bit of empty space in the test booklet so you had room for truth tables, graphs, and such, but if you botched one and had to start over you might find scratch space tight.

I aced analytic reasoning. Shortly after the test, I saw a magazine at the supermarket full of those kinds of problems. The shelf position and the ads in the magazine indicated it was aimed at older women. I bought it, because I enjoyed that part of the test so much, but didn't have much hope because I aced that part of the LSAT! How are puzzles for Grannies going to be a challenge? So I tried a level 3 difficulty puzzle (range was 1 to 5 with 5 the hardest).

It DESTROYED me. I could do level 1 reasonably, and level 2 with a lot of effort.

I vowed that if I did become a lawyer, I would not take cases that would pit me against old ladies. (I did not become a lawyer. I decided near the end of law school that I would rather be a programmer who knew a lot about law than a lawyer who knew a lot about programming. My policy of not going against old ladies in battles of wits remains in force).