Correct Answer: E
Explanation:
The conditions “J and J are holding hands” and “L and L are holding hands” are naturally symbolized as JJ and LL, respectively. The condition “K and K are not holding hands” can be symbolized as K...K. [The symbol ~(KK) would also work well, but the symbol K...K is more descriptive because it shows the space between the Ks.] The condition “One of the Ls is at one end of the line, and one of the Ms is at the other end” can be symbolized as L=1st/last and M=1st/last. The diagram will consist of eight dashed lines numbered 1 through 8, from left to right:
JJ
LL
K ... K
L = First / Last
M = First / Last
No significant conditions can be derived from the given information, and no conditions can be placed on the diagram. So we attack the questions.
This is a moderately hard problem. The condition “the Ks are separated by at most one other person” is somewhat obscure. It is more clearly expressed as “exactly one person separates the Ks.”
Since the two Js must be next to each other, they cannot both be in even-numbered positions. This eliminates both (A) and (C). The same is true for the Ls, which eliminates (B).
Since the Ks are separated by exactly one person, they must either both occupy even-numbered positions or both occupy odd-numbered positions. But choice (D) places only one K in an even-numbered position. This eliminates (D).
As a matter of test-taking strategy, this is sufficient analysis of the question to mark the answer (E). However, it is instructive to work out a valid order for (E).
To this end, place an M in position 1 and the Ls in positions 7 and 8:
Next, place the Ks in positions 2 and 4, with M separating them:
Finally, place the Js in positions 5 and 6:
This diagram satisfies all the conditions, which verifies that (E) is the answer.