There are about a half-dozen issues with the wording of this question. A "set" in math contains distinct elements, so can't have a mode - the question means to describe a 'data set' or a 'list'. And the question makes it sound like we're inserting six values in some set that already exists, and if that were true the answer would be E (if you assume the statements each describe a newly enlarged data set with more than six values in it) but that's not what the question means; we're creating a new data set from scratch from these six values. And I have no idea what they mean when they say the values are "randomly selected" -- from what sample space? If we're selecting the values from some finite set of integers, then there is only one data set that's even possible, without using either of the Statements (the data set 2, 3, 5,7, 7,18). So you wouldn't need any information to answer the question, which never happens on the GMAT, but I guess then the answer would be D. But if we're picking randomly from some infinite set, we're getting into math miles beyond GMAT level (that's impossible to do at all without specifying a distribution, and you'd never end up picking integers for each value).
So the wording is deeply problematic here, and the question is open to several interpretations which lead to different answers. All the question is trying to say is that we have a list of six values, not necessarily integers, with a range of 16, mean of 7, median of 6 and mode of 7. If we let "L" be the largest value in the list, then L cannot equal 7, because then every value in the list would be average or below average, and that's impossible unless every value is the same, which is not true here. So L > 7. If the mode is 7, we must have at least two 7's in our list. We must have only two, and they must be the second and third largest values, because the median is 6, so the fourth largest value is no larger than 6. If the third largest value is 7, and the median is 6, the fourth largest value must be 5. Since the range is 16, the smallest value is L-16. So we have this list, in increasing order:
L-16, a, 5, 7, 7, L
and since the mean is 7, these values sum to 42, and using that you find that a = 39 - 2L, so our list is
L - 16, 39 - 2L, 5, 7, 7, L
If you now solve the inequalities L-16 < 39 - 2L and 39 - 2L < 5 (which need to be true for the list to have only one mode and for the range to be 16), then you find that 17 < L < 18 + 1/3, so only one integer value of L is possible, 18. If L is not necessarily an integer, we'd need more information to answer the question. Statement 1 gives us one equation in the one unknown L, so we can find L from Statement 1. Statement 2 is something we know from the stem alone, so is useless information. So the answer is A.
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