This GMAT quant practice question is a counting methods problem solving question. The concept tested in this question is to find the number of ways some letters from a word can be selected and rearranged with a constraint.
Select 2 letters and rearrange them
MEDITERRANEAN is 13-letter word.
We have to make 4 letter words that start with an 'E' and end with 'R'.
Therefore, in addition to E and R, we have to find two more letters from the remaining 11 letters.
Of the 11 letters, there are 2 Ns, 2Es and 2As and one each of the remaining 5 letters.
The second and third positions can either have two different letters or can have both as same letters.
Case 1: When the two letters are different
One has to choose two different letters from the 8 available different choices.
This can be done in 8 * 7 = 56 ways.
Case 2: When the two letters are same
There are 3 options - the two letters can be Ns or Es or As. Therefore, 3 ways.
Total number of posssibilities = 56 + 3 = 59
Choice A is the correct answer.