以下のGMATの問題の解説が理解できず、どなたか噛み砕いて説明いただけないでしょうか。。BかDまでは絞り込めたのですが、なぜBに特定できるのか理解できず。。 【問題文】 If m is an even integer, v is an odd integer, and m > v > 0, which of the following represents the number of even integers less than m and greater than v ? A. (m−v)/2 − 1 B. (m−v−1)/2 C. (m−v)/2 D. m − v − 1 E. m − v 【回答】 B. (m−v−1)/2 【解説】※見えずらいと思うのですが、画像でも添付します To solve this problem it is not necessary to show that (m−v−1)/2 always gives the correct number of even integers. However, one way this can be done is by the following method, first shown for a specific example and then shown in general. For the specific example, suppose v = 15 and m = 144. Then a list—call it the first list—of the even integers greater than v and less than m is 16, 18, 20, …, 140, 142. Now subtract 14 (chosen so that the second list will begin with 2) from each of the integers in the first list to form a second list, which has the same number of integers as the first list: 2, 4, 6, …, 128. Finally, divide each of the integers in the second list (all of which are even) by 2 to form a third list, which also has the same number of integers as the first list: 1, 2, 3, …, 64. Since the number of integers in the third list is 64, it follows that the number of integers in the first list is 64. For the general situation, the first list is the following list of even integers: v + 1, v + 3, v + 5, …, m − 4, m − 2. Now subtract the even integer v − 1 from (i.e., add – v + 1 to) each of the integers in the first list to obtain the second list: 2, 4, 6, …, m − v − 3, m − v − 1. (Note, for example, that m − 4 − (v − 1) = m − v − 3.) Finally, divide each of the integers (all of which are even) in the second list by 2 to obtain the third list: 1, 2, 3, …, (m−v−3)/2, (m−v−1)/2. Since the number of integers in the third list is (m−v−1)/2, it follows that the number of integers in the first list is (m−v−1)/2.