This question's explanation and your answers so far.
図の作業について，全体の作業終了までの日数は 24 日間であった。作業 C の日数を 3 日短縮できたので，全体の作業終了までの日数が 1 日減った。作業 D の所要日数は何日か。 ・開始ノード →「A／5」→ ノード① ・ノード① →「B／5」→ ノード②（上経路） ・ノード① →「C／10」→ ノード③（下経路） ・ノード② →「D／x」→ ノード④（合流） ・ノード③ →「E／4」→ ノード④（合流） ・ノード④ →「F／5」→ 終了ノード 凡例：矢印の上に「作業名」，下に「所要日数」を記す。
If D = 6 days, the upper path is 15+6 = 21 days. Before the shortening the total is max(21, 24) = 24 days, which meets the condition; but after activity C is shortened by 3 days the lower path becomes 21 days, so the total is max(21, 21) = 21 days. That is a decrease of a full 3 days from 24 days, which contradicts the condition that it decreased by 1 day. This is the case where the whole amount of the shortening is reflected in the total, which is not the situation in this question.
If D = 7 days, the upper path is 15+7 = 22 days. After the shortening the total is max(22, 21) = 22 days, which works out to a decrease of 2 days from 24 days. The decrease is 2 days rather than 1 day, so the condition is not met. The total after the shortening has to be 23 days, which means the upper path has to be exactly 23 days.
正解 The correct answer is ウ (8 days). In an arrow diagram, the number of days until all activities are finished is determined by the length of the longest path, that is, the critical path. This diagram has only two paths: the upper path A→B→D→F takes 5+5+x+5 = 15+x days, and the lower path A→C→E→F takes 5+10+4+5 = 24 days. Since the original total was 24 days, the lower path, which gives 24 days, is the critical path, and the upper path fits within 15+x ≦ 24, that is, x ≦ 9. Now, when activity C is shortened by 3 days, the lower path shrinks to 5+7+4+5 = 21 days. If the lower path were still the critical path after the shortening, the total should fall from 24 days by 3 days to 21 days; but in fact it fell by only 1 day, to 23 days. This means that the shortening switched the critical path over to the upper path, and the length of the upper path became the total directly. Therefore, from 15+x = 23 we get x = 8 days. Checking the result: after the shortening the upper path is 23 days > the lower path 21 days, so the total is indeed 23 days, and before the shortening the upper path is 23 days < the lower path 24 days, so the total is 24 days. All the conditions in the question are satisfied.
If D = 9 days, the upper path is 15+9 = 24 days. Even before the shortening this is the same 24 days as the lower path, so the total is 24 days; but even when activity C is shortened by 3 days, the upper path stays at 24 days, so the total is max(24, 21) = 24 days and does not decrease at all. This contradicts the condition that the number of days until all activities are completed decreased by 1 day. Note that it does satisfy the upper limit x ≦ 9 itself, so it is a typical wrong answer that catches anyone who looks only at that limit.