In 2016, Rajshahi produced \(2/3\) of all the mangoes in Bangladesh. Data of two districts, Natore and Khulna, were not found. If all other districts combined produced 18 million tons mangoes that year, how many million tons did Rajshahi produce in 2016? 1) Natore produced \(1/6\) of all the mangoes in Bangladesh. 2) The climate of Khulna is not very suitable for mangoes.

Explanation: Let \(T\) be the total production. \(R\) is Rajshahi's production. \(O\) is all other districts' production. \(N\) is Natore's production. \(K\) is Khulna's production. \(T = R + N + K + O_{others}\). Given: \(R = 2/3 T\). \(O_{others} = 18\) million tons. \(T = R + N + K + 18\). Statement 1: \(N = 1/6 T\). The fraction of total production accounted for by Rajshahi, Natore, and all others combined is \(R+N+O_{others} = 2/3 T + 1/6 T + 18 = 4/6 T + 1/6 T + 18 = 5/6 T + 18\). Since \(T = 5/6 T + K + 18\), \(T - 5/6 T = K + 18\). \(1/6 T = K + 18\). If we assume Khulna's production \(K\) is \(0\), then \(1/6 T = 18 \Rightarrow T = 108\). \(R = 2/3 T = 2/3 \times 108 = 72\). However, we don't know \(K\), so T cannot be uniquely determined. Let's re-read: "Data of two districts, Natore and Khulna, were not found." and "If all other districts combined produced 18 million tons". The term "all other districts" must refer to all districts **excluding** Rajshahi, Natore, and Khulna. Fraction of all others combined = \(1 - R - N - K\). \(O_{others} = 1 - 2/3 - 1/6 - K_{fraction} = 1/6 - K_{fraction}\). We still need \(K_{fraction}\). Let's re-interpret the question setup. **Re-interpretation**: \(T = R + N + K + O\). \(R = 2/3 T\). Given \(O = 18\) million tons. Statement 1: \(N = 1/6 T\). The remaining fraction is \(K+O = 1 - 2/3 - 1/6 = 1/6 T\). So, \(1/6 T = K+18\). Still can't solve. **Final Re-interpretation (likely intended)**: The "all other districts" refers to everything EXCEPT Rajshahi, Natore, and Khulna. Total: \(T\). \(R = 2/3 T\). Total of Natore, Khulna, and others \(N+K+O_{others} = 1/3 T\). Given \(O_{others} = 18\). Statement 1: \(N = 1/6 T\). Then \(K+O_{others} = 1/3 T - 1/6 T = 1/6 T\). \(K + 18 = 1/6 T\). We still can't find \(T\). The only way S1 is sufficient is if "all other districts combined produced 18 million tons" is the total of Natore, Khulna, and the other districts (i.e. everything but Rajshahi). Let \(R = 2/3 T\). Everything else \(E = 1/3 T = 18\) (million tons). This makes \(T = 54\). \(R = 2/3 \times 54 = 36\) (million tons). This makes S1 and S2 irrelevant, and R is 36, which is an answer. **Assuming this is the intended interpretation:** The total of all districts EXCEPT Rajshahi is 18 million tons. \(1/3 T = 18 \Rightarrow T = 54\). \(R = 2/3 \times 54 = 36\). Statement 1: \(N = 1/6 T = 9\). This is consistent. Statement 2: Irrelevant. This way, the information about Natore and Khulna being unknown is just a distractor, and Statement 1 is sufficient. **Selecting Option 1 based on the logic that $R$ must be determined, and $R=2/3 T$, so $T$ must be found. The simplest interpretation to make the question solvable is that everything except Rajshahi is $18$ million tons, and Statement 1 being sufficient must be the right answer.** **However, the source selected Statement (1) and (2) TOGETHER are NOT sufficient. I will stick to the source's answer 5, but the question is poorly formulated.**