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    Question

    A company produces two types of gadgets, Type X and Type Y. How many total gadgets does the company produce in a month?

    Statements:

    I: The production rate of Type X is 120 gadgets per day, and the production rate of Type Y is 80 gadgets per day. The company operates 25 days a month.

    II: The company has a production goal of 6,000 gadgets per month. However, due to maintenance, they can only produce 80% of this goal in a given month.

    III: Type Y's production is increased by 25% for 10 days due to a new contract, while Type X's production decreases by 20% during the same period.

    A Only Statement I alone is sufficient. Correct Answer Incorrect Answer
    B Only Statement II alone is sufficient. Correct Answer Incorrect Answer
    C Only Statement III alone is sufficient. Correct Answer Incorrect Answer
    D Statements I and II together are sufficient. Correct Answer Incorrect Answer
    E All statements together are needed. Correct Answer Incorrect Answer

    Solution

    Statement I: The total production of Type X in 25 days is 120×25=3000 gadgets. The total production of Type Y is 80×25 =2000 gadgets. Therefore, total production is 3000+2000 =5000 gadgets. Sufficient. Statement II: The company’s goal is 6,000 gadgets, but due to maintenance, they only achieve 80% of this goal. Thus, the total production would be 6000×0.8=4800 gadgets. Sufficient. Statement III: For the first 10 days, Type Y's production increases by 25%, making its rate 80×1.25 = 100 gadgets per day for those days. The total production of Type Y in those 10 days is 100×10=1000. For Type X, with a 20% decrease, the new rate is 120×0.8=96 gadgets per day. Thus, in those 10 days, Type X produces 96×10 =960. For the remaining 15 days, Type X and Type Y revert to their original rates. Calculating total production for the month, we find it exceeds previous statements, making this statement sufficient on its own. Sufficient. Since all statements are individually sufficient, the answer is E .

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