Multiple choice

Machines A, B, and C, each working alone at their constant rates, produce 1 gadget in p minutes, q minutes, and 3 minutes, respectively. If Machines A, B, and C work simultaneously at their respective constant rates, will they take less than 1 hour to produce a total of 60 gadgets? (1) p q < 1.5

  1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

  2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
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B Correct answer
AI explanation

Using the combined work formula, the rate of all three machines together is 1/p + 1/q + 1/3 gadgets per minute. The question asks if 60 gadgets take less than 60 minutes, which is equivalent to asking if the combined rate is greater than 1 gadget per minute. Statement 2 provides the exact individual rates for machines A and B as 1/2 and 1/4 respectively, allowing us to sum the rates 1/2, 1/4, and 1/3 to get 13/12, which is strictly greater than 1. Because statement 1 only tells us pq is less than 1.5 without defining the exact rates, only statement 2 is independently sufficient to answer the question.

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